A 5.00 L sample of N₂(g) is held at a pressure of 2.00 atm and a temperature of 315 K. Assuming ideal-gas behavior, how many moles of N₂(g) are present in this sample?

	a. 2.69 mol
	b. 0.208 mol
	c. 0.387 mol
	d. 0.004 mol

.

At a temperature of 500^oC and a pressure of 699 Torr, sulfur vapor has a density of 3.71 g/dm³. What molecular formula for sulfur is compatible with this set of conditions?

	a. S2
	b. S3
	c. S8
	d. (S2)3

.

Consider a gas for which the equation of state P(V_m – b) = RT (with b = 0.04 dm³/mol) can be used to describe its P-V-T behavior. Suppose a 2-mol sample of this gas is compressed isothermally and reversibly from an initial volume of 10 dm³ to a final volume of 1 dm³. How much work (w) is done on the gas sample in this compression process, and how much is the internal energy (U) of the gas changed?

	a. w = 11.7 kJ and ∆U = 11.7 kJ
	b. w = 11.9 kJ and ∆U = 0
	c. w = 5.85 kJ and ∆U = -5.85 kJ
	d. w = 5.85 kJ and ∆U = 0

.

Consider a process in which a sample of water vapor expands reversibly and adiabatically from a state in which its pressure is 60 Torr and its volume is 0.5 dm³ to a state in which its volume is 3 dm³. If it is assumed that the water vapor behaves as an ideal gas (with respect to its P-V-T properties) and that the ratio of its C_p,m and C_v,m heat-capacity quantities is given by γ = C_p,m/C_v,m = 1.3, what will be the final pressure of the vapor sample?

	a. 5.83 bar
	b. 230 Torr
	c. 5.84 Torr
	d. There is not enough information provided to answer this question.

.

Consider a process in which exactly 107 J of heat is added to 1 mol of CH₃OH(g) under constant-volume conditions. If the initial temperature of the methanol vapor sample is 298 K, what will be the temperature of the vapor after the 107 J of heat is added? You may assume ideal-gas behavior and use a value of 43.89 J/K-mol for C_p,m (the molar heat capacity of methanol vapor under constant-pressure conditions).

	a. 301.0 K
	b. 300.4 K
	c. 295.0 K
	d. None of the above answers is correct.

.

If a person breathes at a rate of 14 respirations per minute, and each respiration involves 0.5 dm³ of air, what will be the total mass of air breathed in a day? (Take T = 300 K and P = 101.3 kPa, and assume that the air behaves as an ideal gas with a molar mass of 0.029 kg/mol).

	a. 11.9 kg
	b. 119 g
	c. 238 g
	d. 14.6 kg

.

If you have 1.55 mol of F₂(g) at 1.11 atm pressure and a temperature of 0^oC, what is the volume of this gas sample, assuming ideal-gas behavior?

	a. 31.3 L
	b. 22.4 L
	c. 3170 L
	d. 0.0821 L

.

The density of ice, H₂O(s), at 273 K, is 0.915 kg/dm³, and that of liquid water is 0.99987 kg/dm³. How much thermodynamic work must be done to melt 1 mol of ice at 1 bar pressure?

	a. 0.167 J
	b. 0.167 kJ
	c. 1.67 J
	d. 39.9 cal

.

The heat capacity of a substance can be measured under either constant-volume or constant-pressure conditions. Which of the following sets of relationships between C_v (heat capacity under constant-volume conditions) and C_p (heat capacity under constant-pressure conditions) are always true?

	a. Cp (gas) > Cv (gas); Cp (solid) ≈ Cv (solid); and Cp (gas) >> Cp (solid)
	b. Cv (gas) ≈ Cv (solid) and Cp (liquid) ≈ Cv (liquid)
	c. Cv (gas) > Cv (liquid) > Cv (solid) and Cv > Cp in all phases
	d. Cp approaches a value of 0 as the sample temperature approaches 0 K but increases without bound as the sample temperature is increased.

.

The Van der Waals equation-of-state for real gases may be written as P = RT(V_m – b)^-1 – a(V_m)^-2, where P denotes pressure, T is temperature, V_m denotes molar volume, and ‘a’ and ‘b’ are parameters (sometimes referred to as the Van der Waals coefficients) that reflect properties of the individual molecules (or atoms) in the gas. Which of the following statements regarding the ‘a’ and ‘b’ parameters is not true?

	a. The Van der Waals ‘a’ parameter reflects the existence and strength of attractive intermolecular interactions in the gas, and the value of ‘a’ is always ≥0.
	b. The van der Waals ‘b’ parameter is related to the physical sizes of the constituent molecules (or atoms) of the gas.
	c. The magnitude of the ‘a’ parameter for N2(g) is expected to be greater than that for NH3(g).
	d. The magnitude of the ‘b’ parameter for Ar(g) is larger than that for He(g).

.

Which of the following corresponds to a concise statement of the zeroth law of thermodynamics?

	a. Three solid bodies that are all in thermal equilibrium will have the same temperature.
	b. Gas molecules in motion tend to stay in motion in the absence of applied forces.
	c. Two material bodies that are separately in thermal equilibrium with a third body are in thermal equilibrium with each other.
	d. Molecules can be treated as non-interacting point-masses when contained in gaseous samples at very low pressures and number densities.

.

Which of the following statements is incorrect?

	a. The most probable value of a velocity component is equal to the most probable speed of the molecules in a dilute gas.
	b. The average kinetic energy of the molecules in a gas is independent of the molecular mass.
	c. The ratio of the most probable speed to the mean speed has the same value for all gases at all temperatures.
	d. Derivation of the ideal-gas equation-of-state from the kinetic-molecular theory of gases requires that the gas molecules be treated as non-interacting point masses.

.

Which of the following statements is incorrect?

	a. The molar heat capacities of He(g) and Ne(g) have identical values at T = 500 K.
	b. The average kinetic energy of the atoms in an He(g) sample is the same as the average kinetic energy of the atoms in an Ne(g) sample.
	c. The average speed of the atoms in an He(g) sample is the same as the average speed of the atoms in an Ne(g) sample.
	d. The average speed of the atoms in an He(g) sample is greater than the average speed of the atoms in an Ar(g) sample.

.

The first law of thermodynamics states that:

	a. The energy of a system always increases in any physical or chemical process.
	b. The energy of a system always decreases in any physical or chemical process.
	c. The entropy of a system always increases in any spontaneous process.
	d. The energy of the universe (encompassing system + surroundings) is always conserved in any physical or chemical process.

.

