Free Gases MCQs with Answers

21. Dalton's law of partial pressures states that the total pressure of a mixture of gases equals

• A. the product of the individual pressures
• B. the sum of the partial pressures of the component gases
• C. the average of the individual pressures
• D. the pressure of the heaviest gas

Explanation: Because ideal gas molecules do not interact, each gas exerts the pressure it would exert alone in the same volume, and these simply add. The partial pressure of a component is its mole fraction multiplied by the total pressure. This is how the composition of air and of respiratory gas mixtures is described.

22. According to Graham's law, the rate of diffusion of a gas is

• A. directly proportional to its molar mass
• B. inversely proportional to the square root of its molar mass
• C. independent of its molar mass
• D. proportional to the square of its molar mass

Explanation: Lighter molecules move faster at a given temperature, so hydrogen diffuses four times as fast as oxygen, whose molar mass is sixteen times greater and whose square root is four. This is the principle behind separating uranium isotopes by gaseous diffusion. The relationship holds for effusion through a small hole as well.

23. The van der Waals equation corrects the ideal gas equation for

• A. the mass of the container
• B. the finite volume of the molecules and the attractive forces between them
• C. the speed of the molecules
• D. the colour of the gas

Explanation: The constant b subtracts the volume actually occupied by the molecules and the constant a adds back the pressure lost to intermolecular attraction, so the equation describes real gases far better. Larger values of a and b indicate a gas that departs further from ideality. As pressure falls towards zero the corrections vanish and the ideal equation is recovered.

24. A gas can be liquefied only if it is cooled below its

• A. boiling point
• B. critical temperature
• C. melting point
• D. triple point

Explanation: Above the critical temperature no amount of pressure will produce a liquid, because the molecules have too much kinetic energy for the attractive forces to hold them together. This is why oxygen and nitrogen must be cooled deeply before they can be liquefied while ammonia liquefies at room temperature under pressure. The pressure needed at that temperature is the critical pressure.

25. At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature. This is

• A. Boyle's law
• B. Charles's law
• C. Gay-Lussac's law
• D. Avogadro's law

Explanation: Gay-Lussac's law covers the pressure temperature relationship at constant volume, and it explains why a sealed aerosol can explode when heated. Boyle's law fixes temperature and relates pressure to volume, while Charles's law fixes pressure and relates volume to temperature. Each law holds one variable constant, which is the quickest way to tell them apart.

26. The average kinetic energy of the molecules of any ideal gas depends only on

• A. the identity of the gas
• B. the absolute temperature
• C. the pressure
• D. the volume of the container

Explanation: At the same temperature, hydrogen and oxygen molecules have the same average kinetic energy, though the lighter hydrogen molecules must move much faster to achieve it. This is the microscopic meaning of temperature. It also explains Graham's law, since equal energy with unequal mass means unequal speed.

27. A fixed mass of gas at 2 atm and 300 K is heated to 600 K at constant volume. The new pressure is

• A. 1 atm
• B. 2 atm
• C. 4 atm
• D. 8 atm

Explanation: Pressure is proportional to absolute temperature at constant volume, so doubling the temperature in kelvin doubles the pressure to 4 atm. Both temperatures are already absolute here, which removes the usual conversion trap. This is why pressurised cylinders carry warnings about heat.

28. Which gas would be expected to behave most ideally at room temperature?

• A. Helium
• B. Ammonia
• C. Water vapour
• D. Carbon dioxide

Explanation: Helium is a small non polar monatomic gas with very weak dispersion forces and negligible molecular volume, so it comes closest to the ideal model. Ammonia and water vapour are strongly hydrogen bonded and deviate considerably. Carbon dioxide, being larger and more polarisable, also departs more than helium.

29. The compressibility factor Z equals PV over nRT. For an ideal gas its value is

• A. zero
• B. exactly 1 at all pressures
• C. always greater than 1
• D. always less than 1

Explanation: By definition an ideal gas satisfies PV equal to nRT exactly, so Z is one under every condition. For a real gas Z falls below one where attractive forces dominate and rises above one at high pressure where molecular volume dominates. Plotting Z against pressure is the standard way of displaying how far a gas departs from ideality.

30. Value of R gas constant in J mol-1 K-1 is

• A. 8.314
• B. 62.4
• C. 0.821
• D. 62400

Explanation: The universal gas constant is 8.314 joules per mole per kelvin, and this is the value to use whenever pressure is in pascals and volume in cubic metres. The figure 0.0821 dm3 atm per mole per kelvin is the same constant expressed for pressure in atmospheres, which is why 0.821 appears as a distractor. Always match the value of R to the units of the other quantities in the problem.