What is Nernst's equation? Write the mathematical relation.

Explanation

Nernst equation is the relationship between electrode potentials and concentration of electrolytic solution.
Consider a general reaction : `M^(n+)(aq)+n e^(-)rarrM(s)`
The Nernst.s equation can be written as ,
`E_("cell")=E_("cell")^(@)-(RT)/(nF)l n([M(s)])/([M^(n+)(aq)])...(i)`
Where, `E_("cell")` = Electrode potential under given condition
`E^(@)` = Electrode potential under standard conditions
R = Gas constant `=8.314 J K^(-1)mol^(-1)`
T = Temperature in kelvin
n = Number of electrons involved in reaction
F = Faraday.s constant
[M(s)] = Molar concentration of metal = 1
`[M^(n+)(aq)]` = Molar concentration of ions in solution
Putting the value of `R(8.314J K^(-1)mol^(-1)),F(96500 C) and T(298 K)`, converting natural logarithm to common logarithmsin equation (i), we have
`E=E_("cell")^(@)-(0.0591)/(n)log""(1)/([M^(n+)(aq)])orE_("cell")=E_("cell")^(@)+(0.591)/(n)log[M^(n+)(aq)]...(ii)`