Question

Calculate the standard cell potential (E∘) for the reaction X(s)+Y+(aq)→X+(aq)+Y(s) if K = 8.97×10−3. Express your answer to three significant figures and include the appropriate units. View Available Hint(s)

Answer 1

Answer: The standard cell potential (E∘) for the reaction
`X(s)+Y^+(aq)\rightarrow X^+(aq)+Y(s)` is -0.121 V

Step-by-step explanation:

The reaction is:

`X(s)+Y^+(aq)\rightarrow X^+(aq)+Y(s)`

Relation between standard Gibbs free energy and equilibrium constant follows:

`\Delta G^o=-RT\ln K`

where,

`\Delta G^o` = Standard Gibbs free energy = ?

R = Gas constant =
`8.314J/K mol`

T = temperature = 298 K

K= equilibrium constant =
`8.97* 10^(-3)`

Putting values in above equation, we get:

`\Delta G^0=-(8.314J/Kmol* 298K* \ln (8.97* 10^(-3))\\\\\Delta G^0=11678.9J/mol`

To calculate standard Gibbs free energy, we use the equation:

`\Delta G^o=-nFE^o_(cell)`

Where,

n = number of electrons transferred = 1

F = Faradays constant = 96500 C

`E^o_(cell)` = standard cell potential = ?

Putting values in above equation, we get:

`11678.9J/mol=-1* 96500* E^0_(cell)`

`(11678.9J/mol)/(-96500)=E^0_(cell)`

`-0.121V=E^0_(cell)`

Thus standard cell potential (E∘) for the reaction
`X(s)+Y^+(aq)\rightarrow X^+(aq)+Y(s)` is -0.121 V