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

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 = $8.97\times 10^{-3}$

Putting values in above equation, we get:

$\Delta G^0=-(8.314J/Kmol\times 298K\times \ln (8.97\times 10^{-3})\\\\\Delta G^0=11678.9J/mol$

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:

$11678.9J/mol=-1\times 96500\times E^0_{cell}$

$\frac{11678.9J/mol}{-96500}=E^0_{cell}$

$-0.121V=E^0_{cell}$

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