Liquefaction of Gases - UNSOLVED PRACTICE SET

Q7. Define critical temperature, critical pressure, and critical volume. What is the significance of the critical point?

Q8. Explain why gases with high values of van der Waals constant 'a' are easily liquefied.

Q9. Why is it impossible to liquefy H₂ or He by simply applying pressure at room temperature? What additional condition is needed?

Q10. Explain Andrews' experiments on CO₂ and what they revealed about the critical point.

Q11. What are 'permanent gases'? Why are they called so? Give two examples.

Q12. Explain the principle behind Linde's process for liquefaction of air.

Q13. (a) Explain the process of liquefaction of gases. What are the two methods by which a gas can be liquefied?

(b) Define critical temperature (Tc), critical pressure (Pc), and critical volume (Vc). Draw a labelled diagram showing Andrews' isotherms for CO₂.

(c) Explain the significance of the critical point in the liquefaction of gases.

Q14. (a) Derive the relationship between van der Waals constants and critical constants:

Tc = 8a/27Rb, Pc = a/27b², Vc = 3b

(b) Calculate the critical constants for CO₂ given: a = 3.59 L²·atm/mol², b = 0.0427 L/mol

(c) The critical temperature of H₂ is 33 K, while that of CO₂ is 304 K. Explain this large difference in terms of intermolecular forces.

Q15. (a) Explain why the liquefaction of gases becomes easier as the temperature is lowered.

(b) Describe Linde's method of liquefaction of air with a neat diagram description.

(c) Explain the role of the Joule-Thomson effect in the liquefaction of gases.

(d) Why is liquid nitrogen used as a coolant in cryosurgery and preservation of biological samples?

Q16. The van der Waals constants for some gases are:

(a) Calculate the critical temperature (Tc) for each gas.

(b) Arrange the gases in order of increasing ease of liquefaction.

(c) Which gases can be liquefied at room temperature (300 K) by applying pressure? Which cannot?

(d) Calculate the critical pressure (Pc) for CO₂ and NH₃.

Q17. Andrews' isotherms for CO₂ show the following behaviour:

(a) At 50°C, CO₂ behaves as an ideal gas at low pressures but deviates at high pressures. Explain why no liquefaction is observed at this temperature, no matter how high the pressure.

(b) At 31.1°C (the critical temperature), CO₂ shows a horizontal point of inflection on the P-V curve. Explain the significance of this point.

(c) At 20°C, CO₂ liquefies at 73 atm. Calculate the volume occupied by 1 mole of liquid CO₂ at this point (approximate).

(d) Draw a rough sketch of Andrews' isotherms showing the three regions: gas, liquid-vapour equilibrium, and liquid. Label the critical point.

Q18. In India, liquefied gases have numerous applications:

(a) LPG (liquefied petroleum gas) is used in almost every Indian household for cooking. Explain why propane and butane can be liquefied under moderate pressure at room temperature, while methane (the main component of CNG) requires much higher pressure or lower temperature.

(b) A domestic LPG cylinder contains a mixture of propane (Tc = 370 K) and butane (Tc = 425 K) at 298 K. Explain which component liquefies first when the cylinder is filled and why.

(c) Liquid nitrogen (boiling point 77 K) is used in cryopreservation of biological samples and in medical applications. Explain how nitrogen gas is liquefied industrially using the Joule-Thomson effect and cascading cooling.

(d) In hospitals, oxygen is stored as a liquid in cryogenic tanks. Calculate the minimum pressure required to liquefy oxygen at 90 K (its normal boiling point). The critical temperature of O₂ is 154.6 K and critical pressure is 49.8 atm. Explain why liquid oxygen tanks must be well-insulated.