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Students can Download Chapter 6 General Principle and Processes of Isolation of Elements Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 6 General Principle and Processes of Isolation of Elements

Metallurgy – the entire scientific and technological processes used for isolation of the metal from their ores. The extraction and isolation of metals from ores involve the following major steps.
1. Concentration of the ore
2. Isolation/extraction of the metal from its concentrated ore and
3. Purification or refining of the metals

Minerals:
Naturally occuring chemical substance in the earth’s crust obtainable by mining.

Ores:
minerals from which the metals are economically and profitably extracted. All ores are minerals but all minerals are not ores.

Gangue :
earthly matter or unwanted materials present in ore.

Occurrence of Metals :
Metals are present in earth’s crust as oxides, sulphides, carbonates etc.

Concentration (dressing or benefaction) of Ores:
process of removal of gangue or matrix from the ore. The different process used are:

Hydraulic Washing or Gravity Seperation:
It is based on the differences in gravities. An upward stream of running water is used to wash the powdered ore. The lighter gangue particles are washed away and the heavier ores are left behind.

Magnetic Separation:
It is based on differences in magnetic properties of the ore components. It is carried out if either the ore or the gangue is capable of being attracted by the magnetic field. The powdered ore is carried on a conveyer belt which passes over a magnetic roller.

Froth Floatation Method:
used to separate sulphide ore from the gangue. Here a suspension of the powdered sulphide ore is agitated with collectors and froth stabilisers by passing a forceful current of air. The froth formed which carries the mineral particles is skimmed off and then dried.

‘Depressants’ are used to separate two sulphide ores. e.g. in case of an ore containing ZnS and PbS, the depressant used is NaCN. It selectively prevents ZnS from coming to the froth but allows PbS to come with the froth.

Leaching:
a method of ore concentration by dissolving the ore in a suitable solvent.

a) Leaching of Alumina from Bauxite:
The powdered bauxite ore is digested with concentrated solution of NaOH at 473-523 K and 35 – 36 bar pressure. The Al₂O₃ is leached out as sodium aluminate leaving the impurities behind. But the impurity SiO₂ is also leached out as sodium silicate.
Al₂O₃ (S)+ 2 NaOH(aq) +3H₂O(l) → 2Na[Al(OH)₄](aq)

The aluminate solution is neutralised with CO₂ gas and hydrated Al₂O₃ precipitated. At this stage, the slution is seeded with freshly prepared samples of hydrated Al₂O₃ which induces the precipitation. The sodium silicate remains in the solution.
2Na[Al(OH)₄](aq) + CO₂(g) → Al₂O₃ + xH₂O(s) + 2 NaHCO₃(aq)

The hydrated alumina is filtered, dried and heated to give back pureAl₂O₃.

b) Other example:
In the metallurgy of silver and gold, the ore is treated with a dilute solution of NaCN or KCN. Later the metal ion in the solution is replaced by Zn metal, which acts as the reducing agent.
4M(s) + 8CN^–(aq) + 2 H₂O(aq) + O₂(g) → 4[M(CN)₂]^–(aq) + 4 OH^–(aq) (M = Ag or Au)
2[M(CN)₂]^–(aq) + Zn(s) [Zn(CN)₄]^2-(aq) + 2 M(s)

Extraction of Crude Metal from Concentrated Ore:
The concentrated ore must be converted to oxide and then reduced to metal. It involves two steps.
a) Conversion to Oxide
i) Calcination:
process in which the ore is heated strongly in the absence of air.

ii) Roasting:
process of heating the ore in a regular supply of air in a furnace at a temperature below the melting point of the metal.
2 ZnS + 3O₂ → 2 ZnO + 2SO₂
2PbS + 3O₂ → 2PbO + 2SO₂
2CU₂S + 3O₂ → 2Cu₂O + 2SO₂

Flux:
substance which combines with gangue present in the ore and form easily fusible materials called the slag.
Flux + Gangue → Slag (fusible)
FeO + SiO₂ → FeSiO₃ (Slag)

b) Reduction of Oxide to the Metal:
The metal oxide is reduced by reducing agents (e.g. C, CO or even another metal) which combine with the oxygen of, the metal oxide.
M_xO_y + yC → xM + yCO

Thermodynamic Principles of Metallurgy:
All those metals which have more negative Gibbs energies of formation of their oxides can reduce the oxides of other metals whose Gibbs energies of formation are less negative.

Ellingham Diagram:
graph of variation of ∆_rG^Θ vs. T for the formation of metal oxide from metals.

When the value of ∆G is negative in the equation ∆G = ∆H —T∆S then the reaction will proceed. If ∆S is positive, on increasing the temperature(T), the value of T∆S would increase (∆H < T∆S) and then AG will become -ve.

If the reactants and products of the coupled reaction (reduction of the metal oxide and oxidation of the reducing agent) are put together in a system and the net ∆G of the two possible reacfions is -ve, the overall reaction will occur.

Applications of Ellingham Diagram

1. It provides a sound basis for considering the choice of reducing agent in the reduction of oxides.
2. It helps in predicting the feasibility of thermal reduction of an ore.

Limitations of Ellingham Diagram

1. It does not say about the kinetics of the reduction process.
2. The interpretations of ∆_rG^Θ is based on equilibrium constant, K. Thus it is presumed that the reactants and products are in equilibrium. But this is not always true due to changes in entropy values associated with phase transformations.

a) Extraction of Iron from its Oxides:
The concentrated ore is mixed with lime stone and coke and fed into a Blast furnace from its top. Here the oxide is reduced to metal.
FeO(s) + C(s) → Fe(s/ \(\ell \)) + CO(g)

Two simpler reactions such as reduction of FeO and oxidation of coke(C) are are coupled in this process so that the Gibbs energy change of the net reaction is negative.

In Blast furnace, above 710 °C (983 K) coke (C) reduces FeO to Fe. At temperatures below 710 °C (983 K) CO reduces Fe₃O₄ and Fe₂O₃to FeO. Hot air is blown from the bottom of the furnace and coke is burnt to give temperature up to 2200 K.

Reactions at lower temperature range (500 – 800 K) –
3Fe₂O₃ + CO → 2Fe₃O₄ + CO₂
Fe₃O₄ + 4CO → 3Fe + 4CO₂
Fe₂O₃ + CO → 2FeO + CO₂

Reactions athighertemperature range (900 -1500 K) –
C + CO₂ → 2CO
FeO + CO → Fe + CO₂

Lime stone is decomposed to CaO which removes silicate impurity of the ore as slag.
CaCO₃ → CaO + CO₂
CaO + SiO₂ → CaSiO₃

Pig iron – iron obtained from the blast furnace which containes about 4% carbon and many impurities.
Cast iron – It contains 3% carbon.
Wrought iron or malleable iron – purest form of commercial iron.

Preparation of Wrought Iron:
It is prepared from; cast iron by oxidising impurities in a reverberatory furnace lined with haematite, which oxidises C to CO.
Fe₂O₃ + 3C → 2Fe + 3CO

Limestone is added as a flux and S, Si and P are oxidised and passed into the slag. The metal is • recovered and freed from the slag by passing through
rollers.

b) Extraction of Copper:
The sulphide ore (Cu₂S) is roasted to give oxide (Cu₂O).
2Cu₂S + 3O₂ → 2Cu₂O + 2SO₂

The oxide can then be easily reduced to metallic copper using coke. This is because the Cu,Cu₂O line is almost at the top in the Ellingham diagram.
Cu₂O + C → 2Cu + CO

The ore is heated in a reverberatory furnace after mixing with silica. The iron oxide ‘slags of as iron silicate and copper forms copper matte. This contains Cu₂S and FeS. Matte is heated in silica lined converter. The remaining Fe is converted to FeSiO₃. The remaining Cu₂S and Cu₂O undergoes self oxidation-reduction to form blister copper.
2Cu₂O + Cu₂S → 6 Cu + SO₂

The solidified copper obtained has blistered appearance due to the evolution of SO₂ and so it is called blister copper.

c. Extraction of Zinc from Zinc Oxide:
ZnO is reduced to metallic Zn by heating with coke.

The metal is distilled of and collected by rapid chilling.

Electrochemical Principles of Metallurgy:
The metal ions in solution or molten state are reduced by electrolysis or adding some reducing element. For the reduction to be feasible E® should be positive so that ∆G^Θ is negative (∆G^Θ = – nFE^Θ)- During electrolysis, the less reactive metal will come out of the solution and the more reactive metal will go to the solution, e.g.
Cu²⁺(aq) + Fe(s) → Cu(s) + Fe²⁺(aq)

More reactive metals have large negative E^Θ values. So their reduction is difficult. Sometimes a flux is added for making the molten mass more conducting.

Extraction of Aluminium (Hall-Heroult Process):
Purified Al₂O₃ is mixed with Na₃AlF₆ or CaF₂ to lower the melting point of the mix and bring conductivity. The fused matrix is electrolysed. Steel cathode and graphite anode are used.

The electrode reactions are:
At cathode : Al³⁺(melt) + 3e^– → Al(l)
At anode : C(s) + O^2-(melt) → CO(g) + 2e
C(s) + 2O^2- (melt) → CO₂(g) + 4e^–

Disadvantage:
For each kg of aluminium produced, about 0.5 kg of carbon anode is burnt away as CO and CO₂.
The overall reaction is,
2Al₂O₃ + 3C → 4Al + 3 CO₂

Refining:
For obtaining high purity metal, several techniques are used.

a) Distillation:
The impure metal is evaporated to get pure metal, e.g. low boiling metals like Zn, Hg

b) Liquation:
low melting metals like tin and lead are made to flow on sloping surface and thus seperated from high melting impurities.

c) Electrolytic Refining:
Anode – impure metal, Cathode – strip of same metal in pure form, Electrolyte – soluble salt of the same metal. On electrolysis pure metal is deposited at the cathode.
e.g. Electrolytic refining of Cu.

Anode:
impure Cu, Cathode: pure Cu strip, Electrolyte: acidified solution of CuSO₄

During electrolysis Cu in the pure form istransfered from the anode to the cathode. Impurities deposit as anode mud which contains valuable elements like Sb, Se, Te, Ag, Au and Pt. Recovery of these elements meets the cost of refining.

Zn is also refined by electrolytic process.

d) Zone Refining:
This method is based on the principle that the impurities are more soluble in the melt than in the solid state of the metal. A circular mobile heater is fixed atone end of a rod of the impure metal. The molten zone moves along with the heater. As the heater moves forward, the pure metal crystallises out of the melt. The process is repeated several times. At one end impurities get concentrated. This end is cut off. e.g., Ge, Si, B, Ga and In.

e) Vapour Phase Refining:
the metal is converted into its volatile compound. It is then decomposed to give pure metal.

Requirements for vapour phase refining:
1. The metal should form a volatile compound with an available reagent.
2. The volatile compound should be easily decomposable, so that the recovery is easy.

i) Mond Process for Refining Nickel:
Nickel is heated in a stream of CO forming a volatile complex, nickel tetracarbonyl.

