Gas Laws & Kinetic Molecular Theory practice questions

Question 1

A rigid vessel contains a mixture of $0.10 \text{ mol}$ of $\text{Ne(g)}$ and $0.30 \text{ mol}$ of $\text{Ar(g)}$ at an initial temperature of $300 \text{ K}$. The total pressure inside the vessel at $300 \text{ K}$ is $8.0 \text{ atm}$. If the vessel is heated to $450 \text{ K}$, what is the partial pressure of $\text{Ne(g)}$ at $450 \text{ K}$?

Accepted Answer

$3.0 \text{ atm}$

Answer

$1.3 \text{ atm}$

Answer

$2.0 \text{ atm}$

Answer

$12.0 \text{ atm}$

Question 2

A student determines the molar mass of an unknown volatile liquid by vaporizing a sample in a container of fixed volume at a constant temperature and pressure. Under these conditions, the density of the unknown vapor is measured to be $3.60 \text{ g/L}$. Under the exact same temperature and pressure, the density of pure $\text{O}_2\text{(g)}$ (molar mass $32.0 \text{ g/mol}$) is $1.20 \text{ g/L}$. Based on these data, what is the molar mass of the unknown liquid?

Accepted Answer

$96.0 \text{ g/mol}$

Answer

$10.7 \text{ g/mol}$

Answer

$32.0 \text{ g/mol}$

Answer

$115 \text{ g/mol}$

Question 3

A student heats a pure limestone sample in a model kiln. The CaCO decomposition occurs according to the equation

$\text{CaCO}_3\text{(s)} \rightarrow \text{CaO(s)} + \text{CO}_2\text{(g)}$

The student completely decomposes $25.0\text{ g}$ of $\text{CaCO}_3$. The molar mass of $\text{CaCO}_3$ is $100.\text{ g/mol}$, and one mole of gas occupies $22.4\text{ L}$ at standard temperature and pressure. What volume of $\text{CO}_2\text{(g)}$ is produced at standard temperature and pressure?

Accepted Answer

$5.60\text{ L}$

Answer

$0.0112\text{ L}$

Answer

$0.560\text{ L}$

Answer

$2.80\text{ L}$

Question 4

Two metal blocks, $\text{Block X}$ and $\text{Block Y}$, are brought into contact inside an insulated container. The initial particulate state of the two blocks is shown in the diagram, where the length of each arrow represents the relative speed of a particle. Which of the following best describes the system after thermal equilibrium is reached?

Accepted Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$, and the average kinetic energy of the particles in $\text{Block X}$ is equal to the average kinetic energy of the particles in $\text{Block Y}$.

Answer

Energy has transferred as heat from $\text{Block Y}$ to $\text{Block X}$, and the average kinetic energy of the particles in $\text{Block X}$ remains greater than that of $\text{Block Y}$.

Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$, and all molecular motion in both blocks has ceased.

Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$ until all particles in $\text{Block X}$ have lower kinetic energy than all particles in $\text{Block Y}$.

Question 5

A student sets up an experiment using two rigid glass bulbs of equal volume connected by a valve, as represented in the particulate diagram. Initially, Bulb 1 contains a gas sample at a constant temperature of 298 K, and Bulb 2 is evacuated. After the valve is opened, the gas expands isothermally until it is evenly distributed across both bulbs. Which of the following best explains why $\Delta S > 0$ for this process based on the particulate representation?

Accepted Answer

The gas particles occupy a larger total volume, which increases the number of possible spatial arrangements (microstates) available to the system.

Answer

The average kinetic energy of the gas particles increases as they enter Bulb $2$, leading to greater thermal disorder in the system.

Answer

The total number of gas particles in the system increases when the valve is opened, creating a greater quantity of matter.

Answer

The attractive forces between the gas particles become stronger as the gas expands, causing a spontaneous increase in energy.

Question 6

A rigid, closed container holds a $1.0 \text{ mol}$ sample of $\text{Ne}(g)$ at $298 \text{ K}$. The Maxwell-Boltzmann distribution curve representing the molecular speeds of the sample at $298 \text{ K}$ is shown below. The gas is subsequently heated to $596 \text{ K}$. Which of the following predictions best describes the change in the average kinetic energy of the gas molecules and the appearance of the speed distribution curve at $596 \text{ K}$?

