Question

The standard cell potential (E°) of a voltaic cell constructed using the cell reaction below is 0.76 V: Zn (s) + 2H+ (aq) → Zn2+ (aq) + H2 (g) With PH2 = 1.0 atm and [Zn2+] = 1.0 M, the cell potential is 0.52 V. The concentration of H+ in the cathode compartment is ________ M.

Answer 1

`H^+ = 8.482 * 10^-5`M

Explanation:

Given

`E = 0.52\\E^o= 0.76\\`

As per the Faraday's law,

`E =  E^o - (RT)/(nF) lnQ\\`

Where E is the Cell Potential

`E^o` is the standard cell potential

n is the number of moles

F is the Faraday's constant

T is the standard temperature

Q
`= (1)/((H^+)^2)`

Substituting the given values in above equation, we get -

`0.52 = 0.76 - ((8.314*298))/((2*96485))ln(1)/((H+)^2) \\0.24 = 0.0128 ln(1)/((H^+)^2)\\ln(1)/((H^+)^2) = 18.75\\(1)/((H^+)^2) = 139002155.8\\H^+ = 8.482 * 10^-5`M