Free Gases MCQs with Answers

1. Boyle's law states that at constant temperature, the volume of a fixed mass of gas is

• A. directly proportional to its pressure
• B. inversely proportional to its pressure
• C. independent of its pressure
• D. proportional to the square of its pressure

Explanation: Boyle's law gives PV equal to a constant, so doubling the pressure halves the volume. A graph of P against V is a hyperbola, while a graph of P against 1 over V is a straight line through the origin, and that straight line is the usual way the law is confirmed experimentally. Volume rising with pressure would describe no real gas.

2. A gas occupies 500 cm3 at 2 atm. At constant temperature, what volume will it occupy at 5 atm?

• A. 200 cm3
• B. 250 cm3
• C. 1250 cm3
• D. 100 cm3

Explanation: Applying P1V1 equal to P2V2 gives V2 equal to 2 times 500 divided by 5, which is 200 cm3. The pressure rose by a factor of 2.5, so the volume must fall by the same factor, and 500 divided by 2.5 is 200. Getting 1250 means the ratio was applied the wrong way round.

3. Standard temperature and pressure (STP) is defined as

• A. 25 degrees C and 1 atm
• B. 0 degrees C and 1 atm
• C. 0 K and 1 atm
• D. 25 degrees C and 760 mm of mercury above atmospheric

Explanation: STP is 273.15 K, which is 0 degrees Celsius, at a pressure of 1 atmosphere or 760 mm of mercury. One mole of any ideal gas occupies 22.4 dm3 under these conditions, which is the molar volume used throughout stoichiometry. The value of 25 degrees Celsius belongs to standard state conditions used in thermochemistry, a different convention.

4. Charles's law predicts that a gas cooled at constant pressure would reach zero volume at

• A. 0 degrees C
• B. -100 degrees C
• C. -273.15 degrees C
• D. -373 degrees C

Explanation: Extrapolating the straight line of volume against temperature backwards, every gas reaches zero volume at minus 273.15 degrees Celsius, which is defined as absolute zero or 0 K. The extrapolation is theoretical, since every real gas liquefies well before that point. This is precisely why the Kelvin scale exists and why gas law calculations must use it.

5. A gas at 27 degrees C is heated at constant pressure until its volume doubles. Its final temperature is

• A. 54 degrees C
• B. 300 degrees C
• C. 327 degrees C
• D. 600 degrees C

Explanation: Charles's law must be applied in kelvin, so the initial temperature is 27 plus 273, which is 300 K. Doubling the volume doubles the absolute temperature to 600 K, and converting back gives 600 minus 273, which is 327 degrees Celsius. Doubling 27 to get 54 is the standard mistake and comes from using Celsius directly.

6. Which assumption is made by the kinetic molecular theory of an ideal gas?

• A. Gas molecules attract one another strongly
• B. The volume of the molecules themselves is negligible compared with the volume of the container
• C. Collisions between molecules lose energy as heat
• D. The molecules all move at the same speed

Explanation: The ideal model treats molecules as point masses with negligible volume and no intermolecular forces, colliding perfectly elastically so no kinetic energy is lost. Molecular speeds are not uniform but spread over the Maxwell-Boltzmann distribution, with only the average kinetic energy fixed by temperature. Real gases deviate exactly where these assumptions fail.

7. The average kinetic energy of the molecules of an ideal gas depends only on

• A. pressure
• B. absolute temperature
• C. volume
• D. molar mass

Explanation: Average kinetic energy equals three halves of kT, so it is fixed by absolute temperature alone. This is why hydrogen and oxygen at the same temperature have the same average kinetic energy even though hydrogen molecules move much faster, being lighter. Molar mass affects speed, not energy.

8. Real gases deviate most from ideal behaviour at

• A. high temperature and low pressure
• B. low temperature and high pressure
• C. high temperature and high pressure
• D. standard temperature and pressure

Explanation: At high pressure the molecules are close enough that their own volume is no longer negligible, and at low temperature they move slowly enough for intermolecular attractions to matter. Both assumptions of the ideal model fail together under those conditions, which is also why gases liquefy there. A gas behaves most ideally when it is hot and dilute.

9. In the van der Waals equation, the constant a corrects for

• A. the volume occupied by the gas molecules
• B. the intermolecular forces of attraction
• C. the number of moles present
• D. the temperature of the gas

Explanation: The term involving a raises the measured pressure to what it would have been without attractions pulling molecules away from the wall, so a is larger for gases that are easily liquefied. The constant b is the excluded volume correction for the finite size of the molecules. Moles and temperature already appear explicitly in the equation.

10. What volume is occupied by 0.5 mole of an ideal gas at STP?

• A. 5.6 dm3
• B. 11.2 dm3
• C. 22.4 dm3
• D. 44.8 dm3

Explanation: One mole of any ideal gas occupies 22.4 dm3 at STP, so half a mole occupies 11.2 dm3. The identity of the gas is irrelevant, which is the point of Avogadro's law. The value 5.6 dm3 would correspond to a quarter of a mole.