Cadmium sulfide (CdS) is used in some semiconductor applications. It is possible to evision the dissolving of this slightly soluble substance as an oxidation-reduction reaction. Calculate the value of the solubility (Ksp) for CdS given the following standard reduction potentials.
CdS + 2e- --> Cd + S-2 E⁰ = -1.21 V
Cd+2 + 2e- --> Cd E⁰ = -0.402 V
To calculate the solubility product constant (Ksp) for CdS, we need to use the standard reduction potentials given for the two half-reactions involved in the dissolution of CdS.
The half-reactions are:
1) CdS + 2e- --> Cd + S-2 (reduction of CdS)
2) Cd+2 + 2e- --> Cd (reduction of Cd^2+ ion)
To obtain the overall reaction, we need to multiply the first half-reaction by 2 to balance the number of electrons:
2CdS + 4e- --> 2Cd + 2S-2
Now, add the two half-reactions together:
2CdS + 4Cd+2 + 4e- --> 6Cd + 2S-2
The overall equation for the dissolution of CdS is:
2CdS + 4Cd+2 --> 6Cd + 2S-2
Now, calculate the overall standard reduction potential (E⁰) for this reaction by summing the reduction potentials for each half-reaction:
E⁰ overall = (-1.21 V) + (-0.402 V)
E⁰ overall = -1.612 V
The Ksp value can be determined by using the Nernst Equation, which relates the standard reduction potential (E⁰), the concentration of the products, and the solubility product constant (Ksp):
E = E⁰ - (0.0592 V/n) * log10(Q)
Where:
E is the actual cell potential
E⁰ is the standard cell potential
n is the number of electrons transferred in the balanced equation
Q is the reaction quotient, which can be used to calculate the concentrations of the products/reactants.
Since CdS is a slightly soluble substance, we can assume that the concentration of Cd+2 and S-2 ions in the solution is equal to the solubility of CdS (s). Thus, we can write the reaction quotient (Q):
Q = [Cd+2]^4 * [S-2]^2
Since the balanced equation shows that 2 moles of CdS dissociate to give 2 moles of S-2 ions and 4 moles of Cd+2 ions, we can express the concentrations as:
[Cd+2] = 4s
[S-2] = 2s
Substituting these values in the reaction quotient:
Q = (4s)^4 * (2s)^2
Q = 16s^4 * 4s^2
Q = 64s^6
Finally, plug in the known values into the Nernst Equation:
-1.612 = -0.0592 * log10(64s^6)
Solving for s:
-1.612 = -0.0592 * 6 * log10(s)
log10(s) = -1.612 / (-0.3552)
Taking the antilog of both sides:
s = 10^(-1.612 / (-0.3552))
Calculating this value will give you the solubility (Ksp) for CdS.