Thermodynamics — Practice Quiz

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

Formulas & key concepts

Entropy Change: Relates entropy change to heat absorbed/released in a reversible process at constant T.

$$\Delta S = \frac{q_{\text{rev}}}{T}$$

Where: \(q_{\text{rev}}\) = reversible heat, \(T\) = temperature

Second Law of Thermodynamics: For irreversible process \(\Delta S_{\text{univ}} > 0\), for reversible process \(\Delta S_{\text{univ}} = 0\).

$$\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0$$

Boltzmann Entropy: Relates entropy to number of microstates.

$$S = k \ln W$$

Where: \(k\) = Boltzmann constant, \(W\) = number of microstates

Standard Entropy Change: Calculate from standard molar entropies.

$$\Delta S^\circ = \sum nS^\circ(\text{products}) - \sum mS^\circ(\text{reactants})$$

Entropy Change of Surroundings: At constant T and P.

$$\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}$$

Gibbs Free Energy: Fundamental equation at constant T.

$$\Delta G = \Delta H - T\Delta S$$

Where: \(\Delta G\) = free energy change

Standard Free Energy Change: Calculate from standard free energies of formation.

$$\Delta G^\circ = \sum n\Delta G^\circ_f(\text{products}) - \sum m\Delta G^\circ_f(\text{reactants})$$

Free Energy and Reversibility: For reversible process \(\Delta G = 0\), for irreversible process \(\Delta G < 0\).

$$\Delta G = \Delta H_{\text{sys}} - T\Delta S_{\text{sys}}$$

Free Energy and Work: Maximum work a process can perform.

$$\Delta G = -w_{\text{max}}$$

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

Free Energy Under Nonstandard Conditions: Relates \(\Delta G\) to reaction quotient.

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

Where: \(Q\) = reaction quotient

Free Energy and Equilibrium Constant: Relates standard free energy to equilibrium constant.

$$\Delta G^\circ = -RT \ln K$$

Where: \(K\) = equilibrium constant

Practice quiz

  1. A system absorbs $100 \text{ J}$ of heat reversibly at a constant temperature of $300 \text{ K}$. What is the entropy change of the system?

    • $0.333 \text{ J/K}$
    • $-0.333 \text{ J/K}$
    • $3.00 \text{ J/K}$
    • $-3.00 \text{ J/K}$

    Answer: $0.333 \text{ J/K}$

  2. For a certain process, the entropy change of the system is $50 \text{ J/K}$ and the entropy change of the surroundings is $-60 \text{ J/K}$. Which of the following statements is true regarding this process?

    • The process is spontaneous.
    • The process is non-spontaneous.
    • The process is at equilibrium.
    • The process is reversible.

    Answer: The process is non-spontaneous.

  3. If a system has $W = 1$ microstate, what is its entropy according to Boltzmann's equation?

    • $S = k$
    • $S = 0$
    • $S = \ln k$
    • $S = \text{undefined}$

    Answer: $S = 0$

  4. An exothermic reaction releases $250 \text{ kJ}$ of heat to the surroundings at a constant temperature of $298 \text{ K}$. What is the entropy change of the surroundings?

    • $839 \text{ J/K}$
    • $-839 \text{ J/K}$
    • $0.839 \text{ J/K}$
    • $-0.839 \text{ J/K}$

    Answer: $839 \text{ J/K}$

  5. Which of the following conditions guarantees a spontaneous reaction at all temperatures?

    • $\Delta H > 0$ and $\Delta S > 0$
    • $\Delta H < 0$ and $\Delta S < 0$
    • $\Delta H < 0$ and $\Delta S > 0$
    • $\Delta H > 0$ and $\Delta S < 0$

    Answer: $\Delta H < 0$ and $\Delta S > 0$

  6. A reaction has $\Delta H = -120 \text{ kJ/mol}$ and $\Delta S = -250 \text{ J/(mol} \cdot \text{K)}$. At what temperature range will this reaction be spontaneous?

    • Spontaneous at all temperatures.
    • Spontaneous at temperatures below $480 \text{ K}$.
    • Spontaneous at temperatures above $480 \text{ K}$.
    • Non-spontaneous at all temperatures.

    Answer: Spontaneous at temperatures below $480 \text{ K}$.

  7. If a chemical process has a Gibbs free energy change of $\Delta G = -50 \text{ kJ/mol}$, what is the maximum amount of non-PV work that can be extracted from this process?

    • $50 \text{ kJ/mol}$
    • $-50 \text{ kJ/mol}$
    • $0 \text{ kJ/mol}$
    • $100 \text{ kJ/mol}$

    Answer: $50 \text{ kJ/mol}$

  8. For a reaction at $298 \text{ K}$ with $\Delta G^\circ = -30 \text{ kJ/mol}$ and a reaction quotient $Q = 0.1$, what is the value of $\Delta G$? (Assume $R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • Approximately $-35.7 \text{ kJ/mol}$
    • Approximately $-24.3 \text{ kJ/mol}$
    • Approximately $-30.0 \text{ kJ/mol}$
    • Approximately $35.7 \text{ kJ/mol}$

    Answer: Approximately $-35.7 \text{ kJ/mol}$

  9. If the standard Gibbs free energy change for a reaction is $\Delta G^\circ = 0$, what can be said about its equilibrium constant $K$ at standard conditions?

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

    Answer: $K = 1$

  10. Consider the reaction $2A(g) + B(g) \rightarrow C(g)$. Given the standard molar entropies: $S^\circ(A) = 150 \text{ J/(mol} \cdot \text{K)}$, $S^\circ(B) = 200 \text{ J/(mol} \cdot \text{K)}$, $S^\circ(C) = 300 \text{ J/(mol} \cdot \text{K)}$. Calculate the standard entropy change for the reaction, $\Delta S^\circ$.

    • $-200 \text{ J/(mol} \cdot \text{K)}$
    • $200 \text{ J/(mol} \cdot \text{K)}$
    • $-50 \text{ J/(mol} \cdot \text{K)}$
    • $50 \text{ J/(mol} \cdot \text{K)}$

    Answer: $-200 \text{ J/(mol} \cdot \text{K)}$

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