I'm self-studying chem right now and was hoping someone could help me out with a specific electrochemistry problem:

Given a galvanic cell @ 25 Co:

Pt(s)|H2(g, 1.0 bar)|H+(pH = ?)||Cl-(aq, 1.0M)|AgCl(s)|Ag(s), E = +0.30V

I need to find the PH on the left side of the cell.

(1) find half-reactions + combined rxn

AgCl(s) + e-

Cl-(aq) + Ag(s) (Eo=+0.22V)

0.5H2(g)

H+(aq) + e- (Eo=0V)

so

AgCl(s) + 0.5H2(g)

Cl-(aq) + Ag(s) + H+(aq)

(2) Use Nernst Equation to find [H+]

ΔE = Eo - (RT/nF) * ln(Q)

(Expanding Q)

ΔE = Eo - (RT/nF) * ln([Cl-][H+] / [H2]0.5)

Knowns:

ΔE = +0.30V (given)

Eo = ER - EL = +0.22V - 0V = +0.22V

n = 1

[Cl-] = 1.0 M (given)

[H2] = 1.0 bar (given, but use P/RT = n/V to get in terms of M) = 1.0 / (0.08314 * 298.15) M

T = 298.15 K

R, F = constants

(3) Solve Nernst Equation symbolically and take -log to solve for unknown pH

-log( e((ΔE - Eo) / -(RT/F)) * ([H2]0.5 / [Cl-])) = pH

This results in a calculated pH of 2, but the solution guide I'm using tells me the pH is 1. Is my issue here a fundamental misunderstanding of how to use the Nernst equation or do you think I'm just making a simple computation mistake somewhere when I plug in the values?

Any comments much appreciated!