# Nernst equation

**Nernst equation**

Let us consider an electrochemical reaction of the following type:

aA +bB + cC + dD

Nernst equation for this can be written as follows:

In case of Daniel cell Nernst equation is as follows:

At 298 K,

At equilibrium, E_{cell} = 0 then, the equation can be rewritten as

**Equilibrium Constant from Nernst Equation**

The Nernst equation relates the standard reduction potential of an electrochemical reaction to the concentration of the reactants and products involved in the reaction. It can also be used to calculate the equilibrium constant of the reaction.

For a general reaction,

aA + bB⇌cC + dD

the Nernst equation is given by:

E = E° - (RT/nF)ln(Q)

where E is the cell potential under non-standard conditions, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the reaction, F is the Faraday constant, and Q is the reaction quotient.

For the above reaction, the reaction quotient Q is given by:

Q = [C]^{c}[D]^{d} / [A]^{a}[B]^{b}

At equilibrium, the reaction quotient Q is equal to the equilibrium constant Kc, thus:

^{c}[D]^{d} / [A]^{a}[B]^{b}

Therefore, the equilibrium constant Kc can be calculated from the Nernst equation by substituting Q with Kc:

E = E° - (RT/nF)ln(Kc)

Rearranging the equation, we get:

ln(Kc) = (nF/RT)(E° - E)

Thus, the equilibrium constant Kc can be determined by measuring the cell potential E under non-standard conditions, knowing the standard cell potential E°, and using the Nernst equation.

**Electrochemical Cell and Gibbs Energy of the Reaction**

· Let E = Emf of the cell

· *nF *= Amount of charge passed

· Δ_{r}*G *= Gibbs energy of the reaction

** Δ _{r}G = -nFE_{cell}**

** **For the reaction,

Zn(s) + Cu^{2+} (aq) --> Zn^{2+} (aq) + Cu(s)

[Δ_{r}*G = -2FE _{cell }*]