Question

The standard oxidation potential of Ni/Ni$^{2+}$ electrode is 0.3 V. If this is combined with a hydrogen electrode in acid solution, at what pH of the solution will the measured e.m.f. be zero at 25°C? (Assume $[Ni^{2+}] = 1M$)

• A. 5.08
• B. 4
• C. 4.5
• D. 5.25

Hint:

Use the Nernst equation to calculate the pH where the e.m.f. of a galvanic cell is zero, considering the ion concentrations and standard electrode potentials.

Answer 1

The Correct Option is A

Step 1: Understanding the Nernst Equation
The Nernst equation relates the electrode potential to the concentration of the ions involved in the reaction: \[ E = E^\circ - \frac{0.0591}{n} \log \frac{[ \text{Red} ]}{[ \text{Ox} ]} \] For the hydrogen electrode (\( H_2/H^+ \)) combined with the Ni/Ni\(^{2+}\) electrode, the equation becomes: \[ E = 0.3 - \frac{0.0591}{2} \log \frac{[H^+]^2}{[Ni^{2+}]} \] Since \([Ni^{2+}] = 1M\), we simplify the equation to: \[ E = 0.3 - \frac{0.0591}{2} \log [H^+]^2 \] This becomes: \[ E = 0.3 - 0.0591 \log [H^+] \]
Step 2: Setting E to 0
At the point where the measured e.m.f.
is zero, the equation becomes: \[ 0 = 0.3 - 0.0591 \log [H^+] \] Solving for \( \log [H^+] \), we get: \[ \log [H^+] = \frac{0.3}{0.0591} \approx 5.08 \] Thus, the pH is: \[ \text{pH} = -\log [H^+] \approx 5.08 \]
Step 3: Conclusion
Thus, the pH at which the e.m.f.
will be zero is 5.08.