 Nernst Equation Chemistry Tutorial

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 25°C the Nernst Equation is simplified to:

E = Eo -(0.0592/n)log10Q

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 25°C, E = 0 and the Nernst Equation is simplified to:

Eo = (0.0592/n)log10K

Eo = standard electrochemical cell potential (voltage)
n = moles of electrons
K = equilibrium expression

No ads = no money for us = no free stuff for you!

Worked Example of E Calculation

Question:

Calculate the voltage produced by the cell Sn(s)|Sn2+||Ag+|Ag(s) at 25°C given:
[Sn2+] = 0.15 mol L-1
[Ag+] = 1.7 mol L-1

Solution:

1. Write the Nernst Equation for 25°C:
E = Eo -0.0592/n × log10Q
2. Calculate Eo for the cell:
 anode: Sn(s) → Sn2+ + 2e Eo = +0.14 V cathode: 2 × [e- + Ag+ → Ag(s)] Eo = +0.80 V cell: Sn(s) + 2Ag+ → Sn2+ + 2Ag(s) Eo = +0.94 V
3. Wite the expression for Q:
Q = [Sn2+]/[Ag+]2
(concentrations of solids is constant and incorporated in the value of Q)
4. Write the Nernst Equation for this example:
E = Eo -0.0592/n × log10([Sn2+]/[Ag+]2)
5. Substitute the values:
Eo = +0.94 V
n = 2 (2 moles of electrons transferred during the redox reaction)
[Sn2+] = 0.15 mol L-1
[Ag+] = 1.7 mol L-1

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

6. Calculate Q:
E = +0.94 -0.0592/2 × log10[0.0519]
7. Calculate logQ:
E = +0.94 -0.0592/2 × -1.285
8. Calculate E:
E = +0.94 -0.0592/2 × -1.285
E = +0.98 V

Note: E > Eo, and positive, so the cell reaction has a greater tendency to take place at these concentrations.

Do you know this?

Play the game now!

Worked Example of K Calculation

Question:

Calculate the equilibrium constant, K, for the reaction Sn(s)|Sn2+||Ag+|Ag(s) at 25°C.

Solution:

1. Write the Nernst Equation:

E = Eo -(0.0592/n)log10Q

2. Write the Nernst Equation for the equilibrium expression:
At equilibrium Q = K and E = 0

Eo = (0.0592/n)log10K

3. Calculate Eo for the equation (as above) = +0.94 V
4. Calculate n (moles of electrons transferred) = 2
5. Substitute values for Eo and n into the equation:
+0.94 = (0.0592/2)log10K
6. Calculate log10K:
+0.94 = 0.0296log10K
log10K = 31.76
7. Calculate K:
K = 1031.76 = 5.71 × 1031

Note: K is very large so the forward reaction is favoured and the equilibrium position lies very far to the right.

Do you understand this?

Take the test now!