The nickel tetracarbonyl is heated at high temperature so that it is decomposed to give pure Ni.

ii) van Arkel Method for Refining Zr or Ti:
The crude metal is heated in an evacuated vessel with l₂. The metal iodide being more covalent, volatilises.
Zr + 2l₂ → Zrl₄ (volatile)

The metal iodide is decomposed on a tungsten filament at 1800 K. The pure metal is deposited on the filament.
Zrl₄ → Zr + 2l₂

Similarly, Ti can be purified.
Ti + 2l₂ → Til₄ (volatile)
Til₄ → Ti + 2 l₂

f) Chromatographic Methods:
based on the principle that different components of a mixture are differently adsorbed on an adsorbent.The mixture containing different metal ions are added into the chromatographic column. Different components are adsorbed at different levels on the column. The adsorbed components are removed (eluted) by using suitable solvents (eluant). Column chromatography is very useful for purification of elements which are available in minute quantities, e.g. Inner transition metals are refined by this method.

Uses of Aluminium, Copper, Zinc and Iron
1. Aluminium:
aluminium foils are used as wrappers for chocolates, fine dust of Al is used in paints and lacqures, in the extraction of Cr and Mn from thier oxides, as electricity conductors, for making alloys, e.g. Duralumin (Al + Mg), Alnico (Al + Ni + Co).

2. Copper:
for making wires used in electrical industry, for making water pipes and steam pipes, for making alloys, e.g. brass (Cu + Zn), bronze (Cu + Sn)

3. Zinc:
for galvanising iron, in batteries, as constituent of many alloys, e.g. brass (Cu – 60%, Zn – 40%), german silver (Cu 25-30%, Zn-25-30%, Ni 40 – 50%), zinc dust is used as a reducing agent in the manufacture of dye-stuffs, paints etc.

4. Iron:
Cast lron:
for casting stoves, railway sleepers, gutter pipes, toys etc; in the manufacture of wrought iron and steel

Wrought Iron:
in making anchors, wires, bolts, chains and agricultural implements.

Steel:
Nickel steel is used for making cables, automobiles and aeroplane parts, pendulum, measuring tapes; Chrome steel is used for cutting tools and crushing machines; Stainless steel is used for cycles, automobiles, utensils, pens etc.

Students can Download Chapter 5 Surface Chemistry Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 5 Surface Chemistry

Surface chemistry deals with phenomena that occurs at the surfaces or interfaces.

Adsorption:
accumulation of molecular species at the surface rather than in the bulk of a solid or liquid, it is a surface phenomenon, e.g. Moisture gets adsorbed on silica gel.

Adsorbate:
molecular species or substance, which accumulates at the surface.

Adsorbent:
material on the surface of which adsorption takes place, e.g. Charcoal, Silica gel, etc.

Desorption:
process of removing adsorbed substance from the surface of adsorbent.

Difference between Adsorption and Absorption:
Adsorption –
the substance is concentrated only at the surface and does not penetrate to the bulk of the adsorbent.

Absorption –
the substance is uniformly distributed throughout the bulk of the solid, e.g. Moisture gets absorbed on anhydrous CaCl₂ while adsorbed on silical gel.

Sorption:
term used when both adsorption and absorption take place simultaneously.

Mechanism of Adsorption :
The unbalanced or residual attractive forces are responsible for attracting the adsorbate particle on adsorbent surface. During adsorption energy decreases, therefore adsorption is exothermic process, i.e., ∆H of adsorption (heat of adsorption) is always negative. The entropy of the system also decreases (∆S = – ve).

Types of Adsorption:
1. Physical Adsorption (Physisorption):
Here the adsorbed molecules are held on the surface of the adsorbent by physical forces such as van der Waals’ forces. It is reversed by reducing pressure or by heating.

Characteristics:
Lack of specificity, easily liquifiable gases readily adsorbed, reversible in nature, extent of adsorption increases with increase in surface area of adsorbent, enthalpy of adsorption quite low (20 – 40 kJ mol’ ).

2. Chemical Adsorption (Chemisorption):
the forces of interaction between the adsorbent and adsorbate are chemical in nature. It cannot be easily reversed.

Characteristics:
High specificity, irreversibility, increases with increase in surface area, enthalpy of adsorption is high (80 -240 kJ mol”1).

Sometimes physisorption and chemisorption occur simultaneously and it is not easy to ascertain the type of adsorption. A physisorption at low temperature may pass into chemisorption as the temperature is increased. For example, dihydrogen is first adsorbed on Ni by van der Waals’forces. Molecules of hydrogen then dissociate to form hydrogen atoms which are held on the surface by chemisorption.

Comparison of Physisorption and Chemisorption

Physisorption	Chemisorption
1) Arises because of van der Waals’ force	1) Caused by chemical bond formation
2) Not specific	2) Highly specific
3) Reversable	3) Irreversible
4) More easily liquefiable gases are adsorbed readily.	4) Gases which can react with the adsorbent show chemisorption.
5) Enthalpy of adsorption is low (20-40 kJ mol’1)	5) Enthalpy of adsorption is high (80-240 kJ mol-1)
6) Low temperature is favourable. It decreases with increase of temperature	6) Hig temperature is favourable. It increases with increase of temperature
7) No appreciable activation energy is needed.	7) High activation energy is sometimes needed.
8) Increases with an increase of surface area.	8) Increases with an increase of surface area.
9) Results into multimolecular layers on adsorbent surface under high pressure.	9) Results into unimolecular layer

Adsorption Isotherms:
The variation in the amount of gas adsorbed by the adsorbent with pressure at constant temperature can be expressed by means of a curve termed as adsorption isotherm.

Freundlich Adsorption isotherm:
empirical relation between the quantity of gas adsorbed by unit mass of the solid adsorbant and pressure at a particular temperature.
x/m = k.P^1/n (n > 1)
x → mass of the gas adsorbed
m → mass of adsorbent
‘k’ and ‘n’ are constants which depend on the nature of the adsorbent and the gas at a particular temperature.
OR log x/m = log k + \(\frac{1}{n}\) log P

Adsorption from Solution Phase:
Freundlich’s equation approximately describes the behaviour of adsorption from solution.
\(\frac{x}{m}\) = k.C^1/n m
C – equilibrium concentration
log x/m = log k + \(\frac{1}{n}\) log C
Plotting log x/m vs log C a straight line is obtained

Applications of Adsorption:
Production of high vacuum, in Gas masks – activated charcoal is filled in gas mask to adsorb poisonous gases, for removal of colouring matter from solution in heterogeneous catalysis, in chromatographies analysis, in froth floatation process.

Catalysis :
The process of altering the rate of chemical reaction by the addition of a foreign substance (catalyst) is called catalysis, e.g. MnO₂ acts as a catalyst in the thermal decomposition of KClO₃.

Promoters:
substances that enhance the activity of a catalyst, e.g. In Haber’s process, iron is used as catalyst and molybdenum acts as a promoter.

Poisons:
substances which decrease the activity of a catalyst.

Homogeneous and Heterogeneous Catalysis
a) Homogeneous Catalysis:
When the reactants and catalyst are in the same phase, the process is said to be homogeneous catalysis.

Here both the reactants and the catalyst are in the liquid phase.

Heterogeneous Catalysis:
If the reactants and the catalyst are in different phase, the catalysis known as heterogeneous catalysis.

Here reactants are gaseous state while the catalysts are in the solid state.

Important Features of Solid Catalysts
a) Activity:
ability of catalysts to accelerate a chemical reaction.

But pure mixture of H₂ and O₂ does not react at all in the absence of a catalyst.

b) Selectivity:
ability of a catalyst to direct a reaction to yield a particular product.

e.g. CO and H₂ combine to form different products by using different catalysts.

Shape Selective Catalysis by Zeolites:
The catalytic reaction that depends upon the pore structure of the catalyst and size of the reactant and the product molecules.

Zeolites are good shape-selective catalysts because of their honey comb-like structures. Zeolites are widely used in petrochemical industries for cracking and isomerisation of hydrocarbon.
e.g. ZSM – 5 – which convert alcohols into petrol.

Enzyme Catalysis:
Enzymes are biological catalysts. They catalyse biological reaction in animals and plants to maintain life. e.g.

1. Invertase – Cane sugar into glucose and fructose
2. Zymase – Glucose into alcohols
3. Maltase – Maltose into glucose
4. Diastase – Starch into maltose
5. Cellulase – Cellulose into glucose
6. Urease – Urea into NH₃ and CO₂

Characteristics:
Highly efficient, highly specific in nature, highly active under optimum temperature, highly active under optimum pH

Mechanism (Lock and key model)
The molecules of the reactant (substrate), which have complementary shape, fit into the cavities on the surface of enzyme particles just like a key fits into a lock. The enzyme catalysed reactions proceeds in two steps:
Step -1 :
Binding of enzyme to sutbstrate to form an activated complex.
E + S → ES*
Step-2 :
Decomposition of the activated complex to form product.
ES* → E + P

Catalysts in Industry

1. Finely divided iron with molybdenum as promoter in Haber’s process. (New catalyst: a mixture of iron oxide, potassium oxide and alumina)
2. Platinised asbestos in Ostwald’s process
3. Platinised asbestos or V205 in Contact process

Colloids:
Heterogeneous system in which one substance is dispersed (dispersed phase) as very fine particles in another substance called dispersion medium, e.g. Starch, Gelatin. In colloids the particle size (diameter) is between 1nm and 1000 nm.

Classification of Colloids:
i) Based on physical state of dispersed phase and dispersion medium:

ii) Based on Nature of Interaction between Dispersed Phase and Dispersion Medium:
1. Lyophilic (solvent attracting) Colloids:
there is strong interaction between the dispersed phase and dispersion medium. They are reversible sols. e.g. Starch, gelatin, albumin etc.

2. Lyophobic (solvent repelling) Colloids:
there is little or no interaction between the dispersed phase and dispersion medium. They are also irreversible colloids and are not stable.

iii) Based on Types of Particle of the Dispersed Phase
a) Multimolecular Colloids :
the individual particles consist of an aggregate of atoms or small molecules with molecular size less than 1 nm, the particles are held together by van der Waals’ forces, e.g. Sulphur sol, Gold sol etc.

b) Macromolecular Colloids :
the particles of dispersed phase are sufficiently big in size, maybe in the colloidal range, e.g. Starch, cellulose, proteins.

c) Associated Colloids (Micelles):
colloids which behave as normal strong electrolytes at low concentration but get associated at higher concentrations and behaves as colloidal solutions. The associated particle formed are called micelles.
e.g. Soap, detergents etc.

The formation of micelles take place only above a particular temperature called Kraft temperature (Tk.) and above a particular concentration called Critical Micelle Concentration(CMC).

Mechanism of micelle formation –
In soaps, the RCOO^– ions are present on the surface with their COO^– groups in water and R staying away from it and remain at the surface. At CMC, the anions are pulled into the bulk of the solution and aggregate to form ‘ionic micelle’ having spherical shape with R pointing towards the centre of the sphere and COO^– part remaining outward on the surface of the sphere.

