Thermodynamics — Hard Practice Quiz

A Chemistry cheat sheet for Thermodynamics — every key formula with its symbols defined — plus a hard-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. Which of the following expressions correctly relates the Gibbs free energy change of a system, $\Delta G$, to the total entropy change of the universe, $\Delta S_{\text{univ}}$, for a process occurring at constant temperature $T$ and pressure $P$?

    • $\Delta G = -T\Delta S_{\text{univ}}$
    • $\Delta G = T\Delta S_{\text{univ}}$
    • $\Delta G = -\frac{\Delta S_{\text{univ}}}{T}$
    • $\Delta G = \Delta H_{\text{sys}} + T\Delta S_{\text{univ}}$

    Answer: $\Delta G = -T\Delta S_{\text{univ}}$

  2. Consider a reaction where the standard enthalpy change is $\Delta H^\circ = -150 \text{ kJ}$ and the standard entropy change is $\Delta S^\circ = -50 \text{ J/K}$. Calculate the standard Gibbs free energy change, $\Delta G^\circ$, for this reaction at $298 \text{ K}$. Is the reaction spontaneous under standard conditions at this temperature?

    • $\Delta G^\circ = -135.1 \text{ kJ}$; Spontaneous
    • $\Delta G^\circ = -164.9 \text{ kJ}$; Spontaneous
    • $\Delta G^\circ = 135.1 \text{ kJ}$; Non-spontaneous
    • $\Delta G^\circ = 164.9 \text{ kJ}$; Non-spontaneous

    Answer: $\Delta G^\circ = -135.1 \text{ kJ}$; Spontaneous

  3. For a certain reaction, the equilibrium constant $K$ is $1.0 \times 10^5$ at $298 \text{ K}$. If the standard enthalpy change for the reaction is $\Delta H^\circ = -75 \text{ kJ/mol}$, what is the approximate equilibrium constant $K'$ at $373 \text{ K}$? Assume $\Delta H^\circ$ and $\Delta S^\circ$ are constant over this temperature range. (Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $4.4 \times 10^7$
    • $2.3 \times 10^3$
    • $1.0 \times 10^5$
    • $1.8 \times 10^6$

    Answer: $4.4 \times 10^7$

  4. A $1.0 \text{ mol}$ sample of supercooled water at $-10 \text{ }^\circ\text{C}$ freezes irreversibly to ice at $-10 \text{ }^\circ\text{C}$ and $1 \text{ atm}$. Given that the enthalpy of fusion for water at $0 \text{ }^\circ\text{C}$ is $\Delta H_{\text{fus}} = 6.01 \text{ kJ/mol}$, the molar heat capacity of liquid water is $C_{p,l} = 75.3 \text{ J/(mol} \cdot \text{K)}$, and for ice is $C_{p,s} = 37.6 \text{ J/(mol} \cdot \text{K)}$. Calculate the total entropy change of the universe, $\Delta S_{\text{univ}}$, for this process. (Hint: Consider a reversible path from supercooled water to ice at $-10 \text{ }^\circ\text{C}$)

    • $0.80 \text{ J/K}$
    • $-0.80 \text{ J/K}$
    • $2.79 \text{ J/K}$
    • $-22.00 \text{ J/K}$

    Answer: $0.80 \text{ J/K}$

  5. A system undergoes a reversible isothermal process at temperature $T$, absorbing $q_{\text{rev}}$ amount of heat. If the initial number of microstates is $W_1$, what is the final number of microstates, $W_2$, in terms of $q_{\text{rev}}$, $T$, and Boltzmann's constant $k$?

    • $W_2 = W_1 e^{\frac{q_{\text{rev}}}{kT}}$
    • $W_2 = W_1 e^{\frac{kT}{q_{\text{rev}}}}$
    • $W_2 = W_1 + \frac{q_{\text{rev}}}{kT}$
    • $W_2 = \frac{q_{\text{rev}}}{kT} \ln W_1$

    Answer: $W_2 = W_1 e^{\frac{q_{\text{rev}}}{kT}}$

  6. For the reaction $2\text{NO(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$, given the standard Gibbs free energies of formation at $298 \text{ K}$: $\Delta G^\circ_f(\text{NO(g)}) = 86.55 \text{ kJ/mol}$ and $\Delta G^\circ_f(\text{NO}_2\text{(g)}) = 51.31 \text{ kJ/mol}$. Calculate the equilibrium constant $K$ for this reaction at $298 \text{ K}$. (Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $2.3 \times 10^{12}$
    • $4.4 \times 10^{-13}$
    • $1.0 \times 10^{-7}$
    • $7.0 \times 10^1$

    Answer: $2.3 \times 10^{12}$

  7. A chemical reaction has a standard enthalpy change of $\Delta H^\circ = -250 \text{ kJ}$ and a standard entropy change of $\Delta S^\circ = -100 \text{ J/K}$. What is the maximum non-PV work that can be extracted from this reaction at $350 \text{ K}$?

    • $215 \text{ kJ}$
    • $-215 \text{ kJ}$
    • $285 \text{ kJ}$
    • $-285 \text{ kJ}$

    Answer: $215 \text{ kJ}$

  8. For a reaction with a positive standard enthalpy change ($\Delta H^\circ > 0$) and a positive standard entropy change ($\Delta S^\circ > 0$), which of the following statements about its spontaneity is true?

    • The reaction is spontaneous at high temperatures.
    • The reaction is spontaneous at low temperatures.
    • The reaction is spontaneous at all temperatures.
    • The reaction is non-spontaneous at all temperatures.

    Answer: The reaction is spontaneous at high temperatures.

  9. For the reaction $2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{SO}_3\text{(g)}$, given the standard molar entropies at $298 \text{ K}$: $S^\circ(\text{SO}_2\text{(g)}) = 248.2 \text{ J/(mol} \cdot \text{K)}$, $S^\circ(\text{O}_2\text{(g)}) = 205.1 \text{ J/(mol} \cdot \text{K)}$, and $S^\circ(\text{SO}_3\text{(g)}) = 256.8 \text{ J/(mol} \cdot \text{K)}$. If the standard enthalpy change for this reaction is $\Delta H^\circ = -197.8 \text{ kJ}$, at what temperature range is this reaction spontaneous under standard conditions?

    • $T < 1053 \text{ K}$
    • $T > 1053 \text{ K}$
    • Spontaneous at all temperatures.
    • Non-spontaneous at all temperatures.

    Answer: $T < 1053 \text{ K}$

  10. A reaction has a standard Gibbs free energy change of $\Delta G^\circ = -30.0 \text{ kJ/mol}$ at $298 \text{ K}$. If the reaction quotient $Q$ is $0.01$ at this temperature, what is the maximum non-PV work that can be obtained from the reaction under these nonstandard conditions? (Use $R = 8.314 \text{ J/(mol} \cdot \text{K)}$)

    • $41.4 \text{ kJ/mol}$
    • $30.0 \text{ kJ/mol}$
    • $18.6 \text{ kJ/mol}$
    • $-41.4 \text{ kJ/mol}$

    Answer: $41.4 \text{ kJ/mol}$

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