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 10.0 atm, and then against an external pressure of 25.0 atm. What is the total work done on the gas during this process?

$$W_{total} = -625 \text{ L atm}$$

Q: Given the reaction $$N_2(g) + 3$$ $$H_2(g$$) \rightarrow 2 $$NH_3(g$$)$$ at 25°C, and the following standard molar entropies: S$$^\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}$$, what is $$\Delta S^\circ$$ for the reaction?

$$\Delta S^\circ = 2 \times 192.5 - (191.6 + 3 \times 130.7) = -189.0 \text{ J K}^{-1}$$

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 10.0 atm, and then against an external pressure of 25.0 atm. What is the total work done on the gas during this process?

Accepted Answer

$$W_{total} = -625 	ext{ L atm}$$

Question 2

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

Accepted Answer

$$\Delta U = nC_v\Delta T$$

Question 3

For the isothermal compression of an ideal gas, which of the following is true about the entropy change of the system ($$\Delta S_{sys}$$)?

Accepted Answer

$$\Delta S_{sys} \u003c 0$$

Question 4

Given the reaction $$N_2(g) + 3$$ $$H_2(g$$) ightarrow 2 $$NH_3(g$$)$$ at 25°C, and the following standard molar entropies: S$$^\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}$$, what is $$\Delta S^\circ$$ for the reaction?

Accepted Answer

$$\Delta S^\circ = 2 	imes 192.5 - (191.6 + 3 	imes 130.7) = -189.0 	ext{ J K}^{-1}$$

Question 5

A pure solid at the vicinity of 0 K has completely ceased thermal motion, but the orientation of molecules remains random. If each molecule has six possible orientations of equal energy, what is the entropy per mole?

Accepted Answer

$$S = R \ln 6$$

Question 6

Consider the reaction $$COCl_2(g) + 2$$ $$H_2(g$$) ightarrow CH_2O(g) + 2 HCl(g)$$ at 25°C. If K_c = 2.26$$ 	imes $$10^4 at 25$$°C, which equation would you use to calculate $$\Delta G$$ under non-standard conditions?

Accepted Answer

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

Question 7

For the formation of water $$H_2(g$$) + \frac{1}{2} $$O_2(g$$) \rightarrow H_2O(l)$$, at what temperature does water become thermodynamically unstable versus its constituent elements?

Accepted Answer

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

Question 8

Why is the spontaneous decomposition of water into $$H_2$$ and $$O_2$$ not observed experimentally, even though it may be thermodynamically favorable at high temperatures?

Accepted Answer

Water is kinetically stable due to a high activation energy barrier.

Question 9

Which of the following correctly expresses the entropy change for the melting of ice at 0°C?

Accepted Answer

$$\Delta S = \frac{\Delta H_{fus}}{T}$$

Question 10

A process occurs at constant pressure and temperature. Which equation best describes the relationship between Gibbs free energy and spontaneity?

Accepted Answer

A process is spontaneous if $$\Delta G \u003c 0$$

Question 11

Which of the following is the correct expression for 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 12

If the number of microstates ($$\Omega) $$for a system is known, what is the entropy ($$S) of $$the system?

Accepted Answer

$$S = k_B \ln \Omega$$

Question 13

During the isothermal compression of an ideal gas, which of the following is true about the heat exchanged ($$q) $$and the work done ($$w$$)?

Accepted Answer

$$q = -w$$

Question 14

Which of the following is the correct formula for calculating the temperature of an ideal gas given pressure, volume, and number of moles?

Accepted Answer

$$T = \frac{PV}{nR}$$

Question 15

Which of the following statements about entropy is correct?

Accepted Answer

Entropy is a measure of the number of possible microstates of a system.

Question 16

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

Accepted Answer

$$\Delta G = 0$$

Question 17

Which of the following is the correct relationship between the equilibrium constant $$K$$ and the standard Gibbs free energy change $$\Delta G^\circ$$?

Accepted Answer

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

Question 18

Which of the following best describes the effect of increasing temperature on the spontaneity of a reaction with $$\Delta H \u003e 0$$ and $$\Delta S \u003e 0$$?

Accepted Answer

The reaction becomes more spontaneous as temperature increases.

Thermodynamics and Entropy in General Chemistry: Study Notes and Worked Examples

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