Ideal Gas Questions

State what is meant by an ideal gas.

• A gas that perfectly follows the ideal gas law

• A gas that does not exist in reality

• A gas with no intermolecular forces

• A gas that cannot be compressed

State the temperature, in degrees Celsius, of absolute zero.

• -273.15

• -100

• 0

• 100

Calculate the number of molecules of the gas in the vessel. A sealed vessel contains a mass of 0.0424 kg of an ideal gas at 227°C. The pressure of the gas is 1.37 × 10^5 Pa and the volume of the gas is 0.640 m^3.

• 1.09 × 10^23

• 2.50 × 10^23

• 3.75 × 10^23

• 4.20 × 10^23

Calculate the mass of one molecule of the gas.

• 7.07 × 10^-26 kg

• 5.00 × 10^-26 kg

• 8.50 × 10^-26 kg

• 6.00 × 10^-26 kg

Calculate the root-mean-square (r.m.s.) speed v of the molecules of the gas.

• 515 m/s

• 400 m/s

• 600 m/s

• 700 m/s

The equation of state for an ideal gas can be written as $ pV = NkT $. What does 'p' represent in this equation?

• Pressure

• Volume

• Number of molecules

• Temperature

Use the equation in (a) to show that the average translational kinetic energy $ E_k $ of a molecule of an ideal gas is given by $ E_k = \frac{3}{2}kT $. Which of the following equations represents this relationship?

• $ E_k = \frac{3}{2}kT $

• $ E_k = \frac{1}{2}kT $

• $ E_k = 2kT $

• $ E_k = 3kT $

The mass of an oxygen molecule is $ 5.31 \times 10^{-26} $ kg. Assume that oxygen behaves as an ideal gas. Use the equation in (b) to determine the root-mean-square (r.m.s.) speed $ u $ of an oxygen molecule at 23°C. What is the r.m.s. speed $ u $ in m s$^{-1}$?

• 500 m s$^{-1}$

• 482 m s$^{-1}$

• 515 m s$^{-1}$

• 470 m s$^{-1}$

The variation with pressure $ p $ of the volume $ V $ of a fixed mass of an ideal gas is shown in Fig. 2.1. What does the graph represent?

• Boyle's Law

• Charles's Law

• Avogadro's Law

• Ideal Gas Law

The gas undergoes a cycle of changes A to B to C to A. During the change A to B, the volume of the gas increases from $ 2.3 \times 10^{-3} \, \text{m}^3 $ to $ 3.8 \times 10^{-3} \, \text{m}^3 $. What is the magnitude of the work done during the change A to B?

• 390 J

• 400 J

• 350 J

• 370 J