Preparation of Colloids
a) Chemical Methods
Some examples:

b) Electrical Disintegration or Bredig’s Arc Method
Metallic sols can be prepared by striking an arc between two electrodes of the metal, immersed in the dispersion medium. The metal is vapourised by the arc which then condenses to form particles of colloidal size. e.g. Gold sol, Platinum sol, Silver sol etc.

c) Peptization:
process of converting a precipitate into colloidal sol by shaking it with dispersion medium in the presence of small amount of electrolyte (peptizing agent), e.g. Freshly prepared Fe(OH)3 is peptized by adding small quantity of FeCI3 solution (peptizing agent).

Mechanism of peptization –
During peptization, the precipitate adsorbs one of the ions of the electrolyte on its surface. This causes the development of positive or negative charge on precipitates, which ultimately break up into smaller particles of the size of a colloid.

Purification of Colloids:
process of reducing the amount of impurities to a requisite minimum from the colloids.
i) Dialysis:
process of removing a dissolved substance from a colloid by means of diffusion through a suitable membrane.

ii) Electro-dialysis:
process of dialysis in presence of an applied electric field. It is faster and is applicable if the dissolved substance in the impure colloid is only an electrolyte. The ions present in the colloid migrate out to the oppositely charged electrodes.

iii) Ultrafilteration:
process of separating the colloidal particles from the solvent and soluble solutes present in the colloid by ultra filters. The ultra filter paper is prepared by soaking the filter paper in a colloidion solution (4% solution of nitro cellulose in a mixture of alcohol and ether). It is then hardened by formaldehyde and finally dried.

Properties of Colloids
1) Colligative Properties:
values of colligative properties as smaller due to smaller number of particles.

2) Tyndall Effect (Optical Property):
phenomenon of the scattering of light by colloidal particles.

Conditions for observing Tyndall effect:
1. The diameter of the dispersed particles is not much smaller than the wavelength of the light used; and

2. The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude. The ultramicroscope used to observe the light scattered by colloidal particles is based on Tyndall effect.

The colour of the sky can be explained by Tyndall effect. The dust and other colloids present in the atmosphere scatter the light. Only blue light reaches to our eyes.

3) Colour:
It depends on the wavelength of lighty scattered by the dispersed particles which in turn depends on the size and nature of the particles and changes with the manner in which the observer receives the light, e.g. a mixture of milk and water appears blue when viewed by the reflected light and red when viewed by transmitted light.

4) Brownian Movement:
The constant zig-zag movement of the colloidal particles. It is due to the unbalanced bombardment of the particles by the molecules of the dispersion medium. It does not permit the particles to settle and is responsible for the stability of sols. ,

5) Charge on Colloidal Particles:
Colloidal particles carry an electric charge.
Positive charged sols: Al₂O₃. xH₂O, CrO₃.xH₂0, basic dye stuffs, blood (Haemoglobin) etc.

Negatively charged sols:
Metal sols (Cu, Ag, Au), metallic sulphides, acid dyes stuffs, starch, gelatin.

Reason for charge:
It is due to
i) electron capture by sol particles during electrodispersion of metals,
ii) preferential adsorption of ions from solution and/ or
iii) formulation of electrical double layer.

Helmholtz Electrical Double Layer:
combination of two layers of opposite charges around the colloidal particle. The first layer of ions is firmly held and is termed fixed layer while the second layer is mobile which is termed as diffused layer.

Electrokinetic Potential or Zeta Potential:
It is the potential difference between the fixed layer and the diffused layer of opposite changes in the electrical ‘ double layer.

Significance of Charge on Colloidal Particles:
provides stability to the colloid because the repulsive forces between charged particles having same charge prevent them from coalescing or aggregating when they come closer to one another.

6) Electrophoresis:
lled anaphoresis and that of cathode is called cataphoresis.

Coagulation/Flocculation/Precipitation:
process of settling of colloidal particles by the addition of electrolyte.

Coagulation of lyophobic sols can be carried out by the following ways:
Electrophoresis, mutual coagulation (mixing two oppositely charged sols), boiling, persistent dialysis, addition of electrolytes, etc.

Addition of electrolytes –
Colloids interact with ion carrying charge opposite to that present on themselves. This causes neutralisation leading to their coagulation.

Hardy – Schulze Rule:
the greater the valence of the flocculating ion added, the greater is its power to cause precipitation.

The ion having opposite charge to sol particles (coagulating ion) cause coagulation.

In the coagulation of negative sol, the flocculating power is in the order: Al³⁺ > Ba²⁺ > Na⁺

In the coagulation of positive sol, the flocculating power in the order:
[Fe(CN)₆]^4- > PO₄^3- > SO₄^2-> Cl^–

Protective Colloids:
the lyophilic sol used for protection of lyophobic sol.

Emulsions:
liquidin liquid colloidal systems i.e., the dispersion of finely divided droplets in another liquid. There are two types of emulsions.
1) Oil dispersed in water (O/W type):
water acts as dispersion medium, e.g. Milk, Vanishing cream.

2) Water dispersed in oil (W/O type):
oil, acts as dispersion medium.e.g. Butter, Creams, Cod liveroil Emulsification – process of making an emulsion. Emulsion may be obtained by vigourously agitating a mixture of both liquids.

Emulsifying agent or emulsifier –
substance used to stabilise an emulsion. It forms an interfacial film between suspended particles and the medium, e.g.

Emulsifying agents for O/W emulsions :
Proteins, gums, natural and synthetic soaps etc.

Emulsifying agents for W/O emulsions:
Heavy metal salts of fatty acids, long chain alcohols, lampblack etc.

Colloids Around Us :
Fog, mist and rain; food materials, blood, soils, formation of delta.

Application of Colloids
I) In Medicine:
Colloidal medicines are more effective because they have large surface area and are, therefore, easily assimilated, e.g. Colloidal silver (Argyrol) – as eye lotion, Colloidal antimony – in curing Kalaazar, Colloidal gold – for intramuscular injection. Milk of magnesia – in stomach disorder.

II) In industries :
Electrical precipitation of smoke – by Cottrell smoke precipitator, purification of water, tanning, cleansing action of soaps and detergents (micelle formation), photographic plates and films, rubber industry and Industrial products.

Students can Download Chapter 4 Chemical Kinetics Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 4 Chemical Kinetics

Chemical kinetics is the branch of chemistry which deals with the study of the velocity of chemical reactions and their mechanism.

Rate of a Chemical Reaction :
amount of chemical change per unit time.

Average Rate of Reaction:
change in concentration of any one of the reactants or products per unit time. Unit of rate of a reaction mol L^-1 s^-1 Fora reaction, R → P

Instantaneous Rate of Reaction:
the rate of change in concentration of any one of the reactants or products at a particular instant of time for a gven temperature. It may be expressed as \(\frac{dx}{dt}\) where dx is the change in concentration at the instant dt.
For the reaction aA + bB → cC + dD

Graphically,- instantaneous rate = slope of the tangent drawn to the concentration vs time graph

corresponding to the time t. i.e., r_inst = \(\frac{dx}{dt}\) , where dx and dt are the intercepts.

Factors affecting rate of reaction:
Concentration of reactants, Nature of reactants and products, Temperature, Pressure (for gaseous reactants), Presence of catalyst, Presence of light (radiation)

Rate Expression and Rate Constant:
According to law of mass action, the rate of a chemical reaction is proportional to the product of molar concentrations of the reactants.
Consider a general reaction.
aA + bB → cC + dD
Rate α [A]^x [B]^y

where exponents ‘x’ and ‘y’ may or may not be equal to ‘a’ and ‘b’ respectively.
The above equation is also written as.
Rate = k[A]^x [B]^v
or \(\frac{-\mathrm{d}[\mathrm{R}]}{\mathrm{dt}}\) = k[A]^x [B]^v
where ‘k’ is a proportionality constant called rate constant. The equation is known as rate expression or rate law.

Rate law:
expression in which reaction rate is given in temis of molar concentration of reactants with each term raised to some power, which may or may not be same as the stiochiometric coefficient of the reacting species in a balanced chemical equation.

Order of Reaction :
sum of powers of the concentration of the reactants in the rate law expression. Considers general reaction,
aA + bB → cC + dD
Rate = k[A]^x [B]^v
Order = x + y

Example: H₂ + l₂ → 2 HI
Rate = k[H₂]¹ [l₂]¹, Order = 1 + 1 = 2

Order of a reaction is an experimentally determined quantity. It may be zero, whole number, fractional and even negative.
Elementary reactions –
reactions taking place in one step.

Complex reactions –
reactions involving a sequence of elementary reactions. These may be consecutive reactions, reverse reactions and side reactions.

Some example of reactions of different orders: First Order:
i) Decomposition of N₂O₅
N₂O₂ → 2NO₂ + ½ O₂
Or 2N₂O₅ → NO₂ + O₂
Rate = k[N₂O₅]¹

ii) Decomposition of NH₄NO₂ in aqueous solution.
NH₄NO₂ → N₂ + 2H₂O
Rate = k[NH₄NO₂]¹

Second order:
i. 2NO₂ → 2NO + O₂ Rate = k[NO₂]²
ii. H₂ + l₂ → 2Hl Rate = k[H₂]¹[l₂]¹

Third order:
i. 2NO + O₂ → 2NO₂
Rate = k[NO]² [O₂]¹
ii. 2NO₂ + Cl₂ → 2NOCl + O₂
Rate = k[NO₂]² [Cl₂]¹

Units of Rate Constant:
For an n^th order reaction, the unit of rate constant is given by the formula, mol^1-n L^n-1 s^-1

Molecularity of a Reaction :
number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which collide simultaneously in order to bring about a chemical reaction. It is always a whole number.

Reactions which involve simultaneous collision between two species are bimolecular.

When one reacting species is involved in the reaction, it is unimolecular.
Example:
NH₄NO₂ → N₂ +2H₂O
O₃ → O₂ + O

Reactions which involve simultaneous collision between two species are bimolecular.
Example:
2 Hl → H₂ + l₂

Reactions which involve simultaneous collision between three species are trimolecular or termolecular.
Example :
2 NO + O₂ → 2 NO₂

The probability that more than 3 molecules can collide and react simultaneously is very small. Hence, molecularity greaterthan 3 is not observed.
In a complex reaction, the slowest step in a reaction determine the rate of reaction, i.e., slowest step is the rate determining step.

Difference between order and molecularity

Order	Molecularity
1. It is sum of the powers of the concentration terms in the rate law expression.	1. It is the number of reacting species undergoing simultaneous collision in the reaction.
2. It is determined experimentally.	2. It is a theoretical concept.
3. It can be a whole number, zero or even fraction.	3. It always a whole number.
4. It gives some idea about reaction machanism.	4. It does not tell us the reaction mechanism.

Integrated Rate Equation :
Integrated rate equation gives a relation between concentrations at different times and rate constant.

Zero Order Reaction :
The rate of reaction is independent of the concentration of the reactants.

For a zero order reaction, R → P,
d[R] = – kdt
[R] = – kt + [R]₀ ………….. (1)
or \(k=\frac{[R]_{0}-[R]}{t}\)

Equation (1) is of the form y = mx + c, equation for a straight line. If we plot [R] versus t, we get a straight line with slope = -k and intercept equal to [R]₀

Note:
R0 initial concentration of reacting species (i.e., at time = 0)
R → concentration of reacting species (i.e., at time = t)

First Order Reaction
Fora reaction, R → P

If we plot a graph between log [R]₀/[R] vs ‘t’ we get a straight line with slope = k/2.303

All natural and artificial radioactive decay take place by first order kinetics.

