SME
General Chemistry II · Problem type
Free energy and K from a cell potential
Use this for “A cell has E° = 0.462 V and moves 2 electrons. Find ΔG° and K at 25 °C.”
Diagram
E° = 0.462 V at 1 M; here Q = [Cu²⁺] ÷ [Ag⁺] = 1.
E
=
E°
−
(
RT
nF
)
ln
Q
E
=
0.462
V
−
(8.314
×
298.15
2 × 96,485
)
×
ln
1
E = 0.462 V
Dots: each beaker's ions in proportion (36 for the richer one).
This is an example. Type your own values to start a new problem.
ΔG° (kJ/mol)
=
−
n
F(
E° (V)
)
T
Temperature
example · K
ln K
Natural log of K
calculated
K
Equilibrium constant
calculated
Formulas
ΔG°
×
1,000
=
−
n
×
96,485
×
E°
−89.2 × 1,000 = −2 × 96,485 × 0.462
ln
K
=
n
×
96,485
×
E°
÷
(8.314
×
T
)
35.9656
=
2
×
96,485
×
0.462
8.314 × 298.15
K
=
e
ln
K
4.17 ×
10
15
=
e
35.9656
Assumptions
•
ΔG° = −nFE° with F = 96,485 C/mol gives ΔG° in J/mol, divided by 1000 for kJ/mol.
•
ln K = nFE° ÷ RT with R = 8.314 J/(mol·K); it comes from ΔG° = −RT ln K, so E° > 0, ΔG° < 0 and K > 1 go together.
•
n is the electrons each half-reaction moves, once the two half-reactions are balanced.
•
Temperatures are in kelvins (°C + 273.15): 25 °C is 298.15 K.
Step-by-step
WE KNOW
n = 2, E° = +0.462 V, T = 298.15 K
FIND
standard free energy change (ΔG°), natural log of K (ln K), equilibrium constant (K)
Step 1 · Find standard free energy change (ΔG°)
Use ΔG° × 1,000 = −n × 96,485 × E°
Multiply
−
n
by
F
and
E°
for
J/mol,
then
divide
by
1000
for
kJ/mol.
ΔG°
=
−
n
×
96,485
×
E°
÷
1,000
ΔG°
=
−2
×
96,485
×
0.462
1,000
ΔG°
=
−192,970
×
0.462
1,000
ΔG°
=
−
89,152.14
1,000
ΔG° = −89.2 kJ/mol
Step 2 · Find natural log of K (ln K)
Use ln K = n × 96,485 × E° ÷ (8.314 × T)
Multiply
n
by
F
and
E°,
then
divide
by
RT.
ln
K
=
2
×
96,485
×
0.462
8.314 × 298.15
ln
K
=
2
×
96,485
×
0.462
2,478.8191
ln
K
=
192,970
×
0.462
2,478.8191
ln
K
=
89,152.14
2,478.8191
ln
K
=
35.9656
Step 3 · Find equilibrium constant (K)
Use K = eˡⁿᴷ
Undo
the
natural
log:
raise
e
to
ln
K
.
K
=
e
35.9656
K
=
4.17 ×
10
15
→
K
>
1:
E°
>
0,
so
the
cell
reaction
favors
products.
Check
Put the numbers back in. Both sides should match.
−89.2 × 1,000 = −2 × 96,485 × 0.462 ✓
35.9656
=
2
×
96,485
×
0.462
8.314 × 298.15
✓
4.17 ×
10
15
=
e
35.9656
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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