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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