Half-Life of a Reaction (t_½):
time required to reduce the concentration of a reactant to half of its initial concentration.
Forzero order reaction,
\(t_{1 / 2}=\frac{[R]_{0}}{2 k}\)
Derivation.
For a zero order reaction R → P, the rate constant is given by the equation,

Derivation:
For a first order reaction R → P, the rate constant is given by the equation,

For first order reactio t_½ is independent of [R]0.

Pseudo First Order Reaction :
Reaction which appear to be of higher order but actually follow lower order kinetics.

Example:
Acid hydrolysis of ethylacetate.

Rate = k[CH₃-COOC₂H₅]

Since the concentration of H₂O is quite large and does not change appreciably, it does not appear in the rate law.
Another example: Inversion of cane sugar in presence of dilute acids.

Temperature Dependence of the Rate of a Reaction :
The rate of the reaction increases considerably with increase in temperature. For a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.

Temperature Coefficient –
The ratio between the rate constant of a reaction at two temperatures differing by 10°.

Arrhenius Equation –
The temperature dependence of the rate of a chemical reaction can be explained by Arrhenius equation.
k = A e^-Ea/RT
A → Arrhenius factor or frequency factor or pre-exponential factor
E_a → Activation energy in J mol^-1
R → Gas constant
T → Temperature in kelvin

Activation energy (E_a)-
The energy required to form activated complex or intermediate. Some energy is released when the complex decomposes to form products.

Most probable kinetic energy –
kinetic energy of maximum fraction of molecules. The peak of the Boltzmann-Maxwell curve corresponds to this.

From the Arrhenius equation,
In k = In A \(\frac{E_{a}}{R T}\)
A polt of In k vs. \(\frac{1}{T}\)

If k₁ and k₂ are the rate constants at temperatures T₁ and T₂ respectively, Arrhenius equation can be written in the form,

Effect of Catalyst :
A catalyst is a substance which alters the rate of a reaction without itself undergoing any permanent chemical change. The function of a catalyst is to provide an alternate path of reaction with a lower energy of activation.

A small amount of the catalyst can catalyse a large amount of reactants. A catalyst does not alter Gibbs energy ∆ G of a reaction. It does not change the equilibrium constant but helps in attaining the equilibrium faster.

Collision Theory of Chemical Reactions :
It is based on kinetic theory of gases.
1. According to collision theory, the reactant molecules are assumed to be hard spheres and a chemical reaction takes place when reactant molecules collide with one another.

2. All collisions are not effective collisions. An effective collision is that collision which results into chemical reaction.

3. For effective collision, the molecule possess a certain minimum amount of energy called threshold energy and should have proper orientation.

Threshold energy – the minimum amount of energy which the colliding molecules must possess to make an effective collision.

4. Collision frequency (Z) – The number of collisions per second per unit volume of the reaction mixture.

5. To account for effective collisions, the probability or steric factor (P) is considered. It accounts for the fact that in a collision, molecules must be properly oriented.
Rate = PZ_ABe-Ea/RT

Thus, in collision theory activation energy and proper orientation of the molecules together determine the criteria for effective collision and hence the rate of ’ reaction.

Students can Download Chapter 3 Electrochemistry Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 3 Electrochemistry

Electrochemistry-
branch of chemistry which deals with the inter-relationship between electrical energy and chemical changes.

Electrolysis – The chemical reaction occuring due to the passage of electric current (i.e., electrical energy is converted into chemical energy).

Electrochemical reaction –
The chemical reaction in which electric current is produced (i.e., chemical energy is converted into electrical energy). Example: Galvanic cell

Electrochemical Cell: – (Galvanic Cell/Voltaic Cell) :
It converts chemical energy into electrical energy during redox reaction, e.g. Daniell Cell
The cell reaction is
Zn(s) + Cu²⁺ (aq) Zn²⁺(aq) + Cu(s)
It has a potential equal to 1.1 V.

If an external opposite potential is applied in the Daniell ce|l, the following features are noted:
a) When E_ext < 1.1 V,
(i) electrons flow from Zn rod to Cu rod and hence current flows from Cu rod to Zn rod.
(ii) Zn dissolves at anode and Cu deposits at cathode.

b) When E_ext= 1.1 V,
(i) No flow of electrons or current,
(ii) No chemical reaction.

c) When E_ext > 1.1 V
(i) Electrons flow from Cu to Zn and current flows from Zn to Cu.
(ii) Zn is deposited at the Zn electrode and Cu dissolves at Cu electrode.

Galvanic Cells :
In this device, the Gibbs energy of the spontaneous redox reaction is converted into electrical work.

The cell reaction in Daniell cell is a combination of the following two half reactions:

1. Zn(s) → Zn²⁺(aq) + 2 \(\overline { e } \) (oxidation half reaction/ anode reaction)
2. Cu²⁺(aq) + 2 \(\overline { e } \) → Cu(s) (reduction half-reaction/ cathode reaction)

These reactions occur in two different vessels of the Daniell cell. The oxidation half reaction takes place at Zn electrode and reduction half reaction takes place at Cu electrode. The two vessels are called half cells or redox couple. Zn electrode is called oxidation half cell and Cu electrode is called reduction half cell. The two half-cells are connected externally by a metallic wire through a voltmeter and switch. The electrolyte of the two half-cells are connected internally through a salt bridge.

Salt Bridge :
It is a U-shaped glass tube filled with agar-agar filled with inert electrolytes like KCl, KNO₃, NH₄NO₃.

Functions of Salt Bridge :

1. It maintains the electrical neutrality of the solution by intermigration of ions into two half-cells.
2. It reduces the liquid-junction potential.
3. It permits electrical contact between the electrode solutions but prevents them from mixing.

Electrode potential –
potential difference developed between the electrode and the electrolyte. According to IUPAC convention, the reduction potential alone is called electrode potential and is represented as \(E_{M^{n+} / M}\)

Standard Electrode Potential :
The electrode potential understandard conditions, (i.e., at 298 K, 1 atm pressure and 1M concentrated solution) is called standard electrode potential. It is represented as E^Θ.

Representation of a Galvanic Cell :
A galvanic cell is generally represented by putting a vertical line between metal and electrolyte solution and putting a double vertical line between the two electrolytes connected by a salt bridge.

For example, the Galvanic cell can be represented as,
Zn (s)|Zn²⁺(aq)||Cu²⁺(aq)|Cu(s)

Cell Potential or EMF of a Cell :
The potential difference between the two electrodes of a galvanic cell is called cell potential (EMF) and is measured in volts.
EMF = E_cell = E_cathode – E_anode = E_Rjght – E_Left
Consider a cell, Cu(s) | Cu2²⁺ (aq) || Ag⁺ (aq) | Ag(s)
E_cell = E_cathode – E_anode = E_Ag⁺/Ag – E_Cu²⁺/Cu

Measurement of Electrode Potential using Standard Hydrogen Electrode (SHE)/Normal Hydrogen Electrode :
SHE or NHE consists of a platinum electrode coated with platinum black. The electrode is dipped in an exactly 1 M HCl solution and pure H₂ gas at 1 bar is bubbled through it at 298 K. The electrode potential is arbitrarily fixed as zero at all temperatures.

Representation of SHE/NHE :
When SHE acts as anode:
Pt(s), Hsub>2(g, 1 bar) / H⁺(aq, 1 M)
When SHE acts as cathode:
H⁺(aq, 1 M)/H₂(g, 1 bar), Pt(s)

Electrochemical Series/Activity series :
The arrangement of various elements in the increasing or decreasing order of their standard electrode potentials.

Applications of Electrochemical Series:
1. To calculate the emf of an electrochemical cell – The electrode with higher electrode potential is taken as cathode and the other as anode.
\(E_{\mathrm{cell}}^{\Theta}=E_{\mathrm{cathode}}^{\Theta}-E_{\mathrm{anodo}}^{\Theta}\)

2. To compare the reactivity of elements – Any metal having lower reduction potential (electode potential) can displace the metal having higher reduction potential from the solutions of their salt, e.g. Zn can displace Cu from solution.
Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)

3. To predict the feasibility of cell reactions -If EMF is positive, the cell reaction is feasible and if it is negative the cell reaction is not feasible.

4. To predict whether H₂ gas will be evolved by reaction of metal with acids – All the metals which have lower reduction potentials compared to that of H₂ electrode can liberate H₂ gas from acids.

5. To predict the products of electrolysis.

Nernst Equation :
It gives a relationship between electrode potential and ionic concentration of the electrolyte. For the electrode reaction,
Mⁿ⁺ (aq) + n \(\overline { e } \) → M(s)
the electrode potential at any concentration measured with respect to SHE can be represented by,

R = gas constant (8.314 J K^-1 mol^-1), T=temperaturein kelvin, n = number of electrons taking part in the electrode reaction, F = Faraday constant (96487 C mol^-1)

By converting the natural logarithm to the base 10 and subsitituting the values of R(8.314 J K^-1 mol^-1),T (298 K) and F (96487 C mol^-1) we get,

Nernst Equation for a Galvanic Cell :
In Daniell cell, the electrode potential for any concentration of Cu²⁺ and Zn²⁺ ions can be written as,

Converting to natural logarithm to the base 10 and substituting the values of R, F and T=298 K, it. reduces to

Consider a general electrochemical reaction,

Equilibrium Constant and Nernst Equation:

where K_c is the equilibrium constant.

Electrochemical Cell and Gibbs Energy of the Reaction (∆_rG):

Conductance of Electrolytic Solutions: .Conductors:
A substance which allows the passage of electricity through it. Conductor are classified as,

Metallic or Electronic Conductors:
In these the conductance is due to the movement of electrons and it depends on:

1. The nature and structure of the metal
2. Number of valence electrons per atom
3. Temperature (it decreases with increase in temperature)
   e.g. Ag, Cu, Al etc.

ii. Electrolytic Conductors
Electrolytes – The substances which conduct electricity either in molten state or in solution, e.g. NaCl, NaOH, HCl, H₂SO₄ etc. The conductance is due to the movement of ions. This is also known as ionic conductance and it depends on:

1. Nature of the electrolyte
2. Size of the ions and their solvation
3. Nature of the solvent and its viscosity
4. Concentration of the electrolyte
5. Temperature (it increases with increase in temperature)

Ohm’s law – It states that the current passing through a conductor (I) is directly proportional to the potential difference (V) applied.
i.e., I ∝ V or I = \(\frac{V}{R}\)
where R – resistance of the conductor- unit ohm. In SI base units it is equal to kg m²/s³ A²

The electrical resistance of any substance/object is directly proportional to its length T, and inversly proportional to its area of cross section ‘A’.
R ∝ \(\frac{\ell}{\mathrm{A}}\) or R = ρ\(\frac{\ell}{\mathrm{A}}\) where,

ρ – (Greek, rho) – resistivity/specific resistance – SI unit ohm metre (Ω m) or ohm cm (Ω cm).

