A voltaic cell is constructed using a Hg22+/Hg couple (E° = +0.85 V) and a Ag+/Ag couple (E° = +0.80 V) as the electrodes. Calculate [Ag+] if [Hg22+] = 0.24 M and Ecell = +0.17 V at 25 °C.

Question

BlackTom AI · Accepted Answer

We start by identifying the cell composition and the overall redox process. The two half-cells are Hg22+/Hg and Ag+/Ag. The one with the higher standard reduction potential is reduced at the cathode, so Hg22+/Hg (E° = +0.85 V) is the cathode, and Ag+/Ag (E° = +0.80 V) is the anode. Therefore, the overall reaction is: Hg2+ + 2 Ag(s) -> Hg(s) + 2 Ag+. The number of electrons transferred in this balanced equation is n = 2.

First, compute the standard cell potential: E°cell = E°cathode − E°anode = 0.85 V − 0.80 V = 0.05 V.

Next, apply the Nernst equation for 25 °C: E = E° − (0.05916/n) log Q, where Q = [Ag+]^2 / [Hg2+] since the activities of solids (Hg, Ag) are 1 and the reaction is Hg2+ + 2 Ag(s) → Hg(s) + 2 Ag+. Substituting n = 2 gives E = E° − (0.05916/2) log([Ag+]^2/[Hg2+]). With E = 0.17 V and [Hg2+] = 0.24 M, we get:

0.17 = 0.05 − 0.02958 log([Ag+]^2 / 0.24)
0.12 = −0.02958 log([Ag+]^2 / 0.24)
log([Ag+]^2 / 0.24) = −0.12 / 0.02958 ≈ −4.056

From here, [Ag+]^2 / 0.24 ≈ 10^(−4.056) ≈ 8.8×10^−5, so [Ag+]^2 ≈ 0.24 × 8.8×10^−5 ≈ 2.1×10^−5. Taking the square root gives [Ag+] ≈ √(2.1×10^−5) ≈ 4.6×10^−3 M.

Now, evaluate each answer option:
- 0.032 M: This value would require a much larger [Ag+] than computed, which would make Q far larger and E significantly different from 0.17 V; it does not satisfy the Nernst relation with the given Hg2+ concentration. Therefore, this is incorrect.
- 0.0046 M: This is numerically consistent with the result from the Nernst calculation above. It yields Q that makes E ≈ 0.17 V at 25 °C given [Hg2+] = 0.24 M, so this is correct.
- 0.00075 M: This would produce a much smaller Q, leading to a higher E (closer to E°cell) than observed; thus it does not match the given Ecell. It’s incorrect.
- 0.00021 M: Similar to the previous option, this would yield a too-small [Ag+] and an E value not equal to the given 0.17 V; hence incorrect.

In summary, applying the Nernst equation with the provided numbers leads to an ad hoc value for [Ag+] around 4.6×10^−3 M, which corresponds to the second option.

A voltaic cell is constructed using a Hg22+/Hg couple (E° = +0.85 V) and a Ag+/Ag couple (E° = +0.80 V) as the electrodes. Calculate [Ag+] if [Hg22+] = 0.24 M and Ecell = +0.17 V at 25 °C.单项选择题

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