# The Nernst Equation

## Key Concepts

• The Nernst Equation allows us to calculate the voltage produced by any electrochemical cell given Eo values for its electrodes and the concentrations of reactants and products.

• The general Nernst Equation: E = Eo -(RT/nF)lnQ
Eo = standard electrochemical cell potential (voltage)
R = ideal gas constant
T = temperature
n = moles of electrons
F = Faraday constant = 96,485 C mol-1
Q = mass-action expression (approximated by the equilibrium expression)

• At 25oC the Nernst Equation is simplified to: E = Eo -(0.0592/n)logQ
Eo = standard electrochemical cell potential (voltage)
n = moles of electrons
Q = mass-action expression (approximated by the equilibrium expression)

• For a system at equilibrium at 25oC, E = 0 and the Nernst Equation is simplified to:
Eo = (0.0592/n)logK
Eo = standard electrochemical cell potential (voltage)
n = moles of electrons
K = equilibrium expression

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## Example of E Calculation

Calculate the voltage produced by the cell Sn(s)|Sn2+||Ag+|Ag(s) at 25oC given:
[Sn2+] = 0.15 M
[Ag+] = 1.7 M
1. Write the Nernst Equation for 25oC:
E = Eo -0.0592/n x logQ

2. Calculate Eo for the cell:
 anode: Sn(s) → Sn2+ + 2e Eo = +0.14V cathode: 2x [e- + Ag+ → Ag(s)] Eo = +0.80V cell: Sn(s) + 2Ag+ → Sn2+ + 2Ag(s) Eo = +0.94V

3. Wite the expression for Q:
Q = [Sn2+]/[Ag+]2
(concentrations of solids = 1)

4. Write the Nernst Equation for this example:
E = Eo -0.0592/n x log([Sn2+]/[Ag+]2)

5. Substitute the values:
Eo = +0.94V
n = 2 (2 moles of electrons transferred during the redox reaction)
[Sn2+] = 0.15 M
[Ag+] = 1.7 M

E = +0.94 -0.0592/2 x log([0.15]/[1.7]2)

6. Calculate Q:
E = +0.94 -0.0592/2 x log[0.0519]

7. Calculate logQ:
E = +0.94 -0.0592/2 x -1.285

8. Calculate E:
E = +0.94 -0.0592/2 x -1.285
E = +0.98V
E > Eo, and positive, so the cell reaction has a greater tendency to take place at these concentrations.

## Example of K Calculation

Calculate the equilibrium constant, K, for the reaction Sn(s)|Sn2+||Ag+|Ag(s) at 25oC.
1. Write the Nernst Equation: E = Eo -(0.0592/n)logQ
At equilibrium Q = K and E = 0

2. Write the Nernst Equation for the equilibrium expression: Eo = (0.0592/n)logK

3. Calculate Eo for the equation (as above) = +0.94

4. Calculate n (moles of electrons transferred) =2

5. Substitute Eo and n into the equation:
+0.94 = (0.0592/2)logK

6. Calculate logK:
+0.94 = 0.0296logK
logK = 31.76

7. Calculate K:
K = 1031.76 = 5.71 x 1031

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