### Electrochemistry

**Ohm's Law**

$$ v = IR $$
$$ R = \rho \frac{l}{a} $$
Where V is Potential difference, R is Resistance, I is current, ρ is specific resistance, l is lenght of conductor and a is the cross-section of conductor.

**Conductance**

$$ G = \frac{1}{R} $$
$$ \text {The specific conductance k =} \frac{1}{\rho} $$

$$ \text { Cell constant } \rho = \frac{l}{a} $$
$$ k = G. \sigma $$

**Molar conductance**

$$ \text {Molar conductance }A_{\,M} ( \Phi _{\,C}) = \frac{\text {1000 x k}}{\text{ C (or M)}} $$
where C is concentration of electrolyte in terms of molarity.

**Equivelant conductance**

$$ \text {Equivelant conductance }A_{\,M} (A _{\,C}) = \frac{\text {1000 x k}}{\text{ C (or N)}} $$
where C is concentration(normality).
A_{M} = A_{N} x (n-factor)
$$ A _{\,o} = \lim_{C \to 0} A _{\,C} $$
where A_{o} = equivalent conductance at infinite dilution.

**Faraday's first law of electrolysis**

$$ m = Zit $$
where m is mass of substance deposited, Z is electrochemical equivalent, i is current and t is time.
$$ Z = \frac {\text{Atomic mass}}{\text{n x F}} $$

**Faraday's second law of electrolysis**

$$ \frac {m _{\,1}} {m _{\,1}} = \frac {E _{\,1}} {E _{\,1}} $$
where E is equivalent weight.