Ideal gases: notes and practice questions

A sealed syringe contains $30.0\ \text{cm}^3$ of air at $101\ \text{kPa}$. The plunger is pushed, at constant temperature, until the pressure inside is $252.5\ \text{kPa}$. What is the new volume of air in the syringe?

A. $12.0\ \text{cm}^3$

B. $27.5\ \text{cm}^3$

C. $75.0\ \text{cm}^3$

D. $151.5\ \text{cm}^3$

What volume of sulfur dioxide gas, in $cm^3$, is required to produce $60\,cm^3$ of sulfur trioxide gas when reacted with $50\,cm^3$ of oxygen gas? Assume all gases are at the same temperature and pressure and the reaction goes to completion.

$2SO_2(g) + O_2(g) \rightarrow 2SO_3(g)$

A. $30$

B. $50$

C. $60$

D. $100$

During an experiment, a student collects a sample of hydrogen gas over water. After correcting for water vapour pressure, the volume of dry hydrogen gas at standard temperature and pressure (STP) is measured to be $678 \text{ cm}^3$.

How many hydrogen molecules are present in this sample?

(Assume standard molar volume of an ideal gas at STP is $22.7 \text{ dm}^3 \text{ mol}^{-1}$ and Avogadro constant $N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$)

A $1.80 \times 10^{22}$

B $2.99 \times 10^{23}$

C $1.80 \times 10^{25}$

D $2.99 \times 10^{-2}$

Which sample contains the largest amount, in mol, of ammonia (NH_3)?

$N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$

Molar volume of an ideal gas at STP = 22.7 dm$^3$ mol$^{-1}$.

A. 8.5 g of $NH_3$ (g)

B. $9.03 \times 10^{23}$ molecules of $NH_3$ (g)

C. 200 cm$^3$ of 1.5 mol dm$^{-3}$ $NH_3$ (aq)

D. 45.4 dm$^3$ of $NH_3$ (g) at STP

A balloon containing $2.00 \text{ dm}^3$ of helium gas at standard temperature ($0^\circ C$) is placed in a freezer. Assuming the pressure remains constant, what will be the volume of the helium gas when the temperature drops to $-25^\circ C$?

A $1.82 \text{ dm}^3$

B $2.00 \text{ dm}^3$

C $2.18 \text{ dm}^3$

D $2.20 \text{ dm}^3$

A weather balloon contains a sample of argon gas with an initial volume of $150 \text{ cm}^3$ at a temperature of $20.0^\circ C$. If the balloon rises to an altitude where the temperature increases to $70.0^\circ C$ and the pressure remains constant, what is the new volume of the argon gas?

A $125 \text{ cm}^3$

B $150 \text{ cm}^3$

C $176 \text{ cm}^3$

D $200 \text{ cm}^3$

A sample of nitrogen gas, $N_2$, is being studied in a laboratory. Under which of the following conditions of temperature and pressure would the behaviour of nitrogen gas be expected to be closest to that of an ideal gas?

A team of environmental scientists collected a sample of an unknown gas from a geothermal vent. They determined that $0.036 \text{ g}$ of the gas occupied a volume of $225 \text{ cm}^3$ at a pressure of $12.0 \text{ kPa}$ and a temperature of $50 \text{ }^\circ C$.

What is the relative molecular mass of this gas?

A $32$

B $36$

C $39$

D $43$

A student collects a sample of hydrogen gas from a reaction in a gas syringe. The initial volume of the gas is $150.0 \text{ cm}^3$ at a pressure of $120.0 \text{ kPa}$ and a temperature of $25.0 \text{ °C}$. The student then moves the syringe to a different lab environment where the pressure is $80.0 \text{ kPa}$ and the temperature is $127.0 \text{ °C}$. What is the new volume of the hydrogen gas?

