Final answer:
To determine the pH of the electrolyte in the galvanic cell, one must use the Nernst equation along with the given cell potential of 0.312 V at 25°C. The calculation involves the hydrogen electrode half-cell reaction and simplifies the Nernst equation due to the standard reduction potential being 0 V and the pressure of H2 being 1 atm. The cell potential allows for solving the H+ concentration, which can then be used to calculate the pH.
Step-by-step explanation:
To find the pH of the electrolyte solution in the galvanic cell, we can use the Nernst equation and the provided cell potential. For the standard hydrogen electrode (SHE) at 25°C, the reaction is:
H2(g) → 2H+(aq) + 2e-
The Nernst equation for this half-cell reaction is:
E = E0 - (RT/nF)ln([H+]2/PH2)
Since the standard reduction potential (E0) for the SHE is 0.00 V, and the partial pressure of H2 is 1 atm, the above equation simplifies to:
E = - (0.0592/n)log([H+]2)
The cell potential E is given as 0.312 V. Furthermore, n is the number of moles of electrons transferred in the reaction, which is 2. Using this information:
0.312 V = - (0.0592/2)log([H+]2)
To find the concentration of H+, we solve for its concentration:
log([H+]2) = -0.312 V / (0.0592/2)
[H+] = 10-pH
pH = -log([H+])
By calculating the concentration of H+, we can find the pH of the solution and understand that the potential of a galvanic cell can be used to measure the pH of a solution.