A 1.50-mol sample of an ideal gas at 245 K and 0.75 bar pressure is altered by some process that takes it to a state in which its temperature is increased to 295 K and its pressure is increased to 0.90 bar. What will be the enthalpy change (∆H) of the gas in this process?

	a. 1.56 kJ
	b. 1.40 kJ
	c. -1.56 kJ
	d. 0.62 kJ

.

A process in which there is no thermal energy exchanged between a system and its surroundings is called:

	a. An isothermal process
	b. An isobaric process
	c. A diathermic process
	d. An adiabatic process.

.

Consider 0.1 mol of an ideal gas contained in a cylinder of volume 2.5 dm³ at a pressure of 1 bar and a temperature of 301 K. Next, suppose you consider three different processes for changing the state of the gas sample to one in which the volume is reduced to 0.25 dm³, the pressure is increased to 10 bar, and the temperature is 301 K (the same as the temperature in the initial state). The paths of the three alternative processes are specified as follow:

Process #1 is a two-step process in which the gas sample is first heated at constant volume until the pressure reaches a value of 10 bar, and then the gas is cooled under constant pressure (10 bar) until its equilibrium volume is reduced to 0.25 dm³ and its temperature is 301 K.

Process #2 is a two-step process in which the gas sample is first cooled under constant pressure (1 bar) until its equilibrium volume is reduced to 0.25 dm³, and then the gas is heated under constant volume conditions until its pressure reaches a value of 10 bar and its temperature is 301 K.

Process #3 is a single-step process in which the gas is isothermally compressed from its initial state to its final state at a fixed temperature of 301 K.

Which of the three processes above would require the least amount of work in effecting the specified change of state, and what would be the ∆U (change in internal energy) for this process?

	a. Process #1; ∆U = 0
	b. Process #2; ∆U = 0
	c. Process #2; ∆U > 0
	d. Process #3; ∆U = 0

.

Consider a cyclic process in which a system performs a net amount of work on its surroundings (i.e., w_net < 0, corresponding to the net work done by the system). Would this process be endothermic (q_net > 0), exothermic (q_net < 0), or adiabatic (q_net = 0) with respect to the net heat (q_net) exchange between system and surroundings? And what would be the relationship between q_net and w_net?

	a. Endothermic, with |qnet | > |wnet|
	b. Exothermic, with qnet = wnet < 0
	c. Endothermic, with qnet = -wnet
	d. Adiabatic, with qnet = 0 and wnet < 0

.

Consider a process in which a gas is expanded adiabatically and reversibly under constant-pressure conditions, and the amount of work done by the gas in this process is 10 kJ. What changes in the internal energy (U) and entropy (S) of the gas will accompany this process?

	a. ∆U = -10 kJ and ∆S = 0
	b. ∆U = 10 kJ and ∆S = 0
	c. ∆U = 0 and ∆S = 10 J/K
	d. There is not enough information to determine the values of ∆U and ∆S.

.

Consider a process in which a system undergoes a change from some initial thermodynamic state (1) to some final thermodynamic state (2). Suppose that the thermodynamic variables of state are well-characterized for both the initial and final states, but the path (through the variable space) between the two states is not well-characterized. Which of the following quantities associated with the (1) → (2) change-of-state process cannot be determined without a detailed specification of path?

	a. The change in the entropy of the system (∆S)
	b. The change in the Gibbs free energy of the system (∆G)
	c. The change in the internal energy of the system (∆U)
	d. The work done and heat exchanged during the process

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Consider the reaction 2 C(s) + Cl₂(g) + 2 F₂(g) → CF₂ClCF₂Cl(g), for which the standard reaction enthalpy has a value of ∆_rH⁰ = -890.4 kJ/mol at a temperature of 298 K. What is the value of ∆_rU⁰ for this reaction at T = 298 K?

	a. 4064 kJ/mol
	b. -895.4 kJ/mol
	c. -890.4 kJ/mol
	d. -885.4 kJ/mol

.

In a free expansion (or Joule expansion) of a gas, no work is done either on or by the gas system. If the gas in such a process behaves as an ideal gas, which of the following statements is also true for the free-expansion process?

Note: In the answer options below, U denotes the internal energy of the gas, S denotes the entropy of the gas, q denotes the heat exchanged between the gas and its surroundings, V_initial denotes the initial volume of the gas (before expansion), and V_final denotes the final volume of the gas (after expansion).

	a. ∆U = 0; q > 0; and ∆S = nR ln (Vfinal/Vinitial)
	b. ∆U > 0; q > 0; and ∆S = nR ln (Vfinal/Vinitial)
	c. ∆U = 0; q = 0; and ∆S = nR ln (Vfinal/Vinitial)
	d. ∆U = 0; q = 0; and ∆S = 0

.

Suppose a 1-mol sample of an ideal gas is expanded isothermally and reversibly from a volume of 10 L to a volume of 20 L at a temperature of 298 K. How much work (w) is done in this process, and what are the changes in the internal energy (∆U) and entropy (∆S) of the gas?

	a. w = 1.717 kJ; ∆U = 0; ∆S = 5.76 J/K
	b. w = -1.717 kJ; ∆U = -1.717 kJ; ∆S = 0
	c. w = 0; ∆U = 1717 J; ∆S = 5.76 J/K
	d. w = -1717 J; ∆U = 0; ∆S = 5.76 J/K

.

Suppose you want to cool a sample of N₂(g) from 25^oC to -195^oC by a one-step process involving a Joule-Thomson expansion in which the final pressure is 1 bar. The Joule-Thomson coefficient for N₂(g) over the specified temperature range may be taken to be μ_J-T = 0.75 K/bar. Calculate the enthalpy change (∆H) associated with this cooling process and determine what the initial pressure (P_initial) of the gas must be in order to realize the desired temperature change. Which of the following equations gives correct results for P_initial and ∆H?

	a. Pinitial = 292 bar and ∆H > 0
	b. Pinitial = 292 bar and ∆H = 0
	c. Pinitial = 225 bar and ∆H = 0
	d. Pinitial = 292 bar and ∆H < 0

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The Joule-Thomson experiment involves an isenthalpic thermodynamic process, and the measurements performed in a Joule-Thomson experiment permit evaluation of the quantity μ_J-T = (∂T/∂P)_H ≈ ∆T/∆P. The observed values of μ_J-T are:

	a. < 0 for nearly all gases.
	b. > 0 for nearly all gases.
	c. > 0 only for gases that exhibit ideal-gas P-V-T behavior.
	d. independent of the initial temperature and pressure of the gas undergoing the Joule-Thomson expansion process.

.

