Q: Given the reaction $$N_2(g) + 3$$ $$H_2(g$$) \rightarrow 2 $$NH_3(g$$)$$ at 25°C, which expression correctly calculates the standard Gibbs free energy change ($$\Delta G^\circ$$) for the reaction?

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

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. Which equation correctly expresses the total work done by the gas during this process?

Accepted Answer

$$w = -P_{ext,1} \Delta V_1$ - P_{ext,2} \Delta V_2$

Question 2

For an isothermal compression of an ideal gas, which of the following is always true?

Accepted Answer

$$\Delta U = 0$$

Question 3

Given the reaction $$N_2(g) + 3$$ $$H_2(g$$) \rightarrow 2 $$NH_3(g$$)$$ at 25°C, which expression correctly calculates the standard Gibbs free energy change ($$\Delta G^\circ$$) for the reaction?

Accepted Answer

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

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 ($$S) of 1.0 $$mol of this solid?

Accepted Answer

$$S = R \ln 6$$

Question 5

Which of the following statements about the entropy change ($$\Delta S) $$for the melting of ice at 0°C is correct?

Accepted Answer

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

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 $$10^4$$, which equation relates the standard Gibbs free energy change to the equilibrium constant?

Accepted Answer

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

Question 7

During the spontaneous melting of 2.0 mol of superheated ice at -2°C under 1.0 atm, which of the following best describes the entropy change of the surroundings ($$\Delta S_{surr}$$)?

Accepted Answer

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

Question 8

For the formation reaction 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 9

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 10

Which of the following correctly expresses the entropy change for a reversible process?

Accepted Answer

$$dS = \frac{dq_{rev}}{T}$$

Question 11

If the entropy of fusion of ice is $$\Delta S_{fus}$$ and the enthalpy of fusion is $$\Delta H_{fus}$$, which equation gives the entropy change for melting 1 mol of ice at 0°C?

Accepted Answer

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

Question 12

Which of the following is the correct expression for the change in entropy when 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 13

For a chemical reaction at equilibrium, which of the following is true?

Accepted Answer

$$\Delta G = 0$$

Question 14

Which of the following is the correct formula for the number of microstates ($$\Omega) $$for a system of $$N$$ molecules, each with $$W$$ possible orientations?

Accepted Answer

$$\Omega = W^N$$

Question 15

Which equation correctly relates the entropy ($$S) of a $$system to the number of microstates ($$\Omega$$)?

Accepted Answer

$$S = k_B \ln \Omega$$

Question 16

A reaction has $$\Delta H^\circ = -100 kJ/$$mol and $$\Delta S^\circ = -200 J/($$mol\cdot K). At what temperature does the reaction become non-spontaneous?

Accepted Answer

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

Question 17

Which of the following is the correct expression for the entropy change of the universe ($$\Delta S_{univ}) $$for a process?

Accepted Answer

$$\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr}$$

Question 18

Which of the following is true for a spontaneous process at constant temperature and pressure?

Accepted Answer

$$\Delta G \u003c 0$$

Thermodynamics and Entropy in General Chemistry: Study Notes from CHEM1320 Midterm Exam 3

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