Question

Calculating the thermodynamic equilibrium constant from the cell `emf`: The standard emf for the following galvanic cell is `0.46 V`
`Cu(s)|Cu^(2+)(aq.)||Ag^(+)(aq.)|Ag(s)`
Calculate the equilibrium cosntant `K_(C)` for the reaction `Cu(s)+2Ag^(+)(aq.)hArr Cu^(2+)(aq.)+2Ag(s)`
Strategy : Substitute the standard `emf` into the Equation (3.9) realting this quantity to the thermodynatmic equilibrium constant,
`K_(eq.).` Solve `K_(eq.).` Note that `K_(eq.). = K_(C^(.))`

Answer 1

The reaction corresponds to the one for the voltaic cell. Note that `n = 2`. Substituting into the equation relating `E_("cell")^(@) and K_(eq)` gives
`0.46 V = (0.0592 V)/(2) "log" K_(C)`
Solving for `"log" K_(C)` we find
`"log" K_(C) = 15.6`
Now take the antilog of both sides:
`K_(C) = "antilog" (15.6) = 4 xx 10^(15)`