The standard heat of combustion of solid glucose (C₆H₁₂O₆) at 298 K is ∆_cH⁰(298 K) = -2801 kJ/mol. What is the value of ∆_cU⁰(298 K) for glucose (where ∆_cU⁰ denotes the change in internal energy accompanying the combustion of glucose at 1 bar pressure)?

	a. -2801 kJ/mol
	b. 3455 kJ/mol
	c. 2801 kJ/mol
	d. 0

.

Which of the following statements is incorrect?

	a. In cyclic thermodynamic processes, it is always true that the net changes in internal energy (∆U), entropy (∆S), and enthalpy (∆H) of a system are zero (i.e., ∆Unet = ∆Snet = ∆Hnet = 0).
	b. The entropy of a system always increases with an increase in temperature under either constant-volume or constant-pressure conditions.
	c. In reversible adiabatic processes, it is always true that ∆S = 0 and ∆U = w (work).
	d. An isothermal expansion of an ideal gas always gives ∆U > 0 and ∆S = 0.

.

Consider a heat engine that operates on a Carnot cycle and uses an ideal gas as a working fluid. Suppose that the heat reservoir of the engine supplies 1 kJ of heat to the system during an isothermal expansion process at a temperature of 900 K, and the system subsequently gives up heat to heat sink during an isothermal compression process at a temperature of 300 K. What would be the maximum efficiency (η_max) achievable with this engine, and what would be the maximum net work (w_net,max) that one could derive from this engine?

	a. ηmax = 0.333; maximum net work from engine = 300 J
	b. ηmax = 0.667; maximum net work from engine = 900 J
	c. ηmax = 0.333; maximum net work from engine = 200 J
	d. ηmax = 0.667; maximum net work from engine = 600 J

.

Consider the following chemical reactions and their standard reaction enthalpies (∆_rH^o) at 298 K.

NH₃ + HCl(g) → NH₄Cl(s) ∆_rH⁰ = -176 kJ/mol
N₂(g) + 3 H₂(g) → 2 NH₃(g) ∆_rH⁰ = -92 kJ/mol
N₂(g) + 4 H₂(g) + Cl₂(g) → 2 NH₄Cl(s) ∆_rH⁰ = -629 kJ/mol

Use this thermochemical data to calculate the standard heat of reaction for the synthesis of hydrogen chloride gas from H₂(g) and Cl(g) at a temperature of 298 K. The value of ∆_rH^o (at 298 K) for the reaction H₂(g) + Cl₂(g) → 2 HCl(g) is:

	a. -242 kJ/mol
	b. -897 kJ/mol
	c. -185 kJ/mol
	d. 391 kJ/mol

.

Consider the reaction C₆H₅COOH(s) + (15/2) O₂(g) → 7 CO₂(g) + 3 H₂O(l), for which the standard reaction enthalpy is ∆_rH^o = -3228.2 kJ. Calculate the ∆_rU^o for this reaction and determine whether any thermodynamic work would be done on (w > 0) or by (w < 0) the reaction system if the reaction is carried out at a constant pressure. (Assume that the gases in this reaction exhibit ideal-gas behavior at T = 298.15 K and P = 1 bar.)

	a. ∆rUo = -3230.7 kJ and w > 0
	b. ∆rUo = -3230.7 kJ and w = 0
	c. ∆rUo = -3228.2 kJ and w = 0
	d. ∆rUo = -3227.0 kJ and w < 0

.

Consider the reaction N₂(g) + 3 H₂(g) → 2 NH₃(g), and the following thermodynamic data: standard heat of formation of NH₃(g), ∆_fH^o = -46.11 kJ/mol; standard molar entropy of N₂(g), SS_m^o = 191.61 J/K-mol; standard molar entropy of H₂(g), S_m^o = 130.684 J/K-mol; and standard molar entropy of NH₃(g), S_m^o = 192.45 J/K-mol. Calculate the ∆H, ∆S, and ∆G for this reaction carried out under standard pressure and temperature conditions. Which of the following are the correct values for ∆H, ∆S, and ∆G?

	a. ∆H = -92.22 kJ; ∆S = -198.76 J/K; ∆G = -32.99 kJ
	b. ∆H = 92.22 kJ; ∆S = 198.76 J/K; ∆G = 32.99 kJ
	c. ∆H = -46.11 kJ; ∆S = -99.38 J/K; ∆G = -16.49 kJ
	d. ∆H = -46.11 kJ; ∆S = -129.8 J/K; ∆G = -7.43 kJ

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The Carnot heat engine operates on a thermodynamic cycle comprised of the following sequence of processes:

	a. An isothermal expansion, an adiabatic expansion, an isothermal compression, and an adiabatic compression
	b. An isothermal expansion, an isochoric expansion, an isothermal compression, and an isochoric compression
	c. An isentropic expansion, an isoenthalpic expansion, an isothermal compression, and an adiabatic compression
	d. An isobaric heating, an isothermal expansion, an isobaric cooling, and an isothermal compression

.

The standard heat of reaction for the decomposition of ZnO(s) is ∆_rH^o = 348 kJ/mol. What does this information tell you about the formation of ZnO(s) under standard STP conditions?

	a. The formation of ZnO(s) is an endothermic process.
	b. The formation of ZnO(s) is an exothermic process.
	c. No thermal energy is either taken up or given off in the formation process.
	d. None of the above answers is correct.

.

Which of the following statements regarding a Carnot-cycle engine is incorrect?

	a. Increasing the temperature of the hot reservoir (i.e., the heat source) will increase the efficiency of the engine.
	b. Decreasing the temperature of the cold reservoir (i.e., the heat sink) will increase the efficiency of the engine.
	c. A Carnot cycle is by definition a reversible cycle.
	d. Since the Carnot cycle is a cyclic process, the net work done is zero.

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Consider a 2-mol sample of an ideal gas, with a molar heat capacity C_v,m = 12.5 J/K-mol, confined to a volume of 5 dm³ at a temperature of 300 K. If this gas sample is heated to 373 K and its volume is allowed to expand to 10 dm³, how much heat (q) is required to perform this process, and what is the entropy change (of the gas) that accompanies this process?

	a. ∆S = 16.97 J/K; the value of q depends on whether the process is carried out reversibly or irreversibly
	b. ∆S = 5.44 J/K; q = 1825 J
	c. ∆S = 11.53 J/K; q = 1825 J
	d. ∆S = 16.97 J/K; q = 1825 J

.

