Electrochemistry
Ohm's Law
$$ v = IR $$
$$ R = \rho \frac{l}{a} $$
$$ \text {Where V is Potential difference,} $$
$$ \text {R is Resistance,} $$
$$ \text {I is current,} $$
$$ \text {ρ is specific resistance,} $$
$$ \text {l is lenght of conductor and } $$
$$ \text {a is the cross-section of conductor.} $$
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
$$ \text {Molar conductance }A_{\,M} ( \Phi _{\,C}) = \frac{\text {1000 x k}}{\text{ C (or M)}} $$
$$ \text {where C is concentration of electrolyte in terms of molarity.} $$
Equivelant conductance
$$ \text {Equivelant conductance }A_{\,M} (A _{\,C}) = \frac{\text {1000 x k}}{\text{ C (or N)}} $$
$$ \text {where C is concentration(normality)} $$
$$ A_M = A_{N} \text { x}(n-factor) $$
$$ A _{\,o} = \lim_{C \to 0} A _{\,C} $$
$$ \text {where} A _{\,o} = \text {equivalent conductance at infinite dilution.} $$
Faraday's first law of electrolysis
$$ m = Zit $$
$$ \text {where m is mass of substance deposited, } $$
$$ \text {Z is electrochemical equivalent,} $$
$$ \text {i is current and} $$
$$ \text {t is time.} $$
$$ Z = \frac {\text{Atomic mass}}{\text{n x F}} $$
$$ \text {Faraday's second law of electrolysis} $$
$$ \frac {m _{\,1}} {m _{\,1}} = \frac {E _{\,1}} {E _{\,1}} $$
$$ \text {where E is equivalent weight.} $$
