Q: A galvanic cell is constructed using the following half-reactions: $$2\ \mathrm{Cu}(s) \rightarrow 2\ \mathrm{Cu}^+(aq) + 2\ e^-$$ $$\mathrm{Cu}_2\mathrm{S}(s) + 2\ e^- \rightarrow 2\ \mathrm{Cu}(s) + \mathrm{S}^{2-}(aq)$$ The overall cell reaction is: $$\mathrm{Cu}_2\mathrm{S}(s) \rightleftharpoons 2\ \mathrm{Cu}^+(aq) + \mathrm{S}^{2-}(aq)$$ Given that the standard cell potential $$E^\circ_{cell} is$$ $$-1.41\ \mathrm{V}$$, what is the solubility product constant $$K_{sp}$$ for $$\mathrm{Cu}_2\mathrm{S} at$$ $$25^\circ\mathrm{C}$$? (Use $$n=2$$, $$F=96485\ \mathrm{C\ $$mol^{-1}$$}$$, $$R=8.314\ \mathrm{J\ $$mol^{-1}$$\ K$$^{-1}$$}$$, $$T=298\ \mathrm{K}$$) $$\Delta G^\circ = -nFE^\circ_{cell}$$ $$\Delta G^\circ = -RT \ln K_{sp}$$

$$K_{sp} = 4.3 \times 10$$^{47}$$

Question 1

A galvanic cell is constructed using the following half-reactions:

$$2\ \mathrm{Cu}(s) \rightarrow 2\ \mathrm{Cu}^+(aq) + 2\ e^-$$

$$\mathrm{Cu}_2\mathrm{S}(s) + 2\ e^- \rightarrow 2\ \mathrm{Cu}(s) + \mathrm{S}^{2-}(aq)$$

The overall cell reaction is:

$$\mathrm{Cu}_2\mathrm{S}(s) \rightleftharpoons 2\ \mathrm{Cu}^+(aq) + \mathrm{S}^{2-}(aq)$$

Given that the standard cell potential $$E^\circ_{cell} is$$ $$-1.41\ \mathrm{V}$$, what is the solubility product constant $$K_{sp}$$ for $$\mathrm{Cu}_2\mathrm{S} at$$ $$25^\circ\mathrm{C}$$? (Use $$n=2$$, $$F=96485\ \mathrm{C\ $$mol^{-1}$$}$$, $$R=8.314\ \mathrm{J\ $$mol^{-1}$$\ K$$^{-1}$$}$$, $$T=298\ \mathrm{K}$$)

$$\Delta G^\circ = -nFE^\circ_{cell}$$

$$\Delta G^\circ = -RT \ln K_{sp}$$

Accepted Answer

$$K_{sp} = 4.3 	imes 10$$^{47}$$

Question 2

Which of the following best explains why the cell potential for the dissolution of $$\mathrm{Cu}_2\mathrm{S} is $$negative under standard conditions?

Accepted Answer

The dissolution of $$\mathrm{Cu}_2\mathrm{S} is $$nonspontaneous under standard conditions.

Question 3

Given the net reaction $$\mathrm{Cu}_2\mathrm{S}(s) \rightleftharpoons 2\ \mathrm{Cu}^+(aq) + \mathrm{S}^{2-}(aq)$$, which of the following correctly expresses the solubility product $$K_{sp}$$?

Accepted Answer

$$K_{sp} = [\mathrm{Cu}^+]^2[\mathrm{S}^{2-}]$$

Question 4

If the measured $$E^\circ_{cell}$$ for the dissolution of $$\mathrm{Cu}_2\mathrm{S}$$ was $$+0.50\ \mathrm{V}$$ instead of $$-1.41\ \mathrm{V}$$, what would this indicate about the spontaneity of the dissolution reaction under standard conditions?

Accepted Answer

The dissolution would be spontaneous under standard conditions.

Question 5

A student incorrectly calculates $$K_{sp}$$ for $$\mathrm{Cu}_2\mathrm{S}$$ using $$n=1$$ instead of $$n=2 in $$the equation $$\Delta G^\circ = -nFE^\circ_{cell}. $$How will this affect the calculated value of $$K_{sp}$$?

Accepted Answer

The calculated $$K_{sp}$$ will be much smaller than the correct value.

Question 6

Which of the following is the correct relationship between the standard cell potential $$E^\circ_{cell}$$ and the equilibrium constant $$K$$ for a redox reaction at $$25^\circ\mathrm{C}$$?

Accepted Answer

$$E^\circ_{cell} = \dfrac{0.0592}{n} \log K$$

Question 7

If the concentration of $$\mathrm{Cu}^+ in $$solution is increased while $$\mathrm{S}^{2-}$$ remains constant, what will happen to the cell potential for the dissolution of $$\mathrm{Cu}_2\mathrm{S}$$?

Accepted Answer

The cell potential will decrease.

Question 8

Which of the following best describes the role of $$\mathrm{Cu}_2\mathrm{S}(s) in $$the electrochemical cell described?

Accepted Answer

$$\mathrm{Cu}_2\mathrm{S}(s)$$ acts as a source of $$\mathrm{Cu}^+$$ and $$\mathrm{S}^{2-}$$ ions.

Question 9

A chemist wants to increase the solubility of $$\mathrm{Cu}_2\mathrm{S} in $$water. Which of the following would be most effective?

Accepted Answer

Adding a strong acid to react with $$\mathrm{S}^{2-}$$ ions.

Question 10

If the temperature is increased, what is the expected effect on the value of $$K_{sp}$$ for $$\mathrm{Cu}_2\mathrm{S}$$, assuming the dissolution is endothermic?

Accepted Answer

$$K_{sp}$$ will increase.

Question 11

Which of the following statements is true regarding the relationship between $$\Delta G^\circ$$ and $$K_{sp}$$ for the dissolution of $$\mathrm{Cu}_2\mathrm{S}$$?

Accepted Answer

$$\Delta G^\circ = -RT \ln K_{sp}$$

Question 12

A laboratory error causes the measured $$E^\circ_{cell} to be $$less negative than the true value. How will this affect the calculated $$K_{sp}$$ for $$\mathrm{Cu}_2\mathrm{S}$$?

Accepted Answer

The calculated $$K_{sp}$$ will be larger than the true value.

Electrochemistry and Solubility Product (Ksp) Calculations

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