The following cell has a potential of 0.45 V at 25°C.

Pt (s) | H2 (1 atm) | H + (? M) || Cl - (1 M) | Hg2Cl2 (s) | Hg (l)

The standard half-cell potential for the half-reaction Hg2Cl2 (s) + 2 e - → 2 Hg (l) + 2 Cl - (aq) is 0.28 V. What is the pH in the anode compartment? The following cell has a potential of 0.45 V at 25°C. Pt (s) | H2 (1 atm) | H + (? M) || Cl - (1 M) | Hg2Cl2 (s) | Hg (l) The standard half-cell potential for the half-reaction Hg2Cl2 (s) + 2 e - → 2 Hg (l) + 2 Cl - (aq) is 0.28 V. What is the pH in the anode compartment?

A. 12.3

B. 4.7

C. 2.9

D. 7.6

C. 2.9

Explanation:

By the Nernst equation:

Ecell = E° - (0.0592/n) * logQ

Where E° = Ecathode - Eanode, n is the number of electrons in the redox reaction (n = 2 in this case), and Q is the reaction coefficient.

The electrode of H₂ has E = 0, an at the way the cell as shown, first we saw the anode (H₂|H⁺) and then the cathode (Cl⁻| Hg₂Cl₂), so

E° = 0.28 - 0 = 0.28 V

The global redox reaction is:

H₂ (g) + Hg₂Cl₂ (s) → 2H⁺ (aq) + 2Cl⁻ (aq) + 2Hg (s) (2 electrons are being replaced, because there'll be 2 H⁺ and 2 Cl⁻)

Q = ([H⁺]²*[Cl⁻]²) / pH₂

Q = ([H⁺]²*1/1)

Q = [H⁺]²

0.45 = 0.28 - (0.0592/2) * log[H⁺]²

0.45 - 0.28 = - 2*0.0592/2*log[H⁺] (-log[H⁺] = pH)

0.17 = 0.0592*pH

pH = 2.9