Accepted Answer

The average kinetic energy doubles, and the distribution curve shifts to the right with a lower peak height.

Answer

The average kinetic energy remains unchanged, and the distribution curve shifts to the right with a taller peak.

Answer

The average kinetic energy doubles, and the distribution curve shifts to the right with a taller peak.

Answer

The average kinetic energy quadruples, and the distribution curve shifts to the right with a lower peak height.

Question 7

Two separate rigid containers of equal volume contain gas samples at identical temperatures of $298 \text{ K}$. Container 1 contains $\text{He(g)}$ and Container 2 contains $\text{SO}_2\text{(g)}$. Which of the following correctly compares the average kinetic energy of the gas molecules and the rate of effusion of the gas in Container 1 relative to Container 2?

Accepted Answer

The average kinetic energy of $\text{He(g)}$ is equal to that of $\text{SO}_2\text{(g)}$, and $\text{He(g)}$ has a greater rate of effusion than $\text{SO}_2\text{(g)}$.

Answer

The average kinetic energy of $\text{He(g)}$ is greater than that of $\text{SO}_2\text{(g)}$, and $\text{He(g)}$ has a greater rate of effusion than $\text{SO}_2\text{(g)}$.

Answer

The average kinetic energy of $\text{He(g)}$ is equal to that of $\text{SO}_2\text{(g)}$, and $\text{He(g)}$ has a smaller rate of effusion than $\text{SO}_2\text{(g)}$.

Answer

The average kinetic energy of $\text{He(g)}$ is less than that of $\text{SO}_2\text{(g)}$, and $\text{He(g)}$ has a smaller rate of effusion than $\text{SO}_2\text{(g)}$.

Question 8

A student prepares a gas mixture in a rigid container by combining 2.8 g of $\text{N}_2\text{(g)}$, 6.4 g of $\text{O}_2\text{(g)}$, and 8.0 g of $\text{Ar(g)}$. The total pressure inside the container is measured to be 1.50 atm. What is the partial pressure of $\text{N}_2\text{(g)}$ in the mixture?

Accepted Answer

$0.30 \text{ atm}$

Answer

$0.50 \text{ atm}$

Answer

$0.60 \text{ atm}$

Answer

$1.20 \text{ atm}$

Question 9

A student measures the molecular speed distribution of a 1.0 mol sample of $\text{Ar(g)}$ in a rigid container under three different thermal conditions, resulting in curves 1, 2, and 3 shown in the graph below.

Which of the following correctly ranks the temperatures $T_1$, $T_2$, and $T_3$ from lowest to highest and provides the correct justification?

Accepted Answer

$T_1 < T_2 < T_3$, because as temperature increases, the average kinetic energy of the gas particles increases, shifting the peak toward higher speeds and broadening the distribution.

Answer

$T_3 < T_2 < T_1$, because curve 1 has the highest peak height, indicating that the molecules at $T_1$ have the greatest average kinetic energy.

Answer

$T_3 < T_2 < T_1$, because lowering the temperature increases particle collisions, causing the speed distribution to spread over a wider range.

Answer

$T_1 < T_2 < T_3$, because the total area under curve 3 is greater than the total area under curve 1, indicating higher total thermal energy.

Question 10

A student reacts a sample of calcium carbonate with excess hydrochloric acid to produce carbon dioxide gas. The gas is collected over water at a total barometric pressure of $1.04 \text{ atm}$ and a temperature of $27^\circ\text{C}$. The volume of gas collected in the tube is $246 \text{ mL}$. At $27^\circ\text{C}$, the vapor pressure of water is $0.040 \text{ atm}$. Based on the data collected, how many moles of $\text{CO}_2\text{(g)}$ were produced in the reaction?

Accepted Answer

$1.0 \times 10^{-2} \text{ mol}$

Answer

$1.0 \times 10^{-3} \text{ mol}$

Answer

$9.6 \times 10^{-3} \text{ mol}$

Answer

$1.04 \times 10^{-2} \text{ mol}$

Question 11

A chemical engineer studies a sample of $1.00\text{ mol}$ of $\text{N}_2\text{(g)}$ at $200\text{ K}$, a temperature at which no phase transition occurs. To isolate the effect of finite molecular volume, the engineer compares the following models.

$$
P_{\text{ideal}}=\dfrac{nRT}{V}
$$

$$
P_{\text{vol}}=\dfrac{nRT}{V-nb}
$$

In the second model, $b$ is a positive constant that accounts for the volume occupied by the gas molecules. As the sample is compressed to progressively smaller container volumes, which statement correctly compares the pressures predicted by the two models and explains the comparison?

