Q: Consider an insulated cubic box of $$2 \times 10^4$ m^3$ filled with air composed of N_2$ and O_2$ treated as ideal gases. What is the probability (P$$_{sep}$$) of a spontaneous separation of the N_2$ and O_2$ molecules into two separate compartments of equal volume?

$$P_{sep} = \left( \frac{1}{2} \$$right)^{N_{N_2}$$} \times \left( \frac{1}{2} \$$right)^{N_{O_2}$$}$$

Question 1

A sample of 2.00 mol of CO\_2(g) is heated from 25 \degree C to 300 \degree C. Assuming CO\_2 behaves as an ideal gas with a molar heat capacity at constant volume $$C_v = 2.5 	imes R$$, what is the change in entropy $$\Delta S_{sys} if $$the process is done at constant volume?

Accepted Answer

$$\Delta S_{sys} = n C_v \ln \left( \frac{T_2$}{T_1$} \right)$$

Question 2

For the same heating of 2.00 mol CO\_2(g) from 25 \degree C to 300 \degree C, what is the change in entropy $$\Delta S_{sys} if $$the process is done at constant pressure?

Accepted Answer

$$\Delta S_{sys} = n C_p \ln \left( \frac{T_2$}{T_1$} \right)$$

Question 3

2.0 mol of an ideal gas at 10.0 atm expands isothermally ($$T$$ constant) from 1.0 L to 10.0 L in two steps: first against an external pressure of 4.0 atm, then against an external pressure of 1.0 atm. What is the total work done by the gas ($$w_{gas}$$)?

Accepted Answer

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

Question 4

During a reversible isothermal expansion of an ideal gas, which of the following correctly describes the relationship between $$q_{rev}$$ and $$w_{rev}$$?

Accepted Answer

$$q_{rev} = -w_{rev}$$

Question 5

A 2.0 mol sample of an ideal gas expands isothermally from 1.0 L to 10.0 L at 10.0 atm. What is the change in entropy of the system ($$\Delta S_{sys}$$)?

Accepted Answer

$$\Delta S_{sys} = nR \ln \left( \frac{V_2$}{V_1$} \right)$$

Question 6

Under constant pressure of 1.0 atm, 2.0 mol of methanol (l) at 25 \degree C is dropped into an intense bath at 100 \degree C. The molar heat capacities of liquid and gaseous methanol are $$C_p(l) = 81 J $$mol$$^{-1} K$^{-1}$$ and $$C_p(g) = 52.3 J $$mol$$^{-1} K$^{-1}$$, respectively. What is the correct expression for the total entropy change of the system ($$\Delta S_{sys}) $$for this process?

Accepted Answer

$$\Delta S_{sys} = \Delta S_{heating,liquid} + \Delta S_{vap} + \Delta S_{heating,gas}$$

Question 7

Consider an insulated cubic box of $$2 	imes 10^4$ m^3$ filled with air composed of N_2$ and O_2$ treated as ideal gases. What is the probability (P$$_{sep}$$) of a spontaneous separation of the N_2$ and O_2$ molecules into two separate compartments of equal volume?

Accepted Answer

$$P_{sep} = \left( \frac{1}{2} \$$right)^{N_{N_2}$$} 	imes \left( \frac{1}{2} \$$right)^{N_{O_2}$$}$$

Question 8

For the formation reaction of COCl$$_2(g) at 25$$ \degree C: $$Cl_2(g) + CO(g$$) \rightarrow $$COCl_2(g$$)$$, which equation correctly gives the standard Gibbs free energy change $$\Delta G^\circ_{rxn}$$?

Accepted Answer

$$\Delta G^\circ_{rxn} = \Delta H^\circ_{rxn} - T \Delta S^\circ_{rxn}$$

Question 9

At what temperature does the formation reaction of COCl$$_2(g) $$become non-spontaneous, given $$\Delta H^\circ_{rxn}$$ and $$\Delta S^\circ_{rxn}$$ are known?

Accepted Answer

$$T = \frac{\Delta H^\circ_{rxn}}{\Delta S^\circ_{rxn}}$$

Question 10

The molar enthalpy of vaporization of methanol ($$\Delta H_{vap}) is 35.2 kJ $$mol$$^{-1} at $$its normal boiling point of 64.6 \degree C. What is the correct equation to calculate the vapor pressure of methanol at 25 \degree C?

Accepted Answer

$$\ln \left( \frac{P_{25}}{P_{64.6}} \right) = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T_{25}} - \frac{1}{T_{64.6}} \right)$$

Question 11

Which of the following statements about entropy ($$S) is $$correct?

Accepted Answer

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

Question 12

Which equation correctly relates the change in entropy of the surroundings ($$\Delta S_{surr}) to $$the heat exchanged at constant pressure?

Accepted Answer

$$\Delta S_{surr} = -\frac{q_p}{T}$$

Question 13

For a spontaneous process at constant temperature and pressure, which of the following must be true?

Accepted Answer

$$\Delta G \u003c 0$$

Question 14

Which of the following is the correct expression for the entropy change of an ideal gas during an isothermal reversible expansion from $$V_1 to$$ $$V_2$$?

Accepted Answer

$$\Delta S = nR \ln \left( \frac{V_2$}{V_1$} \right)$$

Question 15

If the entropy change for the universe ($$\Delta S_{univ}) is $$positive, what does this indicate about the process?

Accepted Answer

The process is spontaneous.

Question 16

Which of the following correctly describes the 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 17

Which of the following is true for the vaporization of a liquid at its normal boiling point?

Accepted Answer

$$\Delta G_{vap} = 0$$

Question 18

A process occurs at constant pressure and temperature. Which of the following is the correct criterion for spontaneity?

Accepted Answer

$$\Delta G \u003c 0$$

Thermochemistry and Thermodynamics: Entropy, Free Energy, and Phase Changes

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