How to caculate the concentration of H+ in the H2-H+ half-cell

Jan 2014
2
0
I have a exercise:
Consider a voltaic cell in which the reaction is
Zn(s) + 2H+(aq) -> Zn2+(aq) + H2(g)
It is found that the cell voltage is +0.460V when [Zn2+] = 1.0 M, P(H2) = 1.0 atm. What must be the concentration of H+ in the H2-H+ half-cell?

I try to solve this problem like this:

Eo cell = (0,0257/n).lnK =0,46
n=2
K=[Zn2+]/[H+]^2
so I can determine [H+]

I'm not sure if I solve this exercise correctly. If I'm wrong, please help me to fix it. Thank you very much.