Electrochemistry — Practice Quiz

A Chemistry cheat sheet for Electrochemistry — every key formula with its symbols defined — plus a medium-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. For a spontaneous electrochemical cell, what is the sign of the Gibbs free energy change, $\Delta G$, and the cell potential, $E$?

    • $\Delta G < 0$ and $E > 0$
    • $\Delta G > 0$ and $E < 0$
    • $\Delta G < 0$ and $E < 0$
    • $\Delta G > 0$ and $E > 0$

    Answer: $\Delta G < 0$ and $E > 0$

  2. Calculate the standard Gibbs free energy change, $\Delta G^\circ$, for a reaction where $n=2$ moles of electrons are transferred and the standard cell potential, $E^\circ$, is $1.10 \text{ V}$. Use $F = 96485 \text{ C/mol}$.

    • $-212.267 \text{ kJ/mol}$
    • $212.267 \text{ kJ/mol}$
    • $-106.134 \text{ kJ/mol}$
    • $106.134 \text{ kJ/mol}$

    Answer: $-212.267 \text{ kJ/mol}$

  3. If the standard cell potential, $E^\circ$, for an electrochemical reaction is positive, what can be concluded about the equilibrium constant, $K$, for the reaction at $298 \text{ K}$?

    • $K > 1$
    • $K < 1$
    • $K = 1$
    • $K = 0$

    Answer: $K > 1$

  4. A voltaic cell operates with a cell potential, $E_{\text{cell}}$, of $0.80 \text{ V}$ and transfers $3$ moles of electrons. What is the maximum electrical work, $w_{\text{max}}$, that can be obtained from this cell? Use $F = 96485 \text{ C/mol}$.

    • $-231.564 \text{ kJ}$
    • $231.564 \text{ kJ}$
    • $-77.188 \text{ kJ}$
    • $77.188 \text{ kJ}$

    Answer: $-231.564 \text{ kJ}$

  5. According to the Nernst equation, if the reaction quotient, $Q$, for a voltaic cell is increased, what happens to the cell potential, $E$?

    • $E$ increases
    • $E$ decreases
    • $E$ remains the same
    • $E$ becomes equal to $E^\circ$

    Answer: $E$ decreases

  6. A cell has a standard potential, $E^\circ$, of $0.50 \text{ V}$. If $n=2$ and the reaction quotient, $Q$, is $100$, what is the cell potential, $E$, at $298 \text{ K}$?

    • $0.4408 \text{ V}$
    • $0.5592 \text{ V}$
    • $0.50 \text{ V}$
    • $0.3816 \text{ V}$

    Answer: $0.4408 \text{ V}$

  7. At equilibrium, what is the relationship between $\Delta G$ and $\Delta G^\circ$?

    • $\Delta G = \Delta G^\circ$
    • $\Delta G = 0$, so $\Delta G^\circ = -RT \ln K$
    • $\Delta G^\circ = 0$, so $\Delta G = RT \ln Q$
    • $\Delta G = \Delta G^\circ + RT \ln K$

    Answer: $\Delta G = 0$, so $\Delta G^\circ = -RT \ln K$

  8. The simplified form of the Nernst equation, $E = E^\circ - \frac{0.0592\text{ V}}{n} \log Q$, is valid under what specific condition?

    • Only at standard pressure
    • Only at $0^\circ \text{ C}$
    • Only at $298 \text{ K}$
    • Only when $Q=1$

    Answer: Only at $298 \text{ K}$

  9. If the equilibrium constant, $K$, for a reaction is $1.0 \times 10^5$ at $298 \text{ K}$ and $n=1$, calculate $\Delta G^\circ$. Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$.

    • $-28.5 \text{ kJ/mol}$
    • $28.5 \text{ kJ/mol}$
    • $-14.2 \text{ kJ/mol}$
    • $14.2 \text{ kJ/mol}$

    Answer: $-28.5 \text{ kJ/mol}$

  10. In the Nernst equation, what does $Q$ represent?

    • The equilibrium constant
    • The standard cell potential
    • The reaction quotient
    • The Gibbs free energy

    Answer: The reaction quotient

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