Conductance (G):
inverse or reciprocal of resistance (R).
\(G=\frac{1}{R}=\frac{A}{\rho \ell}=\kappa \frac{A}{\ell}\)
where K = \(\frac{1}{\rho}\) called conductivity or specific conductance (K – Greek, kappa)

SI unit of conductance – S (siemens) or ohm^-1.
SI unit of conductivity – S m^-1
1 S cm^-1 = 100 S m^-1

Molar Conductance of a Solution (Λ_m):
It is the conductance of the solution containing one mole of the electrolyte when placed between two parallel electrodes 1 cm apart. It is the product of specific conductance (K) and volume (V) in cm³ of the solution containing one mole of the electrolyte.

where M is molarity of the solution.
Unit of Λ_m is ohm’1 cm2 mol’1 Or S cm² mol^-1
Λ_m = \(\frac{K}{C}\) [C-Concentration of the solution.]

Measurement of the Conductivity of Ionic Solutions :
The measurement of an unknown resistance can be done by Wheatstone bridge. To measure resitance of the electrolyte it is taken in a conductivity cell. The resistance of the conductivity cell is given by the equation.
\(R=\rho \frac{\ell}{A}=\frac{1}{\kappa A}\)

The quantity \(\frac{\ell}{\mathrm{A}}\) is called cell constant and isdenoted A by G*. It depends on the distance (/) between the electrodes and their area of cross-section (A).

Variation of Conductivity and Molar Conductivity with Concentration :
Conductivity (K) always decreases with decrease in concentration both for weak and strong electrolytes. This is because the number of ions per unit volume that carry the current in a solution decreases on dilution.

Molar conductivity (Λ_m) increases with decrease in concentration. This is because the total volume, V of the solution containing one mole of electrolyte also increases.

The variation of molar conductance is different for strong and weak electrolytes,

1. Variation of Λ_m with Concentration for Strong Electrolytes:
The molar conductance increases slowly with decrease in concentration (or increase in dilution) as shown below:

There is a tendency for Λ_m to approach a certain limiting value when concentration approaches zero i. e., dilution is infinite. The molar conductance of an electrolyte when the concentration approaches zero is called molar conductance at infinite dilution, Λ_m^∞ or Λ°_m. The molar conductance of strong electrolytes obeys the relationship.
Λ_m = Λ°_m -AC^1/2 where C = Molar concentration, A = constant for a particular type of electrolyte.
This equation is known as Debye-Huckel-Onsagar equation.

2. Variation of Λ_m with Concentration for Weak Electrolytes :
For weak electrolytes the change in Λ_m with dilution is due to increase in the degree of dissociation and consequently increase in the number of ions in total volume of solution that contains 1 mol of electrolyte. Here, Λ_m increases steeply on dilution, especially near lower concentrations.

Thus, the variation of Λ_m with √c is very large so that we cannot obtain molar conductance at infinite dilution Λ°_m by the extrapolation of the graph.

Kohlrausch’s Law:
The law states that, the molar conductivity of an electrolyte at infinite dilution is equal to the sum of the molar ionic conductivities of the cations and anions at infinite dilution.
Λ°_m = γ₊ λ°₊ + γ_– λ°_–
λ°₊ and λ°_– are the molar conductivities of cations and anions respectively at infinite dilution, Y+ and V. are number of cations and anions from a formula unit of the electrolyte.

Applications of Kohlaransch’s Law
1) To calculate Λ°_m of weak electrolytes

2) To calculate degree of dissociation of weak electrolytes
\(\alpha=\frac{\Lambda_{m}}{\Lambda_{m}^{0}}\)

3) To determine the dissociation constant of weak electrolytes

Electrolytic Cell and Electrolysis:
In an electrolytic cell, external source of voltage is used to bring about a chemical reaction. Electrolysis is the phenomenon of chemical decomposition of the electrolyte caused by the passage of electricity through its molten or dissolved state from an external source.

Quantitative Aspects of Electrolysis
Faraday’s Laws of Electrolysis First Law:
The amount of any substance liberated or deposited at an electrode is directly proportional to the quantity of electricity passing through the
electrolyte.
w α Q where ‘Q’ is the quantity of electric charge in coulombs.
w = ZQ .
w = Zlt
(∵ Q = It) where T is the current in amperes , ‘t’ is the time in seconds and ‘Z’ is a constant called electrochemical equivalent.

Second Law:
The amounts of different substances liberated by the same quantity of electricity passing through the electrolytic solution are proportional to their chemical equivalent weights.

The quantity of electricity required to liberate/deposit 1 gram equivalent of any substance is called Faraday constant ‘F’.
1 F = 96487 C/mol ≈ 96500 C/mol

Products of Electrolysis:
It depend on the nature of the material being electrolysed and the type of electrodes being used.

Electrolysis of Sodium Chloride:
When electricity is passed through molten NaCl, Na is deposited at the cathode and Cl₂ is liberated at the anode.
Na+(aq) + \(\overline { e } \) → Na(s) (Reduction at cathode)
Cl^–(aq) → ½ Cl₂(g) + \(\overline { e } \) (Oxidation at anode)

When concentrated aqueous solution of NaCl is electrolysed, Cl₂ is liberated at anode, but at cathode H₂ is liberated instead of Na deposition due to the high reduction potential of hydrogen.

The resultant solution is alkaline due to the formation of NaOH.

Electrolysis of CuSO₄ :
When aqueous CuSO₄ solution is electrolysed using Pt electrodes, Cu is deposited at the cathode and O₂ is liberated at the anode.
Cu²⁺(aq) + 2 \(\overline { e } \) → Cu(s) (at cathode)
H₂O(l) → 2H⁺(aq) + 1/2 O₂(g) + 2 \(\overline { e } \) (at anode)

If Cu electrode is used, Cu is deposited at cathode and an equivalent amount of Cu dissolves in solution from the anode (because oxidation potential of Cu is higherthan that of water).
Cu²⁺(aq) + 2 \(\overline { e } \) → Cu(s) (at cathode)
Cu(s) → Cu²⁺(aq) + 2\(\overline { e } \) (atanode)

Commercial Cells (Batteries)
The electrochemical cells can be used to generate electricity. They are two types:
i) Primary Cells:
Cells in which the electrode reactions cannot be reversed by external energy. These cells cannot be recharged, e.g. Dry cell, Mercury cell.

ii) Secondary Cells :
Cells which can be recharged by passing current through them in the opposite direction so that they can be used again.
e.g. Lead storage battery, Nickel-Cadmium cell.

Primary Cells
a) Dry Cell:
Anode – Zn container
Cathode – Carbon (graphite) rod surrounded by powdered MnO₂ and carbon.
Electrolyte – moist paste of NH₄Cl and ZnCl₂
The electrode reactions are :
Anode : Zn → Zn²⁺ + 2 \(\overline { e } \)
Cathode: MnO₂ + NH₄⁺ + \(\overline { e } \) → MnO(OH) + NH₃
Dry cell has a potential of nearly 1.5 V.

b) Mercury Cell:
Anode – Zn amalgam (Zn/Hg)
Cathode – paste of HgO and carbon
Eelectrolyte – paste of KOH and ZnO. The electrode reactions are,
Anode : Zn/Hg + 2OH^– → ZnO(s) + H₂O + 2 \(\overline { e } \)
Cathode : HgO + H₂O + 2 \(\overline { e } \) → Hg(l) + 2 OH^–
Overall reaction : Zn/Hg + HgO(s) → ZnO(s)+ Hg(l)
The cell potential = 1.35 V

2. Secondary Cells
a) Lead Storage Battery :
Anode – lead plates
Cathode – grids of lead plates packed with lead dioxide (PbO₂)
Electrolyte – 38% (by weight) soution of H₂SO₄.
The cell reactions when the battery is in use are,
Anode: Pb(s) + SO₄^2-(aq) → PbSO₄ + 2 \(\overline { e } \)
Cathode: PbO₂(s) + SO₄^2-(aq) + 4H⁺(aq) + 2 \(\overline { e } \) → PbSO₄(s) + 2H₂O(I)
The overall cell reaction is,
Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l)

The emf of the cell depends on the concentration of H₂SO₄. On recharging the battery the reaction is reversed and PbSO₄(s) on anode is converted to Pb and PbSO₄(s) at cathode is converted into PbO₂.

b) Nickel-Cadmium Cell:
Anode- Cd
Cathode – metal grid containing nickel (IV) oxide. Electrolyte – KOH solution. The overall cell reaction during discharge is,
Cd(s) +2 Ni(OH)₃(s) → CdO(s) + 2Ni(OH)₂(s) + H₂O(l)

3) Fuel Cells :
These are Galvanic cells designed to convert the energy of combustion of fuels directly into electrical energy.

H₂ – O₂ fuel cell – In this, hydrogen and oxygen are bubbled through porous carbon electrodes into concentrated aqueous NaOH solution, which acts as the electrolyte.

The electrode reactions are,
Anode : 2H₂(g) + 4OH^–(aq) → 4H₂O(l) + 4\(\overline { e } \)
Cathode : O₂(g) + 2H₂O(l) + 4\(\overline { e } \) → 4OH^–(aq)
Overall reaction : 2H₂(g) + O₂(g) → 2H₂O(l)

Advantages of Fuel Cells –
pollution free, more efficient than conventional methods, Runs continuously as long as the reactants are supplied, electrodes are not affected.

Other examples:
CH₄ – O₂ fuel cell, CH₃OH – O₂ fuel cell

Corrosion :
Any process of destruction and consequent loss of a solid metallic material by reaction with moisture and other gases present in the atmosphere. More reactive metals are corroded more easily. Corrosion is enhanced by the presence of impurities, air & moisture, electrolytes and defects in metals.
Examples: Rusting of iron, tarnishing of Ag.

Mechanism:
In corrosion a metal is oxidised by loss of electrons to O₂ and form oxides. It is essentially an electro chemical phenomenon. At a particular spot of an object made of iron, oxidation take place and that spot behaves as anode.
2 Fe(s) → 2 Fe²⁺ + 4\(\overline { e } \)E° = -0.44 V

Electrons released at anodic spot move through metal and go to another spot on the metal and reduce 02 in presence of H+. This spot behaves as cathode.
O₂(g) + 4 H⁺(aq) + 4\(\overline { e } \) → 2 H₂O(l) E° = 1.23 V

The overall reaction is,
2 Fe(s) + O₂(g)+ 4H⁺(aq) → 2 Fe²⁺ + 2H₂O(I) E° = 1,67V

The ferrous ions are further oxidised by atmospheric 02 to ferric ions and form hydrated ferric oxide (rust) Fe₂O₃.xH₂O

Prevention of Corrosion
1) Barrier Protection:
Coating the surface with paints, grease, metals like Ni, Cr, Cu etc.

2) Sacrificial Protection:
Coating the surface of iron with a layer of more active metals like Zn, Mg, Al etc. The process of coating a thin film of Zn on iron is known as galvanisation.

3) Anti-rust Solutions:
Applying alkaline phosphate/ alkaline chromate on iron objects which provide a protectve insoluble film. Also, the alkaline nature of the solutions decreases the availability of H⁺ ions and thus decreases the rate of corrosion.

