The cell , `Zn | Zn^(2+) (1M) || Cu^(2+) (1M) Cu (E_("cell")^@ = 1. 10 V)`,
Was allowed to be completely discharfed at `298 K `. The relative concentration of `2+` to `Cu^(2+) [(Zn^(2=))/(Cu^(2+))]` is :

Options

A. `9.65 xx 10^(4)`
B. Antilog `(24.08)`
C. `37.3`
D. `10^(37.3)`

Answer

D

Explanation

Anode
`Zn - 2e rarr Zn^(2+)`
Cathode
`Cu^(2+) +2e rarr Cu`
Net cell reaction
`Zn +Cu^(2+) rarr Zn^(2+) +Cu`
Applying Nernst equation
`E_(cell) = E_(cell)^(@) - (0.059)/(2) log.([ZN^(2+)])/([Cu^(2+)])`
When the cell is completely discharged `E_(cell) = 0`
`0 = 1.1 - (0.059)/(2) log.([ZN^(2+)])/([Cu^(2+)])`
`log.([ZN^(2+)])/([Cu^(2+)]) = (2 xx 1.1)/(0.059) = 37.3`
or `([ZN^(2+)])/([Cu^(2+)]) = 10^(37.3)`