21. A Daniell cell initially has and (). Sufficient is added to the cathode to make the free at equi — Electrochemistry Chemistry Question
Question
21. A Daniell cell initially has $1.0 M Zn^{2+}$ and $1.0 M Cu^{2+}$ ($E^\circ = 1.10 V$). Sufficient $NH_3$ is added to the cathode to make the free $[NH_3] = 2.0 M$ at equilibrium. Given $K_f$ for $[Cu(NH_3)_4]^{2+} = 10^{12}$, what is the new operating cell potential?
Answer: B
💡 Solution & Explanation
The $Cu^{2+}$ is heavily complexed. $K_f = 10^{12} = \frac{[Cu(NH_3)_4^{2+}]}{[Cu^{2+}][NH_3]^4}$. Assume all Cu forms complex, so $[Cu(NH_3)_4^{2+}] \approx 1.0 M$. $[Cu^{2+}] = 1 / (10^{12} \times 2^4) = 6.25 \times 10^{-14} M$. $E = 1.10 - (0.0591/2)\log(1.0 / 6.25 \times 10^{-14}) = 1.10 - 0.02955 \times 13.204 \approx 0.71 V$.
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