Nernst Equation

Introduction

The standard reduction potentials provide potentials for solutes at 1 M or 1 atm partial pressure. At other conditions the next section gives us some idea as to what we might predict for non-standard conditions.

Effect of Concentration on E

You'll see the Nernst equation:

also written as:

where RT/F at 298.15 K = (8.3145 J/mol·K)(298.15 K)/(96485.34 C/mol) = 0.02569 V and 2.303log replaces ln. (Note that J·C is equivalent to a Volt.) We can use either of these forms to:

• calculate the voltage of an electrochemical cell under any conditions
• to find the concentration of one of the components in a system

Let's consider the reaction of tin and bromine again when the tin(II) concentration is 0.050 M and the tin(IV) and bromide concentrations = 0.00010 M.

Sn²⁺_(aq) + Br_{2 (l)} Sn⁴⁺_(aq) + 2 Br^-_(aq)

Q = [Sn⁴⁺][Br^-]² / [Sn²⁺]

(b) The Nernst equation for this reaction is:

             0.0591V      [Sn4+] [Br-]2
E = 0.92 V - ------- log( ------------ )
                2            [Sn2+]

             0.0591V      (0.00010 M)(0.00010 M)2
E = 0.92 V - ------- log( ----------------------- )
                2                  0.050 M

             0.0591V
E = 0.92 V - ------- log(2.0x10-11)
                2

E = 0.92 V - (-0.316 V)

E = 1.24 V

Example of a Concentration Cell

Consider two beakers containing silver nitrate solutions of different concentrations, say 0.010 M and 0.50 M. If we connect the two beakers do we have a system at equilibrium?

No, there is a concentration gradient and there is a driving force for diffusion to attain equal concentrations in both beakers. We can set up an electrochemical cell to capture the chemical potential of this non-equilibrium system.

|         |     |         |
|---------|_____|---------|
|          _____          |
| 0.01 M  |     |  0.5 M  |
|   Ag+   |     |   Ag+   |
|_________|     |_________|

The two half-reactions are:

Ag_(s) Ag⁺_(aq) + e^-          Ag⁺_(aq) + e^- Ag_(s)

Q = [Ag⁺] / [Ag⁺]    (To determine which concentration goes where, on which side of the half-reactions are the silver ion.)

(b) The Nernst equation for this reaction is:

             0.0591V     0.010 M
E = 0.0 V - ------- log( ------- )
                1         0.50 M

E = 0.0 V - (- 0.100 V)

E = 0.10 V