Calculate the potential of hydrogen electrode in contact with a solution whose pH is 10.

Explanation

If pH of solutions is 10 then its `[H^(+)]` ion concentration will be `10^(-10)`. Let us consider a reduction half cell `H^(+)(10^(-10) M) | H_(2) (1 "atm")) | Pt`
Electrode process:
`2H^(+) (10^(-10) M ) + 2e^(-)
`Q = (PH_(2))/[H^(+)]^(2) = 1/[10^(-10)]^(2) = 10^(20)`
According to Nernst equations
`E_(H^(+)//H_(2)) = E_(H^(+)//H_(2))^(@) -(0.059)/n log Q`
`=0-(0.059)/2 log 10^(20) = -0.59 V`