ELECTRODE POTENTIAL
For any electrode → oxidiation potential = - Reduction potential
E_{cell} = R.P of cathode - R.P of anode
E_{cell} = R.P. of cathode + O.P of anode
E_{cell} is always a +ve quantity & Anode will be electrode of low R.P
E°_{Cell} = SRP of cathode - SRP of anode.
GIBBS FREE ENERGY CHANGE :
ΔG = - nFE_{cell}
ΔG° = - nFE°_{cell}
NERNST EQUATION : (Effect of concentration and temp of an emf of cell)
⇒ ΔG = ΔG° + RT lnQ (where Q is raection quotient)
ΔG° = - RT ln K_{eq}
At chemical equilibrium
ΔG = 0 ; E_{Cell} = 0.
CONCENTRATION CELL : A cell in which both the electrods are made up of same material.
For all concentration cell E°_{cell} = 0.
(a) Electrolyte Concentration Cell :
eg. Zn(s) / Zn^{2+} (c_{1}) || Zn^{2+}(c_{2}) / Zn(s)
(b) Electrode Concentration Cell:
eg. Pt, H_{2}(P_{1} atm) / H^{+} (1M) / H_{2}(P_{2}atm) / Pt
DIFFERENT TYPES OF ELECTRODES :
1. Metal-Metal ion Electrode M(s)/M^{n+}. M^{n+} + ne^{-} → M(s)
2. Gas-ion Electrode Pt/H_{2}(Patm)/H^{+}(XM) as a reduction electrode
3. Oxidation-reduction Electrode Pt / Fe^{2+}, Fe^{3+} as a reduction electrode Fe^{3+} + e^{-} → Fe^{2+}
4. Metal-Metal insoluble salt Electrode eg. Ag/AgCI, Cl^{-} as a reduction electrode AgCI(s) + e^{-} → Ag(s) + Cl^{-}
CALCULATION OF DIFFERENT THERMODYNAMICS FUNCTION OF CELL REACTION
ELECTROLYSIS :
(a)
(b) Similarly the an ion which is strogner reducing agent(low value of SRP) is liberated fir stat the anode.
FARADAY’S LAW OF ELECTROLYSIS :
First Law :
Second Law :
W α E W/E = constant
CURRENT EFFICIENCY =
CONDUCTANCE:
KOHLRAUSCH’S LAW:
Variation of λ_{eq} /λ_{M} of a solution with concentration :
(i) Strong electrolyte
(ii) Weak electrolytes : where λ is the molar conductivity
n_{+} = No of cations obtained after dissociation per formula unit
n_{_} = No of anions obtained after dissociation per formula unit
APPLICATION OF KOHLRAUSCH LAW:
1. Calculation of λ^{0}_{M} of weak electrolytes :
2. To calculate degree of diossociation of a week electrolyte
3. Solubility (S) of sparingly soluble salt & their K_{sp}
IONIC MOBILITY: It is the distance travelled by the ion per second under the potential gradient of 1 volts per cm. It’s unit is cm^{2}s^{-1}v^{-1}.
Absolute ionic mobility:
Transport Number:
Where t_{c} = Transport Number of cation & t_{a} = Transport Number of anion
SOLUTION & COLLIGATIVE PROPERTIES
1. OSMOTIC PRESSURE :
(i) π = ρgh
Where, ρ = density of soln., h = equilibrium height.
(ii) Vont - Hoff Formula (For calculation of O.P.)
π = CST
π = CST = n/V (RT) (just like ideal gas equation)
∴ C = total cone, of all types of particles.
= C_{1} + C_{2} + C_{3} + ....
Note : If V_{1} mL of C_{1} cone. + V_{2} mL of C_{2} cone, are mixed.
;
Type of solutions:
(a) Isotonic solution - Two solutions having same O.P.
π_{1} = π_{2} (at same temp.)
(b) Hyper tonic - If π_{1}> π_{2}. ⇒ I^{st} solution is hypertonic solution w.r.t. 2^{nd} solution.
(c) Hypotonic - II^{nd} solution is hypotonic w.r.t. I^{st }solution.
Abnormal Colligative Properties : (In case of association or dissociation)
VANT HOFF CORRECTION FACTOR (i):
Relation between i & α (degree of dissociation) :
i = 1 + (n - 1)α Where, n = x + y.
Relation b/w degree of association β & i.
2. RELATIVE LOWERING OF VAPOUR PRESSURE (RLVP) :
Vapour pressure : P_{Soln.} < P
Lowering in VP = P - P_{s} = ΔP
Relative lowering in vapour pressure
Raoult's law :- (For non - volatile solutes)
Experimentally relative lowering in V.P = mole fraction of the non volatile solute in solutions.
(M = molar mass of solvent)
If solute gets associated or dissociated
3. ELEVATION IN BOILING POINT :
ΔT_{b} = i x K_{b}m
or
4. DEPRESSION IN FREEZING POINT:
∴ ΔT_{f }= i x K_{f} . m.
K_{f }= molal depression constant =
RAOULT’S LAW FOR BINARY (IDEAL) MIXTURE OF VOLATILE LIQUIDS :
x_{A}' = mole fraction of A in vapour about the liquid / solution.
x_{B}' = mole fraction of B
Graphical Representation :
Ideal solutions (mixtures) : Mixtures which follow Raoul'ts law at all temperature.
ΔH_{mix} = 0 ΔV_{mix} = 0 ΔS_{mix} = + ve as for process to proceed : ΔG_{mix} = -ve
eg. (1) Benzene + Toluene.
(2) Hexane + heptane.
(3) C_{2}H_{5}Br + C_{2}H_{5}I.
Non - Ideal solutions : Which do not obey Raoult's law.
(a) Positive deviation :-
eg. H_{2}O + CH_{3}OH.
H_{2}O + C_{2}H_{5}OH
C_{2}H_{6}OH + hexane
C_{2}H_{5}OH + cyclohexane.
CHCI_{3} + CCI_{4} → dipole dipole interaction becomes weak.
(b) Negative deviation
e.g. H_{2}O + HCOOH
H_{2}O + CH_{3}COOH
H_{2}O + HNO_{3}
CHCl_{3} + CH_{3}OCH_{3} ⇒
Immiscible Liquids:
(i) P_{total}= P_{A}+ P_{B}
B.P. of solution is less than the individual B.P.’s of both the liquids.
Henry Law :
This law deals with dissolution of gas in liquid i.e. mass of any gas dissolved in any solvent per unit volume is proportional to pressure of gas in equilibrium with liquid,
m α p
m = kρ
SOLID STATE
CHEMICAL KINETICS & REDIOACTIVITY
RATE/VELOCITY OF CHEMICAL REACTION :
Mol lit^{-1} time^{-1} = mol dm^{-3} time^{-1}
Types of Rates of chemical reaction :
For a reaction R → P
RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF REACTANTS):
Rate = K (conc.)^{order} - differential rate equation or rate expression
Where K = Rate constant = specific reaction rate = rate of reaction when concentration is unity unit of K = (conc)^{1-order} time^{-1}
Order of reaction :
m_{1}A + m_{2}B → products.
R ∝ [A]^{p} [B]^{q} Where p may or may not be equal to m_{1} & similarly q may or may not be equal to m_{2}.
p is order of reaction with respect to reactant A and q is order of reaction with respect to reactant B and (p + q) is overall order of the reaction.
INTEGRATED RATE LAWS:
C_{0} or 'a' is initial concentration and C_{t} or a - x is concentration at time 't'
(a) zero order reactions :
Rate = k [cone.]^{0} = constant
Rate = k = or C_{t} = C_{0} - kt
Unit of K = mol lit^{-1} sec^{-1}, Time for completion = C_{0}/k
∴ t_{1/2} ∝ C_{0}
(b) First Order Reactions :
(i) Let a 1^{st} order reaction is, A → Products
or
⇒ Independent of initial concentration.
Graphical Representation:
(c) Second order reaction :
2^{nd} order Reactions Two types
(d) Psuedo first order reaction :
∴ For A + B → Products [Rate = K [A]^{1} [B]^{1}]
Now if ‘B’ is taken in large excess b > > a.
⇒
∵ ‘b’ is very large can be taken as constant
⇒ k' is psuedo first order rate constant
METHODS TO DETERMINE ORDER OF A REACTION
(a) Initial rate method :
r = k[A]^{a} [B]^{b }[C]^{c} if
then for two different initial concentrations of Awe have
⇒
(b) Using integrated rate law : It is method of trial and error.
(c) Method of half lives :
for n^{th }order reaction
(d) Ostwald Isolation Method :
rate = k [A]^{a} [B]^{b} [C]^{c} = k_{0 }[A]^{a}
METHODS TO MONITOR THE PROGRESS OF THE REACTION :
(a) Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature or by measuring total volume of mixture under constant pressure and temperature. {Formula is not applicable when n = 1, the value of n can be fractional also.}
(b) By titration method:
1. ∴ a ∝ V_{0} a - x ∝ V_{t} ⇒
2. Study of acid hydrolysis of an easter.
(c) By measuring optical roteition produced by the reaction mixture:
EFFECT OF TEMPERATURE ON RATE OF REACTION.
2 to 3 (for most of the reactions)
Arhenius theroy of reaction rate.
Arhenius equation
If k_{1} and k_{2} be the rate constant of a reaction at two different temperature T_{1} and T_{2} respectively, then we have
E_{a} ≥ 0
REVERSIBLE REACTIONS
In
⇒
(ii) REVERSIBLE 1^{st} ORDER REACATION ( both forward and backward)
(iii) SEQUENTIAL 1^{ST} ORDER REACTION
CASE-I K_{1}» K_{2 }
CASE-II K_{2} » K_{1}