Consider a container with rigid, adiabatic walls that is fitted with a partition that separates the container into two chambers (one having twice the volume of the other). The larger chamber contains a 2-mol sample of N₂(g) at 298 K and 1 bar pressure, and the smaller chamber contains a 1-mol sample of He(g) at 298 K and 1 bar pressure. Now suppose that the partition between the chambers is removed and the N₂ and He gases are allowed to mix. This mixing process is isothermal and also adiabatic. Assuming that the gases behave ideally, what would be the ∆U (change in internal energy), ∆H (enthalpy change), and ∆S (entropy change) that accompany this mixing process?

	a. ∆U = ∆H = ∆S = 0
	b. ∆U = 0; ∆S = 15.88 J/K; and there is not enough information to determine ∆H
	c. ∆U = 0; ∆H = 0; ∆S = -15.88 J/K
	d. ∆U = 0; ∆H = 0; ∆S = 15.88 J/K

.

Consider a process in which a 2-mol sample of a certain gas is heated reversibly from 275 K to 375 K under a constant pressure of 1 bar, and the entropy change for the gas is ∆S = 13.3 J/K. What will be the value of ∆S for a process in which the same gas sample is heated irreversibly from 275 K to 375 K under a fixed pressure of 1 bar?

	a. ∆S > 13.3 J/K
	b. ∆S = 13.3 J/K
	c. ∆S < 13.3 J/K
	d. There is not enough information provided to answer this question.

.

Suppose 2 moles of water at 333 K are added to 4 moles of water at 293 K. What would be the entropy change associated with this process, assuming that there is no exchange of heat with the surroundings? (The heat capacity of water is C_p,m = 75.3 J/K-mol and may be considered to be independent of temperature.)

	a. 26 J/K
	b. 0.8 J/K
	c. -12.6 J/K
	d. -0.8 J/K

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The enthalpy of vaporization of methanol is 35.27 kJ/mol at its normal boiling point of 64.1^oC. What is the entropy of vaporization of methanol at this temperature, and what is the entropy change in the surroundings when a mole of methanol is vaporized at a temperature of 64.1^oC and a pressure of 1 bar?

	a. ∆vapS0 = 104.6 J/K-mol for methanol; ∆S(surroundings) = -104.6 J/K-mol
	b. ∆vapS0 = -104.6 J/K-mol for methanol; ∆S(surroundings) = 104.6 J/K-mol
	c. ∆vapS0 = 104.6 J/K-mol for methanol; ∆S(surroundings) = 0
	d. ∆vapS0 = 550.2 J/K-mol for methanol; ∆S(surroundings) = 0

.

The heat of fusion for H₂O at 273.15 K and 1 bar pressure is 6.008 kJ/mol; the heat of vaporization for H₂O at 373.15 K and 1 bar pressure is 40.656 kJ/mol; and the molar heat capacity (C_p,m) of liquid water between 273 K and 373 K has a nearly constant value of 75.29 J/K-mol (under a pressure of 1 bar). Given these conditions, which of the following processes will result in the largest increase in entropy of a 1-mol sample of H₂O?

	a. Vaporizing H2O(l) at 373 K and 1 bar pressure
	b. Melting H2O(s) at 273 K and 1 bar pressure
	c. Heating H2O(l) from 273 K to 373 K under a constant pressure of 1 bar
	d. Melting H2O(s) at 273.15 K and 1 bar pressure, and then heating the liquid water from 273.15 K to just short of the boiling point at 373.15 K under a constant pressure of 1 bar

.

Two 1-mol blocks of aluminum, one at 273 K and the other at 373 K, are brought into thermal contact. What will be the temperature of the two blocks when they have reached thermal equilibrium, and what will be the total entropy change (∆S_tot) that accompanies the thermal equilibration process? (Assume that the two blocks of aluminum are in a container with walls that keep them completely isolated from outside surroundings, and take the heat capacity of the aluminum blocks to be C_p,m = 24.35 J/K-mol.)

	a. Tequil = 323 K and ∆Stot = 0
	b. Tequil = 323 K and ∆Stot = 0.59 J/K
	c. Tequil = 323 K and ∆Stot = -0.59 J/K
	d. Tequil = 373 K and ∆Stot = 6.21 J/K

.

What is the change in the molar entropy of Ar(g) when it undergoes the following process: Ar(298 K, 1 bar) → Ar(100 K, 10 bar)? (You may assume that the argon behaves as an ideal gas and its heat capacity has a fixed value of C_p,m = 20.8 J/K-mol.)

	a. 41.8 J/K-mol
	b. -17.5 J/K-mol
	c. -41.8 J/K-mol
	d. 24.2 kJ/mol

.

Which of the following processes carried out on a 1-mol sample of a monatomic gas (assumed to exhibit ideal-gas P-V-T behavior) will result in the greatest increase in the entropy of the gas?

	a. Isothermal expansion from a volume of 5 L to a volume of 10 L
	b. Heating the gas from 300 K to 600 K under constant-volume conditions
	c. Isothermal expansion from a volume of 10 L to a volume of 15 L
	d. Reversible adiabatic expansion from a volume of 5 L to a volume of 10 L

.

Which of the following provides a succinct statement of the Clausius Inequality?

	a. dS ≥ dq/T for all isothermal processes carried out reversibly or irreversibly at a constant temperature T.
	b. dS ≥ dqrev/T for any reversible process carried out at a constant temperature T.
	c. dS ≥ 0 for all spontaneous processes occurring in any kind of system.
	d. dG ≤ 0 for a spontaneous process occurring in an isolated system.

.

Which of the following represents a necessary condition for a chemical reaction to proceed from reactants to products spontaneously?

	a. The reaction must be endothermic.
	b. The reaction must be exothermic.
	c. The total entropy of the reacting chemical system and its surroundings must increase.
	d. The standard entropy change, ∆rS0, for the chemical reaction must be ≥ 0.

.

Which of the following statements is correct?

	a. For a closed system, ∆S can never have a negative value.
	b. For a reversible process in a closed system, ∆S must be zero.
	c. For an adiabatic process in a closed system, ∆S cannot have a negative value.
	d. For an adiabatic process in a closed system, ∆S must be zero.

.

Identify the FALSE statement among the following choices:

	a. Calorimetry involves the measurement of heat transfer during a physical or chemical process.
	b. According to the third law of thermodynamics, the entropies of all perfectly crystalline substances must be the same at the absolute zero of temperature (i.e., at T = 0 K).
	c. For any given change of state, the work done by a system in an irreversible process is always greater than that in a reversible process.
	d. The Joule-Thompson effect relates to the temperature change occurring in a gas during an isenthalpic expansion of the gas.

.

The translational motions of the molecules in a gas contribute to the total entropy of the gas. What is the translational contribution to the total entropy of a 1-mol sample of N₂(g) at a temperature of 298 K and a pressure of 1 bar?

	a. 15.03 J/K
	b. -15.03 J/K
	c. 150.3 J/K
	d. 198.1 J/K

.