Students can Download Chapter 2 Solutions Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 2 Solutions

Solutions:
homogeneous mixtures of two or more pure substances, having uniform composition and properties throughout. The substances forming a solution are called components.

Solvent and Solute:
The component that is present in the largest quantity is known as solvent.

One or more components present in the solution other than solvent are called solutes. e.g. In sugar solution, water is the solvent and sugar is the solute.

Binary solution:
A solution containing only two components.

Aqueous solutions:
solutions in which the solvent is water.

Types of Solutions

Expressing Concentration of Solutions :
The concentration of a solution is defined as the amount of solute present in the given quantity of the solution.

1. Mass percentage (w/w) :
The mass % of a component in a given solution is the mass of the component (solute) per 100 g of solution.

e.g. 10% glucose solution means 10 g of glucose dissolved in 90 g of water resulting in a 100 g solution.

2. Volume percentage (v/v) :
The volume % of a component in a given solution is the volume of the component per 100 volume of solution.

Example:
10% ethanol solution means 10 mL of ethanol dissolved in 90 mL of water.

3. Mass by volume percentage (w/v):
It is the mass of solute dissolved in 100 mL of the solution. Used in medicine and pharmacy.

4. Parts per million (ppm):
It is the parts of a solute (component) per million parts of the solution. When a solute is present in very minute amounts, parts per million (ppm) is used.

5. Mole fraction (X):
ratio of number of moles of one component to the total number of moles of all the components present in the solution.

For a binary solution, n_A be the number of moles of A and n_B be the number of moles of B.

The sum of mole fractions of all the components present in the solution is always equal to 1.
i.e., χ_A + χ_B = 1
Fora solution containing ‘i’ number of components,
χ₁ + χ₂ +……………… + χ_i = 1
Mole fraction is independent of temperature.

6. Molarity (M):
number of moles of solute dissolved in one litre of the solution.

7. Molality (m):
number of moles of solute per kilogram of the solvent.

Solubility:
Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a particular temperature.

Factors affecting solubility
Nature of the solute, nature of the solvent, temperature ‘ and pressure

Solubility of Solids in Liquids :
Like dissolves like:
Polar solutes are soluble in polar solvents and non-polar solutes are soluble in non-polar solvents.

Unsaturated solution:
Solution in which more solute can be dissolved at the same temperature.

Saturated solution:
Solution in which no more solute can be dissolved at the same temperature and pressure.

Effect of temperature :
Solubility increases with temperature if the reaction is endothermic. Solubility decreases with temperature if the reation is exothermic.

Effect of pressure :
Pressure does not have any significant effect on solubility of solids in liquids because solids and liquids are highly incompressible and practically remain unaffected by changes in pressure.

Solubility of a Gas in a Liquid :
It is greately affected by pressure and temperature.

Effect of pressure
Henry’s law :
The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas.
The most commonly used form of Henry’s law states that the partial pressure of the gas in the vapour phase (p) is proportional to the molefraction of the gas (χ) in the solution.
P = K_H.χ
where K_H is the Henry’s law constant.
Different gases have different K_H values at the same temperature. Thus, K_H is a function of the nature of the gas.

Higher the value of K_H at a given pressure, the lower is the solubility of the gas in the liquid.

The solubility of gases increase with decrease of temperature. Therefore, aquatic species are more comfortable in cold waters rather than in hot waters.

Applications of Henry’s law
1. To increase the solubility of CO₂ in soft drinks and soda water, the bottle is sealed under high pressure.
2. To avoid bends (a medical condition which is painful and dangerous to life caused by the formation of bubbles of N₂ in the blood) the tanks used by scuba divers are filled with air diluted with He (11.7% He, 56.2% N₂ and 32.1% O₂).
3. At high altitudes, low pressure leads to low concentrations of O₂ in blood. It causes climbers to become weak and unable to think clearly (anoxia).

Effect of temperature :
Dissoloution of gases in liquids is an exothermic process. Hence, according to Le Chatelier’s principle solubility of gases in liquids decreases with rise in temperature.

Vapour Pressure of Liquid Solutions

Vapour Pressure of Liquid-Liquid Solutions:
Consider the two volatile liquids denoted as ‘A’ and ‘B’. When both liquids are taken in a closed vessel, both components would evaporate and an equilibrium would be established between liquid and vapour phase.
Let, P_A– Partial vapour pressure of component A’
P_B – Partial vapour pressure of component ‘B’
χ_A Mole fraction of A
χ_B Moiefraction of B

Raoult’s Law :
The law states that fora solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.
For component ‘A’
P_A ∝ χ_A.
P_A= P°_A χ_A
where P°_A is the vapour pressure of pure component ‘A’ at the same temperature.
Similarly, for component ‘B’
P_B ∝ χ_B
P_B= P°_B χ_B
where P_B° is the vapour pressure of pure component ‘B’. Rauolt’s law also states that, at a given temperature for a solution of volatile liquids, the partial vapour pressure of each component is equal to the product of the vapour pressure of pure component and its mole fraction.

According to Dalton’s law of partial pressures,
Total pressure, P_[Total] = P_A + P_B

A plot of P_A or P_B versus the mole fractions χ_A and χ_B for a solution gives a linear plot as shown in the figure.

Raoult’s Law as a special case of Henry’s Law:
According to Raoult’s law, the vapour pressure of volatile liquid in a solution is proportional to its mole fraction, i.e., P_i = P_i° χ_i

According to Henry’s law, the vapour pressure of a gas in a liquid is proportional to its mole fraction, i. e., p=K_Hχ

Thus, Raoult’s law becomes a special case of Henry ’s law in which K_H becomes equal to P_i°.

Vapour Pressure of Solution of Solids in Liquids:
If a non-volatile solute is added to a solvent to give a solution, the surface of solution has both solute and solvent molecules; thereby the fraction of surface covered by the solvent molecules gets reduced. Consequently, the number of solvent molecules escaping from the surface is reduced. Hence, the vapour pressure of solution is lower than vapour pressure of pure solvent.

General form of Raoult’s Law:
For any solution, the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.

In a binary solution, let us denote the solvent by ‘A’ and solute by ‘B’.
According to Raoult’s law,
P_A ∝ χ_A
P_A = P_A° χ_A
Total pressure, P = P_A Here, P_B = 0
(∵ solute is non-volatile)
P = P_A° χ_A
For binary solution,
χ_A + χ_B = 1
χ_A = 1 – χ_B
Thus, the above equation becomes,

lowering of vapour pressure.

Ideal and Non-ideal Solutions :
Ideal Solutions:
The solutions which obey Raoult’s law over the entire range of concentrations.

Important properties of Ideal Solutions
i. P_A = P°_A χ_A ; P_B = P°_B χ_B
ii. Enthalpy of mixing is zero (∆_mixH = 0)
iii. Volume of mixing is zero (∆_mixV = 0)

If the intermolecular attractive forces between A – A and B – Bare nearly equal to those between A – B, it leads to the formation of ideal solution.

Examples:

1. Solution of n-hexane and n-heptane
2. Solution of bromoethane and chloroethane
3. Solution of benzene and toluene

Non-ideal Solutions :
solutions which do not obey Raoult’s law overthe entire range of concentration. The vapour pressure of such solutions is either higher or lower than that predicted by Raoult’s law.

If the vapour pressure is higher, it exhibits positive deviation and if the vapour pressure is lower it exhibits negative deviation from the Raoult’s law.

Solutions showing positive deviation :
the intermolecular attractive forces between the solute- solvent molecules are weaker than those between the solute-solute and solvent-solvent molecules. Thus, in such solutions molecules will find it easier to escape than in pure state. This will increase the vapour pressure and results in the positive deviation.

(dotted line represents graph for ideal solution).
Examples:
Ethanol + Water, Ethanol + Acetone, CCl₄ + Chloroform, C₆H₆ + Acetone , n-Hexane + Ethanol

Solution showing negative deviation:
In the case of negative deviation, the intermolecular attractive forces between solvent-solute molecules are greater than those between solvent-solvent and solute-solute molecules and leads to decrease in the vapour pressure.

Examples:
1. Mixture of phenol and aniline – In this case the intermolecular hydrogen bonding between phenolic proton and lone pair on nitrogen atom of aniline is stronger than the respective intermolecular hydrogen bonding between similar molecules.
2. Mixture of acetone and chloroform – Here chloroform molecule is able to form hydrogen bond with acetone molecule.

3. H₂O + HCl, (4) H₂O + HNO₃, (5) CHCl₃ + (C₂H₅)₂O

Azeotropes:
binary mixtures having same composition in liquid and vapour phase and boil at a constant temperature. It is not possible to separate the components of azeotropes by fractional distillation.

Solutions which show large positve deviation from Raoult’s law form minimum boiling azeotrope at a specific composition. For example, ethanol-water mixture forms a minimum boiling azeotrope (b.p. 351.1 K) when approximately 95% by volume of ethanol is reached.

The solutions that show large negative deviation from Raoult’s law form maximum boiling azeotrope at a specific composition. For example, nitric acid and water form a maximum boiling azeotrope (b.p. 393.5 K) at the approximate composition, 68% nitric acid and 32% water by mass.

Colligative Properties :
properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles present in the solution. These are,
i. Relative lowering of vapour pressure of the solvent \(\left(\frac{\Delta p_{1}}{p_{1}^{0}}\right)\)
ii. Elevation of boiling point of the solvent (∆T_b)
iii. Depression of freezing point of the solvent (∆T_f)
iv. Osmotic pressure of the solution (π)

Relative Lowering of Vapour Pressure:
When a non-volatile solute (B) is dissolved in a liquid solvent (A), the vapour pressure of the solvent is lowered. This phenomenon is called lowering of vapour pressure. It depends only on the concentration of the solute particles and it is independent of their identity. The relation between vapour pressure of solution, mole fraction and vapour pressure of the solvent is given as,
P_A = χ_AP°_A ……………(1)
The lowering of vapour pressure of solvent ∆ P_A is given as,
∆ P_A = P°_A – P_A ……………(2)
Substitute the equation (1) in (2)
∆ P_A = P°_A – P°_Aχ_A
= P°_A(1 – χ_A)
∆ P_A = P°_Aχ_B …………..(3) ∵ (1 – χ_A) = χ_B
The relative lowering of vapour pressure is given as,

of vapour pressure and is equal to the mole fraction of solute.
From equation (4),

For dilute solutions n_B < < n_A, hence neglecting nB In the denominator, the above equation becomes,

where w_A and w_B are the masses and M_A and M_B are the molar masses of solvent and solute respectively.

Elevation of boiling point (∆T_b):
The boiling point of a solution is higher than that of the pure solvent. The elevation in the boiling point depends ‘ on the number of solute molecules rather than on their nature.

Let T°_b be the boiling point of pure solvent and T_b be the boiling point of solution. The increase in the boiling point ∆T_b = T_b – T°_b is known as elevation of boiling point.

For a dilute solution, the elevation of boiling point ( ∆T_b) is directly proportional to the molal concentration of the solute in a solution (i.e., molality).
∆T_b ∝ m
∆T_b = K_bm …………(1)

where, m → molality and K_b → Boiling Point Elevation Constant/Molal Elevation Constant/ Ebullioscopic Constant.
Unit of Kb is K kg mol^-1 Or K m^-1

Substituting the value of‘m’ in equation (1),

Depression of Freezing point (∆T_f) :
The lowering of vapour pressure of a solution causes a lowering of the freezing point compared to that of the pure solvent.

