Deviation from Ideal Behaviour - UNSOLVED PRACTICE SET
Chapter: States of Matter | Topic: Deviation from Ideal Behaviour
DEVIATION FROM IDEAL BEHAVIOUR - UNSOLVED PRACTICE SET
Topic: Deviation from Ideal Behaviour
Multiple Choice Questions
Q1. Real gases deviate from ideal behaviour because:
- Their molecules have zero volume
- There are no intermolecular forces between their molecules
- Their molecules have finite volume and there are intermolecular forces
- They obey Boyle's Law perfectly
Q2. The compressibility factor (Z) for an ideal gas is:
- 0
- 1
- Less than 1
- Greater than 1
Q3. At high pressure, the compressibility factor Z for a real gas is:
- Less than 1
- Equal to 1
- Greater than 1
- Equal to 0
Q4. At low pressure and high temperature, real gases behave ideally because:
- Intermolecular forces are significant and molecular volume is negligible
- Intermolecular forces are negligible and molecular volume is significant
- Both intermolecular forces and molecular volume are negligible
- Both intermolecular forces and molecular volume are significant
Q5. The temperature at which a real gas behaves ideally over a wide range of pressure is called:
- Critical temperature
- Boyle's temperature
- Inversion temperature
- Triple point
Q6. For a real gas, if Z < 1 at a given temperature and pressure, it means:
- The gas is more compressible than an ideal gas
- The gas is less compressible than an ideal gas
- The gas behaves ideally
- The gas cannot be liquefied
Short Answer Questions
Q7. Define compressibility factor (Z). Write its expression and explain its significance.
Q8. Explain why real gases deviate from ideal behaviour at:
(a) High pressure
(b) Low temperature
Q9. Draw a graph showing the variation of compressibility factor Z with pressure for a real gas at different temperatures. Label the regions where Z < 1 and Z > 1.
Q10. Explain the significance of Boyle's temperature. What happens to a real gas at its Boyle's temperature?
Q11. Why does CO₂ deviate more from ideal behaviour than H₂ at the same temperature and pressure?
Q12. At very low pressures, all real gases approach ideal behaviour. Explain why.
Section C: Long Answer Questions
Long Answer Questions
Q13. (a) Explain the two main reasons why real gases deviate from ideal gas behaviour.
(b) Define compressibility factor Z and explain how it helps in understanding the deviation of real gases from ideal behaviour.
(c) Draw graphs of Z vs P for:
(i) An ideal gas
(ii) A real gas at temperatures above Boyle's temperature
(iii) A real gas at temperatures below Boyle's temperature
Q14. (a) Explain the effect of the following on the deviation of real gases from ideal behaviour:
(i) Nature of the gas (polar vs non-polar)
(ii) Temperature
(iii) Pressure
(b) Arrange the following gases in order of increasing deviation from ideal behaviour at the same temperature and pressure: H₂, N₂, CO₂, NH₃. Give reasons for your arrangement.
(c) A student claims that at very high pressures, all real gases have Z > 1. Is this always true? Explain.
Q15. (a) Define Boