Important Electrochemistry Formulas for JEE and NEET

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.

•  Greater the SRP value greater will be oxidising power.

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.

•  
  
  For an electrode M(s)/Mⁿ⁺.
  

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) / Zn²⁺ (c₁) || Zn²⁺(c₂) / Zn(s)

(b) Electrode Concentration Cell:
eg. Pt, H₂(P₁ atm) / H⁺ (1M) / H₂(P₂atm) / Pt

DIFFERENT TYPES OF ELECTRODES :
1. Metal-Metal ion Electrode M(s)/Mⁿ⁺. Mⁿ⁺ + ne^- →  M(s)

2. Gas-ion Electrode Pt/H₂(Patm)/H⁺(XM) as a reduction electrode
3. Oxidation-reduction Electrode Pt / Fe²⁺, Fe³⁺ as a reduction electrode Fe³⁺ + e^- → Fe²⁺ 
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

• ΔG = -n FE_cell
•  (At costant pressure).
• 
•  = Temperature cofficient of e.m.f of the cell.E = a + bT + CT² + ....
• 
• ΔCp 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 =

• CONDITION FOR SIMULTANEOUS DEPOSITION OF Cu & Fe AT CATHODE
  Condition for the simultaneous deposition of Cu & Fe on cathode.

CONDUCTANCE:

• 
• Specific conductance or conductivity :
  (Reciprocal of specific resistance) k = 1/ρ K = specific conductance
• Equivalent conductance:
   unit: -ohm^-1 cm² eq^-1
• Molar conductance:
   unit: -ohm^-1 cm² mole^-1
  specific conductance = conductance x l/a

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 λ⁰_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 cm²s^-1v^-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.
= C₁ + C₂ + C₃ + ....

Note : If V₁ mL of C₁ cone. + V₂ mL of C₂ cone, are mixed.
 ;

Type of solutions:
(a) Isotonic solution - Two solutions having same O.P.
π₁ = π₂ (at same temp.)
(b) Hyper tonic - If π₁> π₂. ⇒ 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):

• i > 1 ⇒ dissociation.
  i < 1 ⇒ association.
• 
  ∴ π = iCRT
  π = (i₁C₁ + i₂C₂ + i₃C₃.....) RT

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

• According to Raoult’s law
  (i)  where X₁ is the mole fraction o f the solvent (liquid).
  (ii) An alternate form →
• Ostwald—Walker Method : Experimental or lab determination of
  

3. ELEVATION IN BOILING POINT :
ΔT_b = i x K_bm
 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) C₂H₅Br + C₂H₅I.
Non - Ideal solutions : Which do not obey Raoult's law.

(a) Positive deviation :-

eg. H₂O + CH₃OH.
H₂O + C₂H₅OH
C₂H₆OH + hexane
C₂H₅OH + cyclohexane.
CHCI₃ + CCI₄ → dipole dipole interaction becomes weak.

(b) Negative deviation

e.g. H₂O + HCOOH
H₂O + CH₃COOH
H₂O + HNO₃
CHCl₃ + CH₃OCH₃ ⇒

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

• Classification of Crystal into Seven System
  
• ANALYSIS OF CUBICAL SYSTEM
  
• NEIGHBOUR HOOD OF A PARTICLE :
  (i) Simple Cubic (SC) Structure :
  
  (ii) Body Centered Cubic (BCC) Structure :
  
  (iii) Face Centered Cubic (FCC) Structure:
• DENSITY OF LATTICE MATTER (d) = 
  where N_A = Avogadro’s No. M = atomic mass or molecular mass.
• IONIC CRYSTALS
  
• EXAMPLES OF A IONIC CRYSTAL
  (a) Rock Salt (NaCI) Coordination number (6 : 6)
  (b) CsCI C.No. (8 : 8) Edge length of unit cell:-
  (c) Zinc Blende (ZnS) C.No. (4 : 4)
  (d) Fluorite structure (CaF₂) C.No. (8 : 4)
• Crystal Defects (Imperfections)
  
  

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 :
m₁A + m₂B → products.
R ∝ [A]^p [B]^q Where p may or may not be equal to m₁ & similarly q may or may not be equal to m₂.
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:
C₀ 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 = C₀ - kt
Unit of K = mol lit^-1 sec^-1, Time for completion = C₀/k
  ∴ t_1/2 ∝ C₀

(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 = k₀ [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 ∝ V₀ 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 k₁ and k₂ be the rate constant of a reaction at two different temperature T₁ and T₂ 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 K₁» K₂ 

CASE-II K₂ » K₁