Electrochemistry — Hard Practice Quiz

A Chemistry cheat sheet for Electrochemistry — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Gibbs Free Energy and Cell Potential: Relates free energy change to cell potential.

$$\Delta G = -nFE$$

Where: \(n\) = moles of electrons, \(F\) = Faraday constant (96,485 C/mol), \(E\) = cell potential

Standard Free Energy and Standard Cell Potential: Relationship under standard conditions.

$$\Delta G^\circ = -nFE^\circ$$

Where: \(E^\circ\) = standard cell potential

Cell Potential and Equilibrium Constant: Relates standard cell potential to equilibrium constant.

$$E^\circ = \frac{RT}{nF} \ln K$$

Where: \(R\) = gas constant, \(T\) = temperature, \(K\) = equilibrium constant

Maximum Electrical Work: Maximum useful work obtainable from a voltaic cell.

$$w_{\text{max}} = -nFE_{\text{cell}}$$

Where: \(w_{\text{max}}\) = maximum work

Free Energy Under Nonstandard Conditions: General relationship involving reaction quotient.

$$\Delta G = \Delta G^\circ + RT \ln Q$$

Where: \(Q\) = reaction quotient

Nernst Equation: Relates cell potential to concentrations (natural log form).

$$E = E^\circ - \frac{RT}{nF} \ln Q$$

Nernst Equation (Base-10): Relates cell potential to concentrations (base-10 log form).

$$E = E^\circ - \frac{2.303RT}{nF} \log Q$$

Nernst Equation Simplified: Simplified form at 298 K for practical calculations.

$$E = E^\circ - \frac{0.0592\text{ V}}{n} \log Q$$

Where: Valid at \(T = 298\text{ K}\)

Practice quiz

  1. If an electrochemical reaction is spontaneous under standard conditions, which of the following statements is true regarding its standard cell potential ($E^\circ$) and equilibrium constant ($K$)?

    • $E^\circ > 0$ and $K > 1$
    • $E^\circ < 0$ and $K < 1$
    • $E^\circ > 0$ and $K < 1$
    • $E^\circ < 0$ and $K > 1$

    Answer: $E^\circ > 0$ and $K > 1$

  2. Which of the following expressions correctly relates the equilibrium constant ($K$) to the standard Gibbs free energy change ($\Delta G^\circ$) for an electrochemical reaction?

    • $K = e^{-\frac{\Delta G^\circ}{RT}}$
    • $K = e^{\frac{\Delta G^\circ}{RT}}$
    • $K = \ln(-\frac{\Delta G^\circ}{RT})$
    • $K = -\frac{\Delta G^\circ}{RT}$

    Answer: $K = e^{-\frac{\Delta G^\circ}{RT}}$

  3. Consider a redox reaction with a constant standard Gibbs free energy change ($\Delta G^\circ$). If the number of electrons transferred ($n$) is doubled, how would the standard cell potential ($E^\circ$) and the equilibrium constant ($K$) be affected?

    • $E^\circ$ halves, $K$ remains unchanged.
    • $E^\circ$ doubles, $K$ remains unchanged.
    • $E^\circ$ halves, $K$ is squared.
    • $E^\circ$ doubles, $K$ is squared.

    Answer: $E^\circ$ halves, $K$ remains unchanged.

  4. A voltaic cell operates at $298 \text{ K}$ with a standard cell potential $E^\circ = 1.10 \text{ V}$. If the reaction quotient $Q = 100$ and $n=2$, calculate the non-standard Gibbs free energy change ($\Delta G$) for the reaction. Use $F = 96485 \text{ C/mol}$.

    • $-200.9 \text{ kJ/mol}$
    • $-212.3 \text{ kJ/mol}$
    • $-190.5 \text{ kJ/mol}$
    • $-220.0 \text{ kJ/mol}$

    Answer: $-200.9 \text{ kJ/mol}$

  5. For an electrochemical cell, if the maximum electrical work ($w_{\text{max}}$) obtainable is negative, what does this imply about the spontaneity of the reaction and the cell potential ($E_{\text{cell}}$)?

    • The reaction is spontaneous, and $E_{\text{cell}} > 0$.
    • The reaction is non-spontaneous, and $E_{\text{cell}} < 0$.
    • The reaction is at equilibrium, and $E_{\text{cell}} = 0$.
    • The reaction is spontaneous, and $E_{\text{cell}} < 0$.

    Answer: The reaction is spontaneous, and $E_{\text{cell}} > 0$.

  6. Which of the following expressions correctly solves for the reaction quotient ($Q$) from the natural logarithm form of the Nernst equation?

    • $Q = e^{\frac{nF(E^\circ - E)}{RT}}$
    • $Q = e^{\frac{RT(E - E^\circ)}{nF}}$
    • $Q = \ln(\frac{nF(E^\circ - E)}{RT})$
    • $Q = \frac{nF(E^\circ - E)}{RT}$

    Answer: $Q = e^{\frac{nF(E^\circ - E)}{RT}}$

  7. At $298 \text{ K}$, an electrochemical reaction has a non-standard Gibbs free energy change $\Delta G = -150 \text{ kJ/mol}$ when the reaction quotient $Q = 0.1$. If $n=2$, calculate the equilibrium constant ($K$) for this reaction. Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$.

    • $2.5 \times 10^{25}$
    • $1.2 \times 10^{24}$
    • $5.8 \times 10^{23}$
    • $3.1 \times 10^{26}$

    Answer: $2.5 \times 10^{25}$

  8. For an electrochemical cell with a positive standard cell potential ($E^\circ > 0$) and a reaction quotient $Q > 1$, how does an increase in temperature ($T$) affect the non-standard cell potential ($E$)?

    • $E$ decreases.
    • $E$ increases.
    • $E$ remains unchanged.
    • $E$ first increases, then decreases.

    Answer: $E$ decreases.

  9. A reaction at $298 \text{ K}$ has an equilibrium constant $K = 1.0 \times 10^{10}$ and involves the transfer of $n=3$ electrons. Calculate the maximum electrical work ($w_{\text{max}}$) that can be obtained from this cell under standard conditions. Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$ and $F = 96485 \text{ C/mol}$.

    • $-57.0 \text{ kJ/mol}$
    • $-62.5 \text{ kJ/mol}$
    • $-48.2 \text{ kJ/mol}$
    • $-71.8 \text{ kJ/mol}$

    Answer: $-57.0 \text{ kJ/mol}$

  10. What is the relationship between the Gibbs free energy change ($\Delta G$) and the cell potential ($E$) when an electrochemical cell reaches equilibrium?

    • $\Delta G = 0$ and $E = 0$.
    • $\Delta G = \Delta G^\circ$ and $E = E^\circ$.
    • $\Delta G < 0$ and $E > 0$.
    • $\Delta G > 0$ and $E < 0$.

    Answer: $\Delta G = 0$ and $E = 0$.

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