What is the standard molar entropy (S_m⁰) of oxygen atoms at 298 K (assumed to behave as an ideal gas)?

	a. 143.4 J/K-mol
	b. 1.43 J/K-mol
	c. 1550 J/K-mol
	d. -143.4 J/K-mol

.

Which of the following played a significant role in developing the concept of entropy and in formulating the second law of thermodynamics?

	a. The Nernst heat theorem
	b. The equipartition-of-energy principle
	c. The formulation and analysis of the Carnot cycle and heat engine
	d. The Heisenberg uncertainty principle

.

Which of the following statements does NOT conform to the laws of thermodynamics?

	a. The entropy of the universe always increases in a spontaneous change-of-state process.
	b. The energy of the universe always remains constant in any change-of-state process.
	c. The entropy of a system always decreases with a decrease in the temperature of the system.
	d. The entropy of any chemically pure substance approaches a value of zero as the temperature of the substance approaches a value of 0 K, and at T = 0 K, S = 0.

.

Among the following processes, which would have a ∆G_m value > 0?

	a. Solid water (ice) melts at 1 bar pressure and a temperature of 0oC.
	b. Solid water (ice) melts at 1 bar pressure and a temperature of 5oC.
	c. Liquid water is vaporized at 1 bar pressure and a temperature of 105oC.
	d. Liquid water is vaporized at 1 bar pressure and a temperature of 95oC.

.

At what pressure will (G – G⁰) be 2000 J/mol for an ideal gas at 25^oC?

	a. 2.1 kPa
	b. 21 atm
	c. 2.24 Pa
	d. 2.24 bar

.

Calcium carbonate can exist in two distinctly different crystalline forms, called calcite and aragonite. The standard Gibbs free energy of formation for calcite at 298 K is ∆_fG⁰ = -1128.79 kJ/mol, and the standard Gibbs free energy of formation for aragonite at 298 K is ∆_fG⁰ = -1127.75 kJ/mol. Which crystalline form is the more thermodynamically stable at a temperature of 298 K and a pressure of 1 bar, and what would be the value of ∆_rG⁰ for the calcite → aragonite transformation at 298 K?

	a. Calcite is more stable; ∆rG0 = -1.04 kJ/mol
	b. Aragonite is more stable; ∆rG0 = 1.04 kJ/mol
	c. Aragonite is more stable; ∆rG0 = -1.04 kJ/mol
	d. Calcite is more stable; ∆rG0 = 1.04 kJ/mol

.

Consider a chemical reaction that is exothermic. If you increase the temperature of the reaction mixture, how will this action change the equilibrium constant for the reaction?

	a. It will increase its value.
	b. It will decrease its value.
	c. It will have no effect on its value.
	d. There is not enough information provided to answer this question.

.

Consider a process in which 1 mol of an ideal gas is isothermally expanded from 0.01 m³ to 0.10 m³ at a temperature of 25^oC. What is the ∆G for this process?

	a. 5.7 kJ
	b. -479 J
	c. -5.70 kJ
	d. 479 J

.

Consider the dimerization reaction 2 NO₂(g) → N₂O₄(g). This reaction is exothermic, since the major chemical change is the formation of a new bond (the N-N bond). The value of ∆_rH⁰ for this reaction carried out at a temperature of 298 K is -57.2 kJ. The standard molar capacity of N₂O₄(g) is C_p,m = 77.28 J/K-mol, and the standard molar heat capacity of NO₂(g) is C_p,m = 37.2 J/K-mol. Given this information, what is the value of ∆_rH⁰ for the dimerization reaction carried out at a temperature of 1298 K?

	a. -54.3 kJ
	b. -60.1 kJ
	c. -43.2 kJ
	d. 12.2 kJ

.

Consider the exothermic reaction CO(g) + 2H₂(g) ↔ CH₃OH(g) at equilibrium at 500 K and 10 bar. Which of the following actions would lead to a decrease in the amount of methanol in the equilibrium reaction mixture?

	a. The temperature is raised from 500 K to 600 K.
	b. The pressure is increased from 10 bar to 12 bar.
	c. An inert (unreactive) gas is pumped into the reaction mixture under constant-volume conditions.
	d. Hydrogen (H2) gas is added to the mixture at constant pressure.

.

Consider the following reaction between glycine and nitrous acid in an aqueous solution: NH₂CH₂COOH(aq) + HNO₂(aq) ↔ HOCH₂COOH(aq) + N₂(g) + H₂O(l). What would be the difference between the ∆_rG⁰ and ∆_rA⁰ for this reaction at 298 K, assuming that the N₂(g) product can be treated as an ideal gas?

	a. 2478 J
	b. -2478 kJ
	c. 12.22 kJ
	d. There is not enough information provided to answer this question.

.

Consider the following reaction for the decomposition of sodium bicarbonate:

2 NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(l)

The ∆_rH⁰ and ∆_rS⁰ for this reaction have values of 85.2 kJ/mol and 215 J/K-mol, respectively. What is the minimum temperature required for an NaHCO₃(s) sample to spontaneously decompose into the products shown above (under 1 bar pressure conditions)?

	a. 275 K
	b. 396 K
	c. 479 K
	d. 301 K

.

Consider the following two reactions: (1) glutamate + NH₄⁺ ↔ glutamine, for which ∆_rG⁰ = 15.7 kJ/mol at 37^oC; and (2) ATP ↔ ADP + Pi, for which ∆_rG⁰ = -31.0 kJ/mol at 37^oC. (In reaction (2), ATP denotes adenosine triphosphate, ADP denotes adenosine diphosphate, and Pi represents inorganic phosphate.) These two reactions can be coupled by an enzyme catalyst (glutamine synthetase), which leads to the following reaction: (3) glutamate + NH₄⁺ + ATP ↔ glutamine + ADP + P_i. What is the equilibrium constant for reaction (3) at a temperature of 37^oC?

	a. 2.3 x 10-3
	b. 1.1
	c. 3.8 x 102
	d. There is not enough information provided to answer this question.

.

Consider the reaction Cu²⁺(aq) + 4NH₃(aq) ↔ Cu(NH₃)₄²⁺(aq), for which ∆_rG⁰ = -70.54 kJ at 298 K. Now suppose you make up a reaction mixture in which the activities (a) of the various species have the following values: a(Cu²⁺) = 0.01; a(NH₃) = 0.01; and a(of the cupric complex product) = 0.01. What will be the value of ∆_rG (at 298 K) for the reaction in the mixture you have prepared?

	a. -116 kJ
	b. -24.9 kJ
	c. 24.9 kJ
	d. There is not enough information provided to answer this question.

