Question 17.3: 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 1.10 V for the reaction
Zn(s) + Cu^{2+}(aq) → Zn^{2+}(aq)+ Cu(s)
Calculate the standard free-energy change for this reaction at 25 °C.
STRATEGY
To calculate ΔG°, we use the equation ΔG° = -nFE°, where can be inferred from the balanced chemical equation, F is 96.500 C/mol e^{-}, and E° is given.
Two moles of electrons are transferred from Zn to Cu^{2+} in this reaction, so n = 2 mol e^{-} and the standard free-energy change is
ΔG° = -nFE° = -(2 mol e^{-})\left(\frac{96,500 C}{mol e^{-}}\right)(1.10 V)\left(\frac{1 J}{1 C · V}\right)
= -212,000 J = -212 kJ
BALLPARK CHECK
F is about 10^{5} C/mol e^{-} and E° is about 1 V, so ΔG° = -nFE° is approximately -(2 mol e^{-})(10^{5} C/mol e^{-})(1 V) = -2 × 10^{5} J, or -200 kJ. The ballpark check and the solution agree. Note that ΔG° is negative, as expected for a spontaneous reaction.