Let T°_f be the freezing point of pure solvent and T_f be the freezing point of solution.
Depression in freezing point ∆T_f= T°_f – T_f
For a dilute solution, depression of freezing point (∆T_f) is directly proportioned to molality (m) of the solution. Thus,
∆T_f ∝ m
∆T_f = K_fm ………………(1)
where, K_f – Freezing Point Depression Constant/ Molal Depression Constant/Cryoscopic Constant.
Unit of K_f is K kg mol^-1 Or K m^-1

[Note: The values of K_b and K_f, depend upon the nature of the solvent. They Can be ascertained from the following equations:

where,
R → Gas constant, MA → Molar mass of solvent
T_b → Boiling point of pure solvent of kelvin
T_f → Freezing point of pure solvent in kelvin
∆_fusH → Enthalpy of fusion, ∆_vapH → enthalpy of vapourisation.
For water, K_b = 0.52 K kg mol^-1 and K_f = 1.86 K kg mol^-1]

Osmosis and Osmotic Pressure:
The process of flow of the solvent molecules from pure solvent to the solution through semipermeable membrane (SPM) is called osmosis.

Semi Permeable Membrane :
The membrane which allows the passage of solvent molecules but ’ not the solute molecule is called SPM.

Example:
Parchment paper, Pig’s bladder, Cell wall, Film of cupric ferrocyanide.

Osmotic Pressure (π):
the excess pressure which must be applied to a solution to prevent osmosis or the pressure that just stops the flow of solvent.

Osmotic pressure (π) is proportional to the molarity (C) of the solution at a given temperature (T K).
π = CRT, where R is the gas constant.
π = \(\frac{n_{B}}{V}\)RT, where nc is the number of moles of the solute and V is the volume of the solution in litres.
π = n_BRT
π V= \(\frac{\mathrm{W}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{B}}}\)RT , where w_B is the mass of the solute and M_B is the molar mass of the solute.
Or M_B = \(\frac{\mathbf{w}_{\mathrm{B}} \mathrm{RT}}{\pi \mathrm{V}}\)

Osmotic pressure measurement is widely used to determine molar mass of proteins, polymers and other macro molecules.

Advantages of osmotic pressure method:
i) pressure measurement is around the room temperature
ii) molarity of the solution is used instead of molality
iii) the magnitude of osmotic pressure is large compared to other colligative properties even for very dilute solutions.

Isotonic Solution :
Two solutions having same (equal) osmotic pressure at a given temperature. A 0.9% solution of NaCI (normal saline solution) is isotonic with human blood, and it is safe to inject intravenously.

Hypertonic Solution :
A solution having higher osmotic pressure than another solution.
Hypotonic Solution :
A solution having lower osmotic pressure than another solution.

Reverse Osmosis:
flow of the pure solvent from solution side to solvent side through semipermeable membrane when a pressure larger than the osmotic pressure is applied to the solution side.

Uses of reverse osmosis:
Desalination of sea water, Purification of water.

Abnormal Molar Mass :
In some cases, the molar mass determined by colligative properties do not agree with the theoretical values. This is due to association ordissociation of the solute particles in the solution.

Association of Solute Particles :
When solute particles undergo association the number of the solute particles in the solution decreases. Consequently, the experimental values of colligative properties are less than the expected values, e.g. Molecules of ethanoic acid (acetic acid) dimerise in benzene due to intermolecular hydrogen bonding.

Similarly, benzoic acid undergo dimerisation when dissolved in benzene.

Dissociation of Solute Particles :
When the solute particles dissociate or ionise in the solvent, the number of particles in solution increases and so the experimental values of the colligative properties are higher than the calculated values.
e.g. KCl in water ionises as
KCl → K⁺ + C^–
Molar mass either lower or higher than the expected or normal value is called as abnormal molar mass.

van’t Hoff factor (i):
It accounts for the extent of association or dissociation.

Significance of van’t Hoff factor.
i > 1 ⇒ there is dissociation of solute particles.
i < 1 ⇒ there is association of solute particles.
i < 1 ⇒ there is no dissociation and association of solute particles.

Inclusion of van’t Hoff factor modifies the equations for colligative properties as follows:
Relative lowering of vapour pressure of solvent,

Students can Download Chapter 1 The Solid State Notes, Plus Two Chemistry Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Chemistry Notes Chapter 1 The Solid State

General Characteristics of Solid State
Definite mass, volume and shape; short inter molecular distances; strong intermolecular forces; constituent particles have fixed position and can only oscillate about their mean positions; incompressible and rigid.

Classification of Solids:
1. Crystalline Solids :
The constituent particles are well orderly arranged. It has long range orcfe/-which means that there is a regular pattern of arrangement of particles which repeats itself periodically overthe entire crystal, e.g. NaCl, Quartz.

2. Amorphous Solids (Greek amorphos = no form):
The constituent particles are irregularly arranged; i.e. they have irregular shape, the arrangement of constituent particles in this solid has only short range order, e.g. rubber, quartz, glass, plastic.

Amorphous solids have a tendency to flow slowly, therefore these are called pseudo solids or supercooled liquids, e.g. Glass – Glass flows down very slowly and makes the bottom portion slightly thicker.

Crystalline solids are anisotropic in nature (i.e. their physical properties like electrical resistance or refractive index show different values in different directions). Amorphous solids on the other hand are isotropic, (i.e. their physical properties would be same along any direction)

Difference between Crystalline and Amorphous Solids

Classification of Crystalline Solids:
Crystalline solids can be classified on the basis of nature of intermolecular forces operating in them into four categories.

Molecular Solids :
In this, molecules are the constituent particles, they are of three categories:

a. Non-polar Molecular Solids :
They are formed by the regular arrangement of either atoms or non-polar molecules held by weak dispersion forces or London forces. They have low melting points and are liquids or gases at room temperature and pressure, e.g. solid forms of argon, He, H₂ and Cl₂, l₂.

b. Polar Molecular Solids :
In these polar molecules are held by relatively stronger dipole-dipole interaction. They are soft and non-conductors of electricity e.g. solid forms of HCl, SO₂, NH₃.

c. Hydrogen bonded Molecular Solids :
Strong H- bonding binds the molecules of these solids. They are non-conductors of electricity and are volatile liquids or soft solids.
e.g. Ice (Solid H₂O)

Ionic Solids :
In these ions are held together by strong coulombic (electrostatic) forces. They are hard and brittle in nature and have high melting point and boiling points. They are electrical insulators in the solid stale, but in molten state/solutions conduct electricity because ions become free to move.
e.g. NaCl, KCl, KNO₃ etc.

Metallic Solids :
In these positive ions are surrounded by and held together by a sea of free electrons. These free and mobile electrons are responsible for high electrical and thermal conductivity. Due to this mobile electrons metals have lustre and colour, e.g. Gold, Silver etc.

Covalent or Network Solids:
They have covalent bonds between adjacent non-metal atoms which are held strongly in their positions. They have high melting points and are insulators, e.g. Diamond, SiC Graphite is an exceptional case – it is soft and conducts electricity due to its typical layer structure.

Crystal Lattice and Unit Cells
The three dimensional arrangement of constituent particles in a crystal, represented by points is called crystal lattice/space lattice.

Unit Cell:
The smallest repeating portion of space lattice/crystal lattice. A unit cell is characterised by,
1. The distance along with three edges: a, b & c
2. Angle between the edges:
α (between b & c)
β (between a & c)
γ (between a & b)

Primitive and Centred Unit Cells
a. Primitive Unit Cell :
the constituent particles are present only on the corner positions of unit cell.

b. Centred Unit Cells
i. Body-Centred Unit Cell (bcc) :
The constituent particles at all the corners as well as at the centre of the unit cell.
ii. Face-Centred Unit Cell (fee) :
The constituent particles at all the corners as well as at the centre of the each face.
iii. End-Centred Unit Cell:
One constituent particle is present at the centre of any two opposite faces besides the one present at its corners.

Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells:

Number of Atoms in a Unit Cell
1. Primitive Cubic Unit Cell or Simple Cubic Unit Cell:
Primitive cubic unit cell has atoms only at its corner. Each atoms at a corner is shared between eight adjacent unit cells. Therefore the contribution of an atom/molecule to a particular unit cell is 1/8

Total number of atoms in unit cell = 8 × 1/8 = 1

2. Body Centred Cubic Unit Cell (bcc):
In bcc unit cell, particles are present not only at the eight corners but also at the centre of the cube.

In a bcc unit cell:
i. 8 corners x 1/8 per corner atom = 8 × 1/8 = 1 atom

ii. 1 body centre atom = 1×1 = 1 atom
∴ Total number of atoms per unit cell = 1 + 1=2 atoms

3. Face Centred Cubic Unit Cell :
A fee unit cell contains atoms at all the corners as well as at the centre of 6 faces of the cube. The atoms at the face centre is shared between two adjacent unit cells and the contribution is only ½ to the unit cell.

In a fcc unit cell:
i. 8 comers x 1/8 per corner atom = 8 × 1/8 = 1 atom
ii. 6 face centre x ½ atom per unit cell = 6 × ½ = 3 atoms
∴ Total number of atoms per unit cell = 1+3 = 4 atoms

Close Packed Structures:
In solids, the constituent particles (considered as identical hard spheres) are close-packed, leaving the minimum vaccnt space.

Coordination number (C.N.) :
The number of nearest neighbouring particles (spheres) in a crystal lattice is called coordination number.

a. Close Packing in One Dimension :
In this arrangment, each sphere is in contact with two of its neighbours. The cordination number is two.

b. Close Packing in Two Dimensions :
Two dimensional close packing can be done in two different ways:

i. Square Close Packing (scp):
The second row is placed in contact with the first one such that the spheres are exactly above those of the first row. The spheres of the two rows are aligned horizontally as well as vertically. Each sphere is in contact with four of its neighbours. Thus coordination number is 4. This is also known as AAA type arrangment.

ii. Hexagonal Close Packing (hep) :
The spheres in every second row are placed in the depressions of the first row. The spheres in the third row are seated in the depressions of the second row and so on. The fourth layer is aligned with the second layer. Hence this type of arrangement is of ABAB type. Each sphere is in contact with 6 neighbouring spheres. Thus the C.N. is 6.

In hexagonal close packing, particles are more closely packed than in square close packing. Hence, it is more efficient than square close packing.

c. Close Packing in Three Dimensions :
i. Three-dimensional close packing from two-dimensional square close-packed layers :
the second layer is placed over the first layer such that the spheres of the upper layers are exactly above those of the first layer. Here, spheres of both the layers are perfectly aligned horizontally as well as vertically. This type of arrangement has AAA type pattern. This arrangement generates the simple cubic lattice.

ii. Three dimensional close packing from two-dimensional hexagonal close-packed layers
a. Placing second layer over the first layer :
The spheres of the second layer are placed in the depressions of the first 2 dimensional hep layer. Wherever a sphere of the second layer is above the triangular void of the first layer (or vice versa) a tetrahedral void is formed.|

The vaccant space/sites in close packed structure are called voids/interstitial voids.