Accepted Answer

The finite-volume model predicts a higher pressure, with an increasing discrepancy, because \(V-nb

Answer

The finite-volume model predicts a lower pressure, with an increasing discrepancy, because subtracting $nb$ makes the denominator smaller and therefore makes the calculated pressure smaller.

Answer

The finite-volume model predicts a lower pressure, with an increasing discrepancy, because intermolecular attractions become more important at low temperatures and reduce collisions with the container walls.

Answer

The finite-volume model predicts a higher pressure, with an increasing discrepancy, because the value of $b$ increases as the molecules are compressed closer together.

Question 12

A student evaluates a pure molecular substance for use in a thermal-storage device. The initially solid sample is heated at constant pressure, and the student records its temperature as energy is added. The resulting heating curve is shown.

Which statement correctly describes the primary changes in the particles’ average kinetic energy and potential energy during regions III and IV of the graph?

Accepted Answer

In region III, average kinetic energy increases while potential energy remains approximately constant; in region IV, average kinetic energy remains constant while potential energy increases, because the added energy overcomes intermolecular attractions during vaporization.

Answer

In region III, potential energy increases while average kinetic energy remains constant; in region IV, average kinetic energy increases while potential energy remains approximately constant, because a sloped segment represents a phase change and a plateau represents warming within one phase.

Answer

In both regions III and IV, average kinetic energy increases while potential energy remains approximately constant, because continued energy transfer always increases particle speed.

Answer

In region III, average kinetic energy increases while potential energy remains approximately constant; in region IV, average kinetic energy remains constant while potential energy decreases, because separating the particles lowers their intermolecular potential energy.

Question 13

In a gas-recovery study, a student places separate samples containing identical numbers of gas molecules into identical rigid vessels at the same temperature. The vessels are maintained at high pressure, and both samples remain single phases. The student calculates the compressibility factor, defined as $Z=\dfrac{PV}{nRT}$. For an ideal gas, $Z=1$.

| Gas | Molecular description | Measured $Z$ |
|-----|-----------------------|----------------|
| $\text{CH}_4$ | Tetrahedral and nonpolar | $0.96$ |
| $\text{SO}_2$ | Bent and polar | $0.72$ |

Which choice ranks the gases from greatest to least magnitude of deviation from ideal behavior and best explains the ranking?

Accepted Answer

$\text{SO}_2 > \text{CH}_4$, because dipole-dipole attractions between $\text{SO}_2$ molecules reduce momentum transfer to the vessel walls more strongly than the dispersion forces between $\text{CH}_4$ molecules do.

Answer

$\text{CH}_4 > \text{SO}_2$, because a value of $Z$ closer to 1 indicates a larger fractional pressure decrease caused by intermolecular attractions.

Answer

$\text{CH}_4 > \text{SO}_2$, because the lower molar mass of $\text{CH}_4$ gives its molecules a greater average speed, which produces a greater departure from ideal behavior.

Answer

$\text{SO}_2 > \text{CH}_4$, because the larger volume occupied by individual $\text{SO}_2$ molecules lowers the measured pressure below the ideal pressure.

Question 14

A sealed cylinder contains an equilibrium mixture represented by the equation

$2\text{NO}_2\text{(g)} \rightleftharpoons \text{N}_2\text{O}_4\text{(g)}$

At time $t_1$, the volume of the cylinder is rapidly decreased to one-half its original value while the temperature remains constant. The concentrations are recorded in the graph.

Which statement best explains the concentration changes shown after $t_1$?

Accepted Answer

The equilibrium shifts toward the products because, for $Q=\dfrac{[\text{N}_2\text{O}_4]}{[\text{NO}_2]^2}$, doubling both concentrations makes $Q$ less than $K$.

Answer

The equilibrium shifts toward the reactants because decreasing the volume favors the side with the greater number of gas particles.

Answer

The equilibrium does not shift after the initial jump because doubling both concentrations leaves $Q$ equal to $K$.

Answer

The equilibrium shifts toward the products because decreasing the volume increases $K$ at constant temperature.

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