Question 19.5: Calculating a Standard Free-Energy Change from a Standard Ce...
Calculating a Standard Free-Energy Change from a Standard Cell Potential
The standard cell potential at 25 °C is 0.90 V for the reaction
2 Al(s) + 3 Zn^{2+}(aq) → 2 Al^{3+}(aq) + 3 Zn(s)
Calculate the standard free-energy change for this reaction at 25 °C.
STRATEGY
To calculate ∆G°, we use the equation ∆G° = -nFE°, where n can be determined from the balanced chemical equation, F is 96,500 C/mol e^{-}, and E° is given.
IDENTIFY
| Known | Unknown |
| Standard cell potential (E° = 0.90 V) | Standard free-energy change(∆G°) |
When two moles of Al are oxidized to 2 moles of Al^{3+} ions, six moles of electrons are transferred to three moles of Zn^{2+} ions, which are reduced to three moles of Zn. Therefore, n = 6 mol e^{-} for this reaction, and the standard free-energy change is
∆G° = -nFE° = -(6 mol e^{-})(\frac{96,500 C}{mol e^{-}})(0.90 V) (\frac{1 J}{1 C · V})= -5.2 × 10^{5} J = -520 kJ
CHECK
The sign of ∆G° is negative, as expected for a spontaneous reaction. F is approximately 10^{5} C/mol e^{-} and E° is approximately 1 V, so ∆G° = -nFE° is approximately -(6 mol e^{-}) (10^{5} C/mol e^{-}) (1 V) = -6 × 10^{5} J, or about -600 kJ. The estimate of -600 kJ has the same magnitude and sign as the solution, -520 kJ.