Discussion
The value of standard half cell potential of Cu+2, Cu couple (E0Cu(+2), Cu) is 0.34 V. A wire of pure copper is immersed into a solution of copper nitrate. If the measured cell potential against standard hydrogen electrode at 298 K is 0.24 V, the molar concentration of copper nitrate is
{Assume activity of Cu+2 = [Cu+2]}.
Answer: A
The copper nitrate concentration is about \(4.1 \times 10^{-4}\) M.
For the half reaction \(\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu}\), the Nernst equation at 298 K is
\[ \begin{aligned} E &= E^{0} + \frac{0.0591}{2}\log[\text{Cu}^{2+}] \\ 0.24 &= 0.34 + 0.02955\log[\text{Cu}^{2+}] \\ \log[\text{Cu}^{2+}] &= -0.10/0.02955 = -3.38 \\ [\text{Cu}^{2+}] &= 4.1 \times 10^{-4}\ \text{M} \end{aligned} \]
The measured potential is 0.10 V below the standard value, so the concentration must be well below 1 M. Using n = 1 instead of 2 gives about \(2.0 \times 10^{-2}\) M, a common slip; the other values do not satisfy the equation.
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