A $151 \text{ cm}^3$

B $242 \text{ cm}^3$

C $302 \text{ cm}^3$

D $362 \text{ cm}^3$

Under conditions of high pressure and low temperature, real gases deviate from ideal behaviour. Which of the following gases would be expected to show the largest deviation from the ideal gas law?

A. Argon, Ar

B. Ethene, $C_2H_4$

C. Fluorine, $F_2$

D. Fluoromethane, $CH_3F$

A student investigates the behaviour of a fixed mass of an ideal gas. Which of the following statements correctly describes a graphical relationship for this gas?

A. A plot of volume against temperature in degrees Celsius ($^{\circ}\text{C}$) at constant pressure is a straight line passing through the origin.

B. A plot of pressure against volume at constant temperature is a straight line with a negative gradient.

C. A plot of the product of pressure and volume ($PV$) against pressure at constant temperature is a horizontal line.

D. A plot of pressure against absolute temperature (K) at constant volume is a curve.

A sealed aerosol can contains a propellant gas at an initial pressure of $101 \text{ kPa}$ at a temperature of $25.0^\circ C$. The can is accidentally left near a heat source, causing the internal pressure to increase. If the can is designed to rupture when the internal pressure reaches $350 \text{ kPa}$, at what temperature will the can rupture, assuming the volume of the gas remains constant?

A $86^\circ C$

B $298^\circ C$

C $760^\circ C$

D $1030^\circ C$

A research team is investigating the behavior of a gas in a flexible container. Initially, $0.50 \text{ mol}$ of the gas occupies a volume of $10.0 \text{ dm}^3$ at a pressure of $1.20 \times 10^5 \text{ Pa}$ and a temperature of $298 \text{ K}$.

The team then adds more gas, increasing the amount to $1.50 \text{ mol}$, while simultaneously changing the pressure to $2.00 \times 10^5 \text{ Pa}$ and the temperature to $350 \text{ K}$. What is the new volume of the gas?

A $0.0106 \text{ m}^3$

B $0.0169 \text{ m}^3$

C $0.0211 \text{ m}^3$

D $0.0254 \text{ m}^3$

In an industrial synthesis, equal volumes of nitrogen gas ($N_2$) and hydrogen gas ($H_2$) are mixed in a sealed reactor at constant temperature and pressure to produce ammonia gas ($NH_3$).

$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

After the reaction reaches completion, the volume of ammonia gas produced is measured to be $30\text{ cm}^3$.

What was the initial volume, in $\text{cm}^3$, of nitrogen gas at the beginning of the reaction?

A. $15$

B. $30$

C. $45$

D. $90$

A student investigates the thermal decomposition of calcium carbonate. What is the volume of carbon dioxide, in $\text{cm}^3$, produced at STP when $5.00\text{ g}$ of calcium carbonate undergoes complete thermal decomposition?

$CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$

Molar volume of an ideal gas at STP is $22.7\text{ dm}^3 \text{ mol}^{-1}$

A. $567$

B. $756$

C. $1130$

D. $1510$

A $50 \text{ cm}^3$ sample of butane gas, $C_4H_{10}(g)$, was completely combusted in $350 \text{ cm}^3$ of oxygen gas, $O_2(g)$, at constant temperature and pressure.

The reaction is represented by the following equation:

$2C_4H_{10}(g) + 13O_2(g) \rightarrow 8CO_2(g) + 10H_2O(l)$

What is the volume of unreacted oxygen gas remaining at the original conditions?

A. $25 \text{ cm}^3$

B. $50 \text{ cm}^3$

C. $75 \text{ cm}^3$

D. $100 \text{ cm}^3$

A fixed amount of gas is contained within a flexible balloon at constant temperature. If the volume of the balloon is reduced to 75% of its initial value, how does this affect the pressure of the gas inside the balloon? ($pV = nRT$)

A. Pressure increases by 25%.

B. Pressure decreases by 25%.

C. Pressure increases by 33.3%.

D. Pressure decreases by 33.3%.

Which row shows a gas that would deviate the most from ideal gas behaviour?