Questions 32-36 refer to the following. Two half-cells are set up as follows: Half-Cell A: Strip of \(\mathrm{Cu}(s)\) in \(\mathrm{CuNO}_{3}(a q)\) Half-Cell B: Strip of \(\mathrm{Zn}(s)\) in \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\) (aq) When the cells are connected according to the diagram below, the following reaction occurs: GRAPH CAN'T COPY $$2 \mathrm{Cu}^{+}(a q)+\mathrm{Zn}(s) \rightarrow 2 \mathrm{Cu}(s)+\mathrm{Zn}^{2+}(a q) E^{\circ}=+1.28 \mathrm{V}$$ If the \(\mathrm{Cu}^{+}+e^{-} \rightarrow \mathrm{Cu}(s)\) half-reaction has a standard reduction potential of \(+0.52 \mathrm{V},\) what is the standard reduction potential for the \(\mathrm{Zn}^{2+}+2 e^{-} \rightarrow \mathrm{Zn}(s)\) half-reaction? (A) \(+0.76 \mathrm{V}\) (B) \(-0.76 \mathrm{V}\) (C) \(+0.24 \mathrm{V}\) (D) \(-0.24 \mathrm{V}\)

Step by step solution

01

Identify the half-reactions

The two half-reactions are: \(Cu^{+}+e^{-}\rightarrow Cu(s)\) and \(Zn^{2+}+2e^{-}\rightarrow Zn(s)\). In the provided overall reaction, Copper is getting reduced (gains electrons) and Zinc is getting oxidized (loses electrons). This corresponds to the half-reactions except Zinc is undergoing oxidation, not reduction. Therefore, when calculating the potential, we need to be aware of the change.

02

Write down the known reduction potentials

We know that the standard reduction potential of the \(Cu^{+}+e^{-}\rightarrow Cu(s)\) reaction is \(+0.52V\). And the overall cell potential given is \(+1.28V\).

03

Calculate the standard reduction potential for the Zn half-reaction

The standard cell potential is the sum of the standard reduction potentials of the two half-reactions when the reactions are added together. The reduction potential of the Zinc reaction is the unknown we need to find. We use the equation: \(E_{cell} = E_{red, Cu} + E_{red, Zn}\). Substituting the known values: \(1.28V = 0.52V + E_{red, Zn}\). Solving for \(E_{red, Zn}\), we find \(E_{red, Zn} = 1.28V - 0.52V = 0.76V\). However, this is the value if Zinc was being reduced. In the overall reaction, it is being oxidised. Therefore, the reduction potential of the Zinc reaction is \(-0.76V\).

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