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Chapter 18: Problem 5

For the overall reaction $$ \mathrm{Cu}^{2+}\left(\mathrm{C}_{1} \mathrm{aq}\right)+\mathrm{Zn}(\mathrm{s}) \rightarrow \mathrm{Zn}^{2+}\left(C_{2} \mathrm{aq}\right)+\mathrm{Cu}(\mathrm{s}) $$ (a) \(\ln C_{1}\) (b) \(\ln \left(C_{2} / C_{1}\right)\) (c) \(\ln C_{2}\) (d) \(\ln \left(C_{1}+C_{2}\right)\) of an electrochemical cell, the change in the free energy \(\Delta G\) at a given temperature is a function of (a) \(\ln C_{1}\) (b) \(\ln \left(C_{2} / C_{1}\right)\) (c) \(\ln C_{2}\) (d) \(\ln \left(C_{1}+C_{2}\right)\)

Short Answer

Expert verified
The change in the free energy ΔG at a given temperature of an electrochemical cell is a function of ln(C2/C1)

Step by step solution

01

Identify the Reaction Quotient (Q)

Start by identifying the reaction quotient for the given reaction. The reaction quotient Q in this context is \(Q = [Zn^{2+}] / [Cu^{2+}]\), where each species inside the square brackets represents its molar concentration (C).
02

Apply the Nernst Equation

Next, apply the Nernst Equation, which relates the free energy change, ΔG, to the reaction quotient, Q. Here, ΔG = -RTln(Q). In this equation, R is the ideal gas constant, T is the absolute temperature, and ln indicates the natural logarithm.
03

Substitute the Reaction Quotient

Substitute the expression for Q into the Nernst Equation. This substitution gives ΔG = -RTln([Zn^{2+}]/[Cu^{2+}]) = -RT(ln C2 - ln C1). From this, it's clear that the change in free energy ΔG is a function of ln C1 and ln C2, which means option (b), ln(C2/C1), correctly describes this relationship.

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