.

Consider the reaction glycerol(aq) + HPO₄^2-(aq) ↔ DL-glycerol-1-phosphate^2-(aq) + H₂O(l). The equilibrium constant for this reaction at 37^oC is 0.012, and the value of ∆_rG⁰ at 25^oC is 9.37 kJ. Given this information, what is the equilibrium constant (K_eq) for the reaction at 25^oC, and what is the value of ∆_rH⁰ for the reaction? (You may assume that the ∆_rH⁰ of the reaction is independent of temperature.)

	a. Keq = 0.462 at 25oC; ∆rH0 = 40.1 kJ
	b. Keq = 0.046 at 25oC; ∆rH0 = 21.2 kJ
	c. Keq = 0.003 at 25oC; ∆rH0 = -40.1 kJ
	d. Keq = 0.023 at 25oC; ∆rH0 = -40.1 kJ

.

Consider the reaction H₂(g) + I₂(g) → 2 HI(g). It is reported that an equilibrium mixture of this reaction system contains the following concentrations of the reacting species: [H₂] = 1.14 x 10^-2 M; [I₂] = 1.2 x 10^-3 M; and [HI] = 2.52 x 10^-2 M. Given this information, the equilibrium constant for this reaction may be calculated to have a value of:

	a. 1842
	b. 46.4
	c. 18.4
	d. 12.6

.

Consider the reaction N₂(g) + O₂(g) ↔ 2NO(g). The equilibrium constant for this reaction has a value of 2.5 x 10^-3 at a temperature of 2400 K. What would be the partial pressure of NO in an equilibrium mixture that is at 2400 K and contains N₂(g) at a partial pressure of 0.1 bar and O₂(g) at a partial pressure of 0.1 bar?

	a. 2.5 x 10-5 bar
	b. 5.0 x 10-3 bar
	c. 0.2 bar
	d. There is not enough information provided to answer this question.

.

For the process H₂O(l) → H₂O(s), occurring at a temperature of -10^oC, the ∆S_m has a value of -20.54 J/K-mol. Which of the following would reflect the values of ∆H_m and ∆G_m associated with the freezing of water at a temperature of -10^oC?

	a. ∆Hm < 0; ∆Gm < 0
	b. ∆Hm < 0; ∆Gm = 0
	c. ∆Hm < 0; ∆Gm > 0
	d. ∆Hm > 0; ∆Gm = 0

.

Methanol boils at a temperature of 337.2 K under standard pressure (P = 1 bar) conditions, and its standard enthalpy of vaporization is ∆_vapH⁰ = 35.27 kJ/mol. What is the standard entropy of vaporization of methanol?

	a. 104.6 kJ/K-mol
	b. 104.6 J/K-mol
	c. -104.6 J/K-mol
	d. There is not enough information provided to answer this question.

.

Suppose you wanted to shift the equilibrium position of the reaction 2 NO₂(g) → N₂O₄(g) in the direction that favors more dimer formation. Which of the following changes in reaction conditions would help achieve that goal?

	a. An increase in the total pressure of the reaction mixture, with temperature held constant
	b. An increase in the temperature of the reaction mixture, with total pressure held constant
	c. A decrease in the total pressure of the reaction mixture, with temperature held constant
	d. A simultaneous increase in temperature and increase in pressure

.

The enzyme catalase catalyzes the decomposition of hydrogen peroxide by the exothermic reaction H₂O₂(aq) → H₂O(l) + ½ O₂(g). Suppose that a small amount of solid catalase is added to a 0.1 M aqueous solution of hydrogen peroxide in a calorimeter, with the initial temperature of the solution being 25^oC. If all the heat liberated in the reaction is retained by the solution, what will be the final temperature of the solution after the reaction mixture has reached its final equilibrium state? (The relevant heats of formation for H₂O₂(aq) and H₂O(l) are: ∆_fH = -191.17 kJ/mol (for aqueous H₂O₂) and ∆_fH = -285.83 kJ/mol (for liquid H₂O). (The heat capacity of the solution may be taken as having a value of 4.18 kJ/K-L (i.e., 4.18 kJ/K per liter of solution).)

	a. 47.6oC
	b. 27.3oC
	c. 25.2oC
	d. 22.7oC

.

The equilibrium constant (K_c) for the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate is 1.67 x 10⁵ mol/dm³ at 37^oC, and the ∆_rH⁰ for this reaction has a value of -20.1 kJ/mol. Given this information, what is the value of ∆_rS⁰ for the reaction?

	a. 35.1 J/K-mol
	b. 35.1 J/mol
	c. 295 J/K-mol
	d. -35.1 J/K-mol

.

The equilibrium constant for the dimerization reaction 2 NO₂(g) → N₂O₄(g) has a value of 6.75 at a temperature of 298 K. What is the value of ∆_rG⁰ for this reaction at 298 K?

	a. 4.73 kJ
	b. 9.46 kJ
	c. -4.73 kJ
	d. -2.85 kJ

.

The equilibrium constant for the reaction H₂(g) + ½O₂(g) ↔ H₂O(l) is reported to have a value of 3.5 x 10⁴¹ at a temperature of 298 K. Given this information, what is the value of ∆_rG⁰ for this reaction at 298 K?

	a. 237 kJ
	b. -237 kJ
	c. 237 J
	d. -116 kJ

.

What is the equilibrium pressure of NH₃(g) over a sample of NH₄Cl(s) as a result of decomposition at 25h^oC, given that ∆_rG⁰ = 91.12 kJ for the reaction NH₄Cl(s) ↔ NH₃(g) + HCl(g)?

	a. 1.03 x 10-8 bar
	b. 1.06 x 10-16 bar
	c. 0.65 bar
	d. 0.81 bar

.

What is the equilibrium pressure of O₂(g) over a sample of NiO(s) at 298 K, given that ∆_rG⁰ = 211.7 kJ for the reaction NiO(s) ↔ Ni(s) + ½O₂(g)?

	a. 0.843 bar
	b. 7.78 x 10-38 bar
	c. 6.05 x 10-75 bar
	d. 8.05 x 10-5 bar

.

What is the pressure of CO₂(g) over a sample of CaCO₃(s) at a temperature of 1000 K, given that ∆_rG⁰ = 22.9 kJ for the reaction CaCO₃(s) ↔ CaO(s) + CO₂(g)?

	a. 0.99 bar
	b. 15.7 bar
	c. 6.4 x 10-4 bar
	d. 6.4 x 10-2 bar

.

