[chubbymonkey1]

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!

[chenbeier]

In the Nernstequation only the redox  elements, here hydrogen and silver are involved. The chloride doesn't matter, because it will not change.

The voltage Ag => Ag⁺ + e- is 0,8 V

[mjc123]

Your error is converting the hydrogen pressure to a molar concentration. This is because the standard state of a gas is not a concentration of 1M but a pressure of 1 bar (equivalent to 0.04 M at 298K).

You should realise that in the Nernst equation (and equilibrium constant expressions generally) [X] or P_X should really be understood as [X]/[X]° or P_X/P°, where [X]° and P° are the standard concentration and pressure. You can simply use the numerical values of [X] or P_X if the standard state has a value of 1 in the same units - which it does for solution concentration in M, or gas pressure in bar, but not for gas concentration in M. This is often not explained, and it's not surprising that you haven't picked it up if you're self-studying, but it's really important to understand.

Having said that, physical logic should guide you to see that if the hydrogen is at standard pressure (1 bar), it makes no difference to the electrode potential.