van der Waals Equation - UNSOLVED PRACTICE SET

Q7. Write the van der Waals equation for one mole of a real gas. Explain the physical significance of the correction terms 'a' and 'b'.

Q8. Why is the pressure correction term in the van der Waals equation written as an²/V² and not simply as a constant?

Q9. Explain why the volume correction term is (V – nb) and not (V – b) for n moles of gas.

Q10. A gas has a = 0 and b = 0. What type of gas is this? Explain.

Q11. Compare the values of 'a' for H₂ and CO₂. Which gas will deviate more from ideal behaviour? Explain.

Q12. At very high temperatures, the van der Waals equation approaches the ideal gas equation. Explain why.

Q13. (a) Starting from the postulates of Kinetic Molecular Theory, explain why real gases deviate from ideal behaviour. Identify the two faulty assumptions.

(b) Derive the van der Waals equation by introducing corrections for:

(i) The finite volume of gas molecules

(ii) The intermolecular attractive forces

(c) Explain the significance of the van der Waals constants 'a' and 'b'. How are they determined experimentally?

Q14. (a) Compare the van der Waals constants for the following gases:

(i) Which gas has the strongest intermolecular forces? Justify.

(ii) Which gas has the largest molecular size? Justify.

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

(b) Explain why NH₃ has a higher 'a' value than CO₂ despite having a lower molecular mass.

Q15. (a) Show that at low pressures, the van der Waals equation can be written as:

Z = 1 + (b – a/RT)(P/RT)

(b) Explain how this equation predicts:

(i) Z < 1 at low temperatures

(ii) Z > 1 at high temperatures

(c) Calculate the pressure exerted by 2.0 moles of CO₂ in a 1.0 L container at 300 K using:

(i) The ideal gas equation

(ii) The van der Waals equation

(a = 3.59 L²·atm/mol², b = 0.0427 L/mol)

(d) Which result is more accurate? Explain why.

Q16. Calculate the pressure exerted by 1.0 mole of CO₂ in a 500 mL container at 300 K using:

(a) The ideal gas equation

(b) The van der Waals equation (a = 3.59 L²·atm/mol², b = 0.0427 L/mol)

(c) Calculate the compressibility factor Z from both calculations.

(d) Comment on the deviation from ideal behaviour under these conditions.

Q17. The van der Waals constants for some gases are:

(a) Calculate the Boyle's temperature for each gas using TB = a/Rb. (R = 0.0821 L·atm/mol·K)

(b) Which gas will behave most ideally at room temperature (300 K)? Explain.

(c) At 300 K and 10 atm, calculate Z for CH₄ using the approximate expression Z = 1 + (b – a/RT)(P/RT).

(d) A student wants to liquefy SO₂. Explain how the value of 'a' helps predict the ease of liquefaction. Calculate the critical temperature of SO₂ using Tc = 8a/27Rb.

Q18. In India, the van der Waals equation has practical relevance in gas storage and transport:

(a) LPG cylinders contain propane and butane under pressure. Explain why the ideal gas equation significantly overestimates the amount of gas that can be stored in a cylinder. How does the van der Waals equation provide a better estimate?

(b) A 50 L cylinder contains 20 kg of propane (C₃H₈) at 27°C. Calculate the pressure in the cylinder using:

(i) The ideal gas equation

(ii) The van der Waals equation (a = 9.39 L²·atm/mol², b = 0.0905 L/mol)

(M of C₃H₈ = 44 g/mol)

(c) An oxygen cylinder for medical use contains gas at 150 atm. Explain why O₂ behaves non-ideally at this pressure and how the van der Waals corrections become important.

(d) In the design of natural gas pipelines, engineers must account for non-ideal behaviour. Explain how knowledge of 'a' and 'b' helps in pipeline design and safety calculations.