Consider a process in which liquid water is vaporized under constant pressure and temperature conditions, with P = 1 atm and T = 373.15 K. Which of the following would be true for the ∆A_m and ∆G_m quantities associated with this process? (Note that A_m denotes the molar Helmholtz free-energy function and G_m denotes the molar Gibbs free-energy function.)

	a. ∆Am < 0; ∆Gm = 0
	b. ∆Am > 0; ∆Gm = 0
	c. ∆Am = 0; ∆Gm = 0
	d. ∆Am < 0; ∆Gm < 0

.

Consider the phase transformation process C(graphite) → C(diamond). The ∆G for this process at 1 bar pressure and a temperature of 298 K has a value of 2.900 kJ/mol, and the ∆S for the process under these same pressure and temperature conditions has a value of -3.36 J/K-mol. If you raised the temperature from 298 K to 1000 K, but kept the pressure constant at 1 bar, would this increase, decrease, or not change the thermodynamic stability of graphite versus diamond?

	a. Increase
	b. Decrease
	c. Not change
	d. There is not enough information provided to answer this question.

.

For H₂O(s) at 0^oC and 1 atm and H₂O(l) at 0^oC and 1 atm, which of the following quantities must be equal for the two phases?

	a. The molar entropy (Sm)
	b. The molar enthalpy (Hm)
	c. The molar Gibbs free energy (Gm)
	d. The molar volume (Vm)

.

The equilibrium vapor pressure of water at 298 K is 24 Torr. Is the chemical potential of H₂O(l) at 298 K and 20 Torr less than, equal to, or greater than the chemical potential of H₂O(g) at the same temperature and pressure?

	a. Greater than
	b. Equal to
	c. Less than
	d. There is not enough information provided to answer this question.

.

The molar enthalpy of sublimation of CO₂(s) is 25.23 kJ/mol at the standard sublimation temperature, 194.6 K. What is the molar entropy of sublimation of CO₂(s) at the standard sublimation temperature?

	a. 0.13 J/K-mol
	b. 129.7 J/K-mol
	c. -129.7 J/K-mol
	d. There is not enough information provided to answer this question.

.

The normal boiling point of Br₂ is 331.9 K, and its vapor pressure at 298 K is 0.287 bar. Within the approximations inherent to the Clausius-Clapeyron equation, what value of ∆_vapH_m (the molar enthalpy of vaporization) for Br₂ would be compatible with this data?

	a. -30.7 kJ/mol
	b. 30.7 kJ/mol
	c. 70.6 kJ/mol
	d. -12.6 kJ/mol

.

Which of the following statements is incorrect?

	a. For a one-component system, the maximum number of phases that can coexist in equilibrium is three.
	b. When three phases coexist in equilibrium in a one-component system, one of the phases must be a gas, one must be a liquid, and one must be a solid.
	c. For a one-component system, the most stable phase at a given T and P is the phase with the lowest Gm (molar Gibbs free energy).
	d. For a pure substance, the vapor pressure of the solid is equal to the vapor pressure of the liquid at the triple-point temperature.

.

Which of the following statements is incorrect?

	a. It is impossible for four phases of a single pure substance to coexist at equilibrium.
	b. The maximum number of phases that can coexist in a system composed of four components is equal to six.
	c. The Clausius-Clapeyron equation can be used in the characterization of solid-liquid phase equilibria.
	d. Two phases at equilibrium must have the same pressure.

.

Consider a 0.01 M aqueous solution of KCl. How will the vapor pressure of this solution compare with the vapor pressure of pure liquid water?

	a. It will be higher.
	b. It will be lower.
	c. It will be the same.
	d. There is not enough information provided to answer this question.

.

Consider a binary liquid solution in which the constituent species are labeled A and B. Suppose that the A-B pairwise attractive interactions are stronger than the average of the A-A and B-B pairwise attractive interactions. Which of the following statements about the properties of this solution is incorrect?

	a. The vapor pressure of the solution will exhibit negative deviations from Raoult’s law behavior.
	b. The vapor pressure of the solution will be less than ½(PA* + PB*) when species A and B are present in equimolar amounts (where PA* and PB* denote the vapor pressures of pure liquid A and pure liquid B, respectively).
	c. The vapor pressure of the solution will exhibit positive deviations from Raoult’s law behavior.
	d. If the mole-fraction of species A (XA) is much larger than the mole-fraction of species B (XB), then the vapor pressure of B will follow Henry’s law behavior.

.

Consider a dilute benzene-in-ethanol solution in which the mole-fraction of benzene is 0.013. The partial vapor pressure of the benzene component of this solution has a value of 12.8 Torr. Given this information, what would be the value of the Henry’s law constant for the benzene in this solution?

	a. 0.166 Torr
	b. 1.02 L-atm
	c. 985 Torr
	d. 985 Torr/mol

.

Consider a dilute liquid solution comprised of solvent A and solute B. For this system, which of the following statements is incorrect?

	a. The chemical potential of A in solution is always less than the chemical potential of pure liquid A (at fixed values of pressure and temperature).
	b. Additions of more solute to the solution will always lower the chemical potential of the solvent.
	c. Additions of a nonvolatile solute to the solution will always lower the vapor pressure of the solution.
	d. At any given temperature, the vapor pressure of the solution will always be less than the vapor pressure of the pure solvent.

.

Consider a process in which 0.2 mol of liquid acetone is mixed with 0.8 mol of liquid chloroform at a temperature of 35^oC and a pressure of 1 bar. Under these conditions, measurements show that the activity coefficients of the acetone and chloroform constituents of the mixture have the values 0.544 (for acetone) and 0.957 (for chloroform). Given this information, what would be the ∆G associated with the mixing process?

	a. 1683 J
	b. -1683 J
	c. -1282 J
	d. 440 J

.

Consider a real gas which, at a temperature of 298 K and some particular pressure P, has a fugacity coefficient with a value of 1.75. At the given pressure P, what is the difference between the chemical potential of the real gas versus that of an ideal gas? That is, what is the value of μ(real gas) – μ(ideal gas)?

	a. -1.39 kJ/mol
	b. 0
	c. 1.39 kJ/mol
	d. There is not enough information provided to answer this question.

.

Consider a solution made by dissolving 342 g of sucrose in 127 ml of water at 45^oC. The vapor pressure of water at 45^oC is 0.095 atm and the density of water at 45^oC is 0.992 g/ml. What is the vapor pressure of the sucrose/water solution? (Note: The molar mass of sucrose is 180.2 g/mol.)

	a. 0.075 atm
	b. 0.115 atm
	c. 0.224 atm
	d. 0.008 atm

.

