Q: A sample of 2.0 mol of an ideal gas at 5.0 atm is compressed isothermally (T = constant) from 5.0 L to 1.0 L in two steps: first, against an external pressure of 1.0 atm, and then against an external pressure of 25.0 atm. What is the total work done by the gas during this process?

$W_{total} = -875 \ \text{L atm}$

Q: A pure solid at 0 K has random orientations of its molecules, each with six possible orientations of equal energy. What is the entropy of 1.0 mol of this solid?

$S = 14.9 \ \text{J} \ \text{K}^{-1}$

Q: Given the reaction $N_2(g) + 3 H_2(g) \rightarrow 2 NH_3(g)$ at 25°C, and the following data: $\Delta H^\circ = -45.9 \ \text{kJ mol}^{-1}$, $S^\circ(N_2) = 191.6 \ \text{J mol}^{-1} \ \text{K}^{-1}$, $S^\circ(H_2) = 130.7 \ \text{J mol}^{-1} \ \text{K}^{-1}$, $S^\circ(NH_3) = 192.5 \ \text{J mol}^{-1} \ \text{K}^{-1}$, calculate $\Delta G^\circ$ for the reaction at 25°C.

$\Delta G^\circ = -32.7 \ \text{kJ}$

Question 1

A sample of 2.0 mol of an ideal gas at 5.0 atm is compressed isothermally (T = constant) from 5.0 L to 1.0 L in two steps: first, against an external pressure of 1.0 atm, and then against an external pressure of 25.0 atm. What is the total work done by the gas during this process?

Accepted Answer

$W_{total} = -875 \ 	ext{L atm}$

Question 2

Which equation correctly expresses the change in internal energy for an isothermal process involving an ideal gas?

Accepted Answer

$\Delta U = 0$

Question 3

For the isothermal compression of an ideal gas, which formula gives the entropy change of the system?

Accepted Answer

$\Delta S_{sys} = nR \ln \left( \frac{V_f}{V_i} \right)$

Question 4

A pure solid at 0 K has random orientations of its molecules, each with six possible orientations of equal energy. What is the entropy of 1.0 mol of this solid?

Accepted Answer

$S = 14.9 \ 	ext{J} \ 	ext{K}^{-1}$

Question 5

Given the reaction $N_2(g) + 3 H_2(g) ightarrow 2 NH_3(g)$ at 25°C, and the following data: $\Delta H^\circ = -45.9 \ 	ext{kJ mol}^{-1}$, $S^\circ(N_2) = 191.6 \ 	ext{J mol}^{-1} \ 	ext{K}^{-1}$, $S^\circ(H_2) = 130.7 \ 	ext{J mol}^{-1} \ 	ext{K}^{-1}$, $S^\circ(NH_3) = 192.5 \ 	ext{J mol}^{-1} \ 	ext{K}^{-1}$, calculate $\Delta G^\circ$ for the reaction at 25°C.

Accepted Answer

$\Delta G^\circ = -32.7 \ 	ext{kJ}$

Question 6

Which of the following correctly describes the entropy change of the surroundings ($\Delta S_{surr}$) for a process at constant pressure?

Accepted Answer

$\Delta S_{surr} = \frac{q_{p}}{T}$

Question 7

Consider the reaction $COCl_2(g) + 2 H_2(g) ightarrow CH_2O(g) + 2 HCl(g)$ with $K_c = 2.26 	imes 10^4$ at 25°C. What is the relationship between $\Delta G^\circ$ and $K_c$?

Accepted Answer

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

Question 8

At what temperature does the formation of water from $H_2(g)$ and $O_2(g)$ become thermodynamically favorable under standard conditions, given $\Delta H^\circ = -285.8 \ 	ext{kJ mol}^{-1}$ and $\Delta S^\circ = 69.9 \ 	ext{J mol}^{-1} \ 	ext{K}^{-1}$?

Accepted Answer

$T = \frac{\Delta H^\circ}{-\Delta S^\circ}$

Question 9

Why is the spontaneous formation of water from $H_2(g)$ and $O_2(g)$ not observed experimentally, even though it is thermodynamically favorable?

Accepted Answer

Because the reaction is kinetically stable due to a high activation energy barrier.

Question 10

Which equation is used to calculate the entropy change for heating a substance from $T_1$ to $T_2$ at constant pressure?

Accepted Answer

$\Delta S = C_p \ln \left( \frac{T_2}{T_1} \right)$

Question 11

During the melting of ice at 0°C, which expression gives the entropy change of the system?

Accepted Answer

$\Delta S_{sys} = \frac{q_{rev}}{T}$

Question 12

If a process is carried out reversibly, what is the relationship between the entropy change of the universe ($\Delta S_{univ}$) and the entropy change of the system ($\Delta S_{sys}$)?

Accepted Answer

$\Delta S_{univ} = 0$

Question 13

Which of the following statements about Gibbs free energy is correct?

Accepted Answer

A negative $\Delta G$ indicates a spontaneous process.

Question 14

For a chemical reaction at equilibrium, what is the value of $\Delta G$?

Accepted Answer

$\Delta G = 0$

Question 15

Which of the following is the correct expression for the entropy of a system with $W$ microstates?

Accepted Answer

$S = k_B \ln W$

Question 16

A process occurs at constant temperature and pressure. Which thermodynamic quantity determines whether the process is spontaneous?

Accepted Answer

Gibbs free energy ($\Delta G$)

Question 17

Which of the following correctly describes the standard entropy change for a reaction?

Accepted Answer

$\Delta S^\circ = \sum S^\circ_{products} - \sum S^\circ_{reactants}$

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