The Ideal Gas Law
Which of the following is not one of the four assumptions of the classical ideal gas model?
A sealed, rigid flask contains an ideal gas at a pressure of 3.0 × 10⁵ Pa and a temperature of 600 K. The gas is cooled until its temperature reaches 200 K. Calculate the new pressure.
Explain why the internal energy of an ideal gas depends only on its temperature and not on its volume or pressure. Which statement correctly captures this reasoning?
A balloon contains 0.080 mol of helium at 1.50 × 10⁵ Pa and 47 °C. Determine the volume of the balloon.
A laboratory contains 5.0 × 10²⁵ gas molecules at 1.01 × 10⁵ Pa and 25 °C. Calculate the volume of the laboratory.
On a graph of pressure (vertical axis) versus volume (horizontal axis) for a fixed amount of ideal gas at constant temperature, which description correctly characterises the shape?
A researcher plots pressure versus temperature in degrees Celsius for an ideal gas at constant volume. The data form a straight line. She extrapolates the line to where pressure equals zero. Which temperature does the extrapolated line intersect on the horizontal axis, and what does this value represent?
An ideal gas in a rigid sealed container has its absolute temperature doubled while the amount of gas remains constant. A student claims the pressure quadruples. Determine whether the student is correct and justify your answer using the ideal gas law.
A container holds 0.25 mol of an ideal gas at 1.00 × 10⁵ Pa and a temperature of 77 °C. Calculate the volume of the gas.
Two identical rigid containers hold the same type of ideal gas at the same temperature. Container X holds 2.0 mol and Container Y holds 6.0 mol. The pressure in Container X is 1.5 × 10⁵ Pa. What is the pressure in Container Y?
A fixed quantity of ideal gas occupies 2.0 × 10⁻³ m³ at 3.0 × 10⁵ Pa and 300 K. The gas is heated to 900 K while the volume is allowed to expand to 4.0 × 10⁻³ m³. Determine the new pressure.
Under which conditions does a real gas deviate most from ideal gas behavior?
A sealed vessel of volume 8.0 m³ contains an ideal gas at 2.07 × 10⁵ Pa and 27 °C. Calculate the number of gas molecules in the vessel.
A weather balloon is released at ground level where the temperature is 17 °C and pressure is 1.01 × 10⁵ Pa. At altitude, the temperature drops to −33 °C and the pressure falls to 5.05 × 10⁴ Pa. If the initial volume of the balloon is 1.5 m³, determine the volume at altitude.
The connection between the Boltzmann constant $k_{\mathrm{B}}$, the universal gas constant R, and Avogadro’s number $N_{\mathrm{A}}$ is $k_{\mathrm{B}}$ = R/$N_{\mathrm{A}}$. If R = 8.314 J/(mol·K) and $N_{\mathrm{A}}$ = 6.022 × 10²³ mol⁻¹, which value is closest to $k_{\mathrm{B}}$?
A student heats an ideal gas in a sealed rigid container from 200 K to 600 K. She measures the initial pressure as 1.0 × 10⁵ Pa. She predicts the final pressure will be 2.0 × 10⁵ Pa because “the temperature increased by 400 K, and 400 is twice 200.” Identify the error in her reasoning and state the correct final pressure.
An astronaut seals a flexible plastic bag containing air on the International Space Station, where the cabin is at 1.01 × 10⁵ Pa and 22 °C. She then places the bag in an airlock that is slowly depressurised to 5.05 × 10³ Pa while the temperature drops to −3 °C. By what factor does the volume of the bag change?
On a P vs T (kelvin) graph, two straight lines pass through the origin. Line A represents 2.0 mol of gas in a 0.10 m³ container. Line B represents 2.0 mol of gas in a 0.20 m³ container. Determine the ratio of the slope of Line A to the slope of Line B.