Consider a toluene-benzene solution in which the mole-fraction of toluene is 0.33. At a temperature of 300 K, the total vapor pressure of this solution is 7.89 kPa, and the partial pressures of the toluene and benzene constituents of the vapor are P_toluene = 1.214 kPa and P_benzene = 6.677 kPa, respectively. At 300 K, the vapor pressure of pure liquid toluene is P* = 3.572 kPa and the vapor pressure of pure liquid benzene is P* = 9.657 kPa. What are the activities (a) and activity coefficients (γ) of the toluene and benzene constituents of the solution?

	a. a(toluene) = 0.3399; a(benzene) = 0.6914; γ(toluene) = 1.03; γ(benzene) = 1.03
	b. a(toluene) = 0.77; a(benzene) = 0.23; γ(toluene) = 1.11; γ(benzene) = 0.89
	c. a(toluene) = 0.46; a(benzene) = 0.54; γ(toluene) = 0.79; γ(benzene) = 0.93
	d. There is not enough information provided to answer this question.

.

If 5.0 g of glucose, C₆H₁₂O₆, is dissolved in 1.0 L of water at 300 K, what osmotic pressure will the solution exhibit?

	a. 0.69 bar
	b. 0.012 atm
	c. 6.9 atm
	d. 69 Pa

.

If a 1-molal solution of NaCl in water shows a freezing-point depression of 3.7^oC, what is the freezing-point depression observed for a 1-molal solution of CaCl₂ in water? (Recall that both NaCl and CaCl₂ are completely dissociated in aqueous solution.)

	a. 5.55oC
	b. 11.1oC
	c. 2.47oC
	d. There is not enough information provided to answer this question.

.

The solubility of argon in water is 5.15 x 10^-3 g of Ar per 100 g of H₂O at 25^oC and an argon pressure of 1 atm. Given this information, what is the value of the Henry’s law constant for an argon-water mixture at 25^oC?

	a. 4.31 atm
	b. 4.31 x 105 Pa
	c. 12.4 bar/mol
	d. 4.31 x 104 atm

.

The vapor pressure of pure liquid toluene at 300 K is P* = 3.572 kPa, and the vapor pressure of pure liquid benzene at 300 K is P* = 9.657 kPa. Assuming that mixtures of toluene and benzene behave as ideal solutions, what will be the total vapor pressure (P_T) of a toluene-benzene mixture containing 0.60 mole-fraction of toluene at a temperature of 300 K, and what will be the mole-fraction of toluene (X_toluene) in the vapor over this mixture?

	a. PT = 7.219 kPa; Xtoluene = 0.643 (in vapor)
	b. PT = 6.006 kPa; Xtoluene = 0.643 (in vapor)
	c. PT = 6.006 kPa; Xtoluene = 0.357 (in vapor)
	d. There is not enough information provided to answer this question.

.

When 2.8 x 10^-4 kg of a certain chemical compound is dissolved in 0.579 L of water at 27^oC, the osmotic pressure of the resultant solution is measured and found to have a value of 0.1625 atm. What is the molar mass of the chemical compound?

	a. 107.5 g/mol
	b. 6.602 g/mol
	c. 73.3 g/mol
	d. 57.9 g/mol

.

When 6.29 g of a certain nonvolatile solute is dissolved in 500 g of water, the freezing point of the resultant aqueous solution is 0.646^oC lower than that of pure water. The cryoscopic constant for water is K_f = 1.856 K-kg/mol. Given this information, what is the molar mass of the solute species?

	a. 36.1 g/mol
	b. 72.2 g/mol
	c. 36.1 kg/mol
	d. 18.1 g/mol

.

Which of the following will have the highest boiling-point temperature?

	a. A 0.01 M aqueous solution of BaCl2
	b. A 0.1 M aqueous solution of CaCl2
	c. A 0.1 M aqueous solution of sucrose
	d. A 0.1 M aqueous solution of KCl

.

Which of the following will have the lowest boiling-point temperature?

	a. Pure liquid water
	b. A 0.01 M aqueous solution of NaHCO3
	c. A 12 M solution of sulfuric acid
	d. A 0.1 M aqueous solution of glucose

.

Which of the following will have the lowest freezing-point temperature?

	a. A 0.01 M aqueous solution of NaCl
	b. A 0.01 M aqueous solution of BaCl2
	c. A 0.01 M aqueous solution of KBr
	d. A 0.01 M aqueous solution of FeCl3

.

Among the following statements, which one is incorrect?

	a. The molar entropy of a substance is an extensive property.
	b. The molar entropy of a substance always increases with an increase in temperature.
	c. The molar entropy of a molecular gas depends on the molar mass of the constituent molecules.
	d. The entropy of a molecular system depends on the spacings between the rotational and vibrational energy levels of the constituent molecules.

.

Consider two systems that are identical in all respects, except that in one the molecules are distinguishable, whereas in the other the molecules are indistinguishable. What would be the difference between the molar entropies of these two systems?

	a. 446.9 J/K-mol
	b. 53.8 J/K-mol
	c. There is no difference.
	d. There is not enough information provided to answer this question.

.

The electronic ground state of molecular oxygen is three-fold degenerate, and the first electronic excited state is two-fold degenerate and is located at an energy 15.72 x 10^-20 J above the ground state. In a sample of O₂(g), maintained at an equilibrium temperature of 298 K, what would be the ratio of the populations of O₂ molecules in the first electronic excited state versus the electronic ground state?

	a. 2.50 x 10-17
	b. 3.75 x 10-17
	c. 1.67 x 10-17
	d. 1.67 x 1017

.

The fundamental vibrational frequency of an oxygen molecule (O₂) is 4.741 x 10¹³ s^-1. What would be the value of the vibrational partition function for O₂ at a temperature of 1000 K, assuming that the molecular vibrational motion can be treated in the harmonic oscillator approximation?

	a. 1115
	b. 1.115
	c. 10.15 s-1
	d. 10.15 J

.

The ground electronic state of atomic oxygen is five-fold degenerate, the first electronic excited state is three-fold degenerate and is located 3.142 x 10^-24 J above ground, and the second electronic excited state is nondegenerate and is located 4.498 x 10^-24 J above ground. No other electronic excited states of atomic oxygen are thermally accessible at 300 K. Given this information, what is the value of the electronic partition function for atomic oxygen at a temperature of 300 K?

	a. 9
	b. 6.74 x 10-24
	c. 4.03 x 10-24
	d. 6.743

.

What is the value of the molecular translational partition function for the nitrogen molecules in a sample of N₂(g) confined to a container of volume 1 m³ and a temperature of 300 K?

	a. 2.41 x 108
	b. 1.45 x 1032
	c. 1.45 x 1032 J/m3
	d. 2.41 x 108 kJ/molecule

.