Tetrahedral void (td void) :
The vacant space surrounded by 4 spheres are called tetrahedral voids.

Octahedral void (oh void):
The vaccant space surrounded by six spheres in a close packed arrangement.

If ‘N’ is the number of spheres in close packed structure,

b. Placing third layer over the second layer :
If particles in the third layer are arranger) in the tetrahedral voids, the spheres of the third layer are exactly aligned with those of the first layer. Thus, the pattern of spheres is repeated in alternate layers. This is known as ABAB or hexagonal close packed (hep) structure, e.g. Mg, Zn, Cd etc.

If particles in the third layer are arranged in the octahedral voids, spheres of the fourth layer are aligned with those of the first layer. Thus, ABCABC … arrangement is obtained. This is known as cubic close packed (ccp) structure or face-centred cubic (fee) structure, e.g. Cu, Ag, Au etc.

Both the hep and ccp are highly efficient and 74% space in the crystal is filled. Coordination number is 12 in either of these two structures.

Packing Efficiency
It is the percentage of total space filled by the particles.
Let ‘a’ be the edge length of a unit cell and ‘r’ the radius of sphere.

Packing Efficiency in ccp and hep Structures:
In the case of ccp and hep, the edge length,

Packing Efficiency of Body Centred Cubic Structures :
In this case radius of a sphere,

Packing Efficiency in Simple Cubic Lattice :
In simple cubic lattice edge length, ‘a’ and radius of the sphere ‘r’ are related as,
a = 2r
r = a/2
We know that a simple cubic unit cell contains only one sphere.

Calculations Involving Unit Cell Dimensions :
Edge length of unit cell = a
Volume of the unit cell = a³
Mass of unit cell = Number of atoms in unit cell × mass of each atom = z × m
Mass of an atom in unit cell m = \(\frac{M}{N_{A}}\) (M-molar mass)

Note:
The density of the unit cell is the same as the density of the substance.

Imperfection in Solids :
The crystal defects are irregularities in the arrangement of constituent particles. There are two types of defects:
1. Point Defects:-
Irregularities from ideal arrangement around a point or an atom.
2. Line Defects:-
Irregularities/deviations from ideal arrangement in entire rows of lattice points.

Point Defects:
They can be classified into three types – stoichiometric defects, impurity defects and non-stoichiometric defects.

a. Stoichiometric Defects:
These are the point defects that do not disturb the stoichiometry of the solid. They are also called intrinsic or thermodynamic defects. These are of two types:
i. Vacancy Defect:
When some of the lattice sites are vacant (missing of constituent particles), the crystal is said to have vacancy defect. As a result density of the substance decreases.

ii. Interstitial Defect:
When some constituent particles occupy an interstitial site, the crystal is said to have interstitial defect.

There are two types of stoichiometric defects in ionic solids : Schottky Defect and Frenkel Defect.

Schottky Defect:
It arises due to the missing of equal number of cations and anions from their normal positions leaving behind a pair of holes. It is observed in ionic compounds having high coordination numberwith ions of almost similar size. Since equal number of cations and anions are missing they maintain electrical neutrality. Density of the substance decreases.
e.g. NaCl, KCl, CsCl and AgBr.

Frenkel Defect:
It arises due to an ion, usually cation which is dislocated from its normal site to an interstitial site. It creates a vaccancy defect at its original site and an interstitial defect at its new location. This is also called dislocation defect. It is usually observed in ionic compounds having low coordination number and crystals with anions much larger in size than the cations. Since no ions are missing, density of the solid does not change, e.g. ZnS, AgCI, AgBrandAgl.
Note: AgBr shows both Schottky as well as Frenkel defects.

Note: AgBr shows both Schottky as well as Frenkel defects.

b. Impurity Defects :
Defect caused by foreign ions. e.g. If molten NaCl containing a little amount of SrCl₂ is crystallised, some of the sites of Na⁺ ions are occupied by Sr²⁺. Each Sr²⁺ replaces two Na⁺ ions. It occupies the site of one Na⁺ ion and the othersite remains vaccant. The cationic vaccancies thus pro duced are equal in number to that of Sr²⁺ ions. Another example is the solid solution of CdCl₂ and AgCl.

c. Non-Stoichiometric Defects:
The stoichiometry of the crystal is altered due to defects. These defects are of two types:
i. Metal Excess Defect
ii. Metal Deficiency Defect

i. Metal Excess Defect
1. Due to anionic vacancies :
A compound may have excess of metal ion if a negative ion is absent from its lattice site leaving a hole which is occupied by electron. The anionic sites occupied by unpaired electrons are called F-centres. (German word Farbenzenter means colour centre). These can impart colourto the crystal by excitation of electrons when they absorb energy from visible light, e.g. When crystals of NaCl are heated in an atmosphere of Na vapour, F-centres are formed. As a result, the crystal has an excess of sodium which imparts yellow colour.
Excess Li in LiCl – imparts pink colour
Excess K in KCl – imparts violet(lilac) colour

2. Metal excess defect due to extra cations at interstitial sites :
Here, electrical neutrality is maintained by the presence of an electron in the interstitial site. e.g. Zinc oxide (ZnO) is white in colour at room temperature. On heating it loses O₂ and turns yellow.

Now there is excess of zinc in the crystal and its formula becomes Zn_1+x O. The excessZn²⁺ ions move to interstitial sites and electrons move to neighbouring interstitial sites.

ii. Metal Deficiency Defect
1. Due to cation vaccancies:
A positive ion is missing from its lattice postion and the extra negative charge thus created is balanced by the adjacent metal ion which attains one additional positive charge.
e.g. FeO. It is mostly found with a composition of Fe_0.95O. In crystal of FeO some Fe²⁺ cations are missing and the loss of positive charge is made up by the presence of required number of Fe³⁺ ions. As a result, the crystal has metallic lustre. Other example is FeS (fool’s gold).

2. Due to the presence of anions in interstitial site:
An extra negative ion would occupy an interstitial site and the extra negative charge thus formed is balanced by an adjacent cation possessing additonal positive change. This defect is not common because anions are bigger than cations and cannot be occupied in interstitial sites.

Properties of Solids
Electrical Properties :
Solids can be classified into 3 types on the basis of their conductivities.

1. Conductors :
Solids with conductivities of the order of 10⁴ to 10⁷ ohm^-1 m^-1. Metals are good conductors of electricity and the conductivity is in the order of 10⁷ ohm^-1 m^-1.

ii. Insulators :
The solids which almost do not allow the passage of electricity, e.g. S, P, wood, paper, rubber. Conductivity order 10^-20– 10^-10 ohm^-1 m^-1

iii. Semiconductors :
The solids whose conductivity lies between metallic conductors and insulators. Conductivity range from 10^-6 to 10⁴ ohm^-1 m^-1 (or 10^-8 to 10² ohm^-1cm^-1).

Oxides like TiO, VO, ReO₃ etc. are good conductors. But oxides like Ti₂O₃, V₂O₃ etc. behave as insulators at centain termperature. TiO₂, V₂O₅ etc. are perfect insulators. The conductivity of semiconductors increases with temperature while that of metals decreases with temperature.

Conduction of Electricity in Metals :
Metals conduct electricity in solid as well as molten state through movement of electrons. The conductivity of metals depend upon the number of valence electrons available per atom. The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each other as to form a band. If this band is partially filled or if overlap with a higher energy unoccupied conduction band, then the electrons can flow easily under an applied electric field.

Conduction of Electricity in Semiconductors :
Here, the energy gap between the valence band and conduction band is small. Therefore some electrons may jump to conduction band and show some conductivity. Electrical conductivity of semi conductors increases with rise in temperature, since more electrons can jump to conduction band. This type of semiconductors are known as intrinsic semiconductors, e.g. Silicon, Germanium.

The conductivity of intrinsic semi conductors is increased by adding appropriate amount of suitable impurities, which introduce electronic defects. This process is called dopping. It can be done in two ways:

a. By adding electron rich impurities (n-type semiconductors) :
If Si and Ge are dopped with group 15 elements like P or As, the 5th electron is extra and becomes delocalised which is responsible for electrical conductivity. Since conductivity is due to the negatively charged electron it is called n-type semiconductor.

b. By adding electron deficit impurities (p-type semi conductors):
If Si and Ge are dopped with group 13 elements like B, Al or Ga an electron deficient bond or electron hole is produced. Under the influence of electric field, electrons move towards the positively charged plate through electronic holes. It appears as if electron holes are positively charged and are moving towards negatively charged plate. This type semi conductors are called p-type semi conductors.

Application of n-type and p-type semi conductors:

1. Diode is a combination of n-type and p-type semi conductors and is used as a rectifier.
2. The npn and pnp types of transistors are used to amplify radio or audio signals.
3. Photo-diode is used for conversion of light energy into electrical energy.

Magnetic Properties :
Every substance has some magnetic properties associated with it. Each electron in an atom behaves like a tiny magnet. Its magnetic moment originates from two types of motions.
i. Electron’s orbital motion around the nucleus
ii. Electron’s spin around its own axis
Magnetic moment is measured in Bohr magneton
(B.M), µ_B. 1 B.M. = 9.27 × 10^-24 A m²
Magnetic properties are of 5 types:

i. Paramagnetism :
It is due to the presence of one or more unpaired electrons. Paramagnetic substances are weakly attracted by a magnetic field.
e.g. O₂, Cu²⁺, Fe³⁺, Cr³⁺ Ni²⁺, VO, VO₂, CuO, NO

ii. Diamagnetism :
It is due to paired electrons in the substance. Diamagnetic substances are weakly repelled by a magnetic field.
e.g. H₂O, NaCl, C₆H₆, TiO₂, N₂

iii. Ferromagnetism :
It is considered as an extreme case of paramagentism and is caused by spontaneous alignment of magnetic domains (metal ions grouped into small regions) in the direction of the magnetic field. Ferromagnetic substances are strongly attracted by magnetic field. They retain a permanent magnetism even when the field is removed, e.g. Fe, Co, Ni, Alloys of Fe, Co and Ni, CrO₂ Once such a material is magnetised, it remains permanently magnetised.
Alignment of magnetic moments: ↑↑↑↑↑↑

iv. Antiferromagnetism:
It arises due to the alignment of magnetic domains in opposite direction and the resulting moment is zero. Antiferromagnetic substances are expected to possess paramagnetism or ferromagnetism on the basis of unpaired electrons but actually they possess zero net magnetic moment.
e.g. MnO, MnO₂, Mn₂O₃, FeO, NiO, CuO
Alignment of magnetic moments: ↑↓↑↓↑↓

v. Ferrimagnetism :
It is due to the alignment of magnetic moments in opposite directions in unequal numbers resulting in a net magnetic moment. These substances are expected to possess large magnetism on the basis of unpaired electrons but actually have small net magnetic moment and are weakly attracted by magnetic field as compared to ferromagnetic substances.
e.g. Fe₃O₄ (magnetite), MgFe₂O₄ & ZnFe₂O₄.
Alignment of magnetic moments: ↑↑↓↑↑↓