The measured voltage of the cell Pt(s) | H₂ (1.0 atm) | H⁺(aq) || Ag⁺(1.0 M) | Ag(s) is 1.02 V at 25^$\circ$C. Calculate the pH of the solution.

Question

Quizplus · Accepted Answer

The cell notation can be written as: Pt(s) | H2 (1 atm) | H+ (x M) || Ag+ (1 M) | Ag(s)
Since the reaction happens in standard conditions, the Nernst equation can be simplified as:
E°cell = E°reduction of Ag+ - E°reduction of H+ = 0.80 V - 0 V = 0.80 V
At 25°C, the Nernst equation can be written as:
Ecell = E°cell - (RT/nF) * lnQ
where Q is the reaction quotient:
Q = [Ag+] / [H+] = 1 / [H+]
and n=1 since it is a one-electron transfer reaction.
Solving the expression for [H+], we get:
[H+] = 10^(- (Ecell - E°cell) / (0.0591 V)) = 10^(-1.86)
Therefore, the pH of the solution is:
pH = -log[H+] = 1.86
So, the best choice is C.

The Measured Voltage of the Cell Pt(s) | H2 (1 ∘\circ∘

The Measured Voltage of the Cell Pt(s) | H₂ (1 $\circ$