Electrochemical cell potentials can be used to determine equilibrium constants that would be otherwise difficult to determine because concentrations are small. Calculate the value of K_sp for CdS from the following data. $~~~~~~~~$ E $\circ$ = -1.21 V $~~~~~~~~$ E $\circ$ = -0.40 V

Question

Quizplus · Accepted Answer

The equilibrium constant for the formation of CdS can be calculated using the Nernst equation:
KS1U1B1spS1U1B0 = exp[-(nFΔE°)/RT]
where n is the number of electrons transferred (2 for CdS), F is Faraday's constant, R is the gas constant, and T is the temperature in Kelvin. 
Substituting the given values,
KS1U1B1spS1U1B0 = exp[-(2 * 96485 * (1.21 - 0.40))/(8.314 * 298)]
KS1U1B1spS1U1B0 = 1.02 x 10^-28
To get the answer in the desired format, we can simplify the result as follows:
KS1U1B1spS1U1B0 = (4 x 10^-28)/4 = 1 x 10^-28
Multiplying both sides by 10^28 and rearranging gives:
4S1U1P114S1S1P0 = 2F1F1F1S1 x F1F1F10^10 / KS1U1B1spS1U1B0
Plugging in the values, we get:
4S1U1P114S1S1P0 = 2 x 1 x 10^10 / 1 x 10^-28
Solving for S1S1P0 gives:
S1S1P0 = 128

Electrochemical Cell Potentials Can Be Used to Determine Equilibrium Constants ~~~~~~~~

Electrochemical Cell Potentials Can Be Used to Determine Equilibrium Constants $~~~~~~~~$