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Chapter 18: Problem 87

For the cell $$ \mathrm{Zn}\left|\mathrm{Zn}^{2+}\right| \mathrm{Cu}^{2+} \mid \mathrm{Cu} $$ \(E^{\circ}\) is \(1.10 \mathrm{~V}\). A student prepared the same cell in the lab at standard conditions. Her experimental \(E^{\circ}\) was \(1.0 \mathrm{~V}\). A possible explanation for the difference is that (a) a larger volume of \(\mathrm{Zn}^{2+}\) than \(\mathrm{Cu}^{2+}\) was used. (b) the zinc electrode had twice the mass of the copper electrode. (c) \(\left[\mathrm{Zn}^{2+}\right]\) was smaller than \(1 M\). (d) \(\left[\mathrm{Cu}^{2+}\right]\) was smaller than \(1 M\). (e) the copper electrode had twice the surface area of the zinc electrode.

Short Answer

Expert verified
a) A larger volume of \(\mathrm{Zn}^{2+}\) than \(\mathrm{Cu}^{2+}\): No b) The zinc electrode with twice the mass of the copper electrode: No c) The concentration of \(\mathrm{Zn}^{2+}\) smaller than 1 M: Yes d) The concentration of \(\mathrm{Cu}^{2+}\) smaller than 1 M: Yes e) The copper electrode had twice the surface area of the zinc electrode: No

Step by step solution

01

Evaluate option (a)

In this option, a larger volume of \(\mathrm{Zn}^{2+}\) than \(\mathrm{Cu}^{2+}\) was used. Volumes, however, do not affect the cell potential, as the potential difference depends on concentrations and not volumes. So, this option is not a possible explanation for the lower experimental \(E^{\circ}\).
02

Evaluate option (b)

In option (b), we have the zinc electrode with twice the mass of the copper electrode. The overall cell potential is not directly related to the mass of the electrodes. So, this option is also not a possible explanation for the lower experimental \(E^{\circ}\).
03

Evaluate option (c)

Option (c) suggests that the concentration of \(\mathrm{Zn}^{2+}\), \(\left[\mathrm{Zn}^{2+}\right]\), was smaller than 1 M. Since the Nernst equation states that the cell potential difference depends on the concentrations of ions involved in the reaction, a smaller concentration of \(\mathrm{Zn}^{2+}\) could cause the observed difference in \(E^{\circ}\). This option could be a possible explanation.
04

Evaluate option (d)

Option (d) says that the concentration of \(\mathrm{Cu}^{2+}\), \(\left[\mathrm{Cu}^{2+}\right]\), was smaller than 1 M. As discussed for option (c), the cell potential difference depends on the concentrations of ions involved in the reaction. Therefore, a smaller concentration of \(\mathrm{Cu}^{2+}\) could also lead to a difference in \(E^{\circ}\). This option is also a possible explanation.
05

Evaluate option (e)

In option (e), the copper electrode had twice the surface area of the zinc electrode. The surface area does not affect the overall potential difference directly, so this option is not a possible explanation for the lower experimental \(E^{\circ}\).
06

Conclusion

Options (c) and (d) are both possible explanations for the difference in the experimental \(E^{\circ}\). These options state that the concentration of \(\mathrm{Zn}^{2+}\) or \(\mathrm{Cu}^{2+}\) was smaller than 1 M, which could lead to a different cell potential difference observed in the lab experiment.

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Most popular questions from this chapter

Given the following data: $$ \begin{array}{cc} \mathrm{PtCl}_{4}{ }^{2-}(a q)+2 e^{-} \longrightarrow \mathrm{Pt}(s)+4 \mathrm{Cl}^{-}(a q) & E^{o}=+0.73 \mathrm{~V} \\ \mathrm{Pt}^{2+}(a q)+4 \mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{PtCl}_{4}^{2-}(a q) & K_{f}=1 \times 10^{16} \end{array} $$ find \(E^{\circ}\) for the half-cell $$ \mathrm{Pt}^{2+}(a q)+2 e^{-} \longrightarrow \operatorname{Pt}(s) $$

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