Final answer:
To calculate the pH of the anode compartment, the Nernst equation is applied using the cell's EMF, standard reduction potential, the given 2.303RT/F value, and the number of electrons involved in the hydrogen half-reaction. The cell potential relates to the hydrogen ion concentration, from which the pH is determined.
Step-by-step explanation:
The EMF (Electromotive Force) of the galvanic cell Pt|H₂ (1 atm)|H⁺(aq)||Hg²⁺₂ (aq. 1 N)|Hg(l) is given as 0.634 volts at 298 K. We are provided with the standard reduction potential for Hg²⁺₂|Hg, which is 0.28 volts and given the relationship 2.303RT/F = 0.059. To find the pH of the anode compartment, we use the Nernst equation for the half-reaction of hydrogen. The half-cell reaction at the anode can be represented as 2H+ (aq) + 2e- → H₂ (g).
Using the Nernst equation, E = E° - (0.059/n) * log [H+]^n, where n is the number of electrons transferred (which is 2 for the hydrogen half-reaction). The concentration of H+ ions, [H+], can be determined from the observed cell EMF. Substituting the given values, we calculate the pH of the anode compartment.
Thus, the cell potential can be calculated and used in conjunction with the Nernst equation to measure the pH of a solution. Working through the Nernst equation will give us the pH as a measure of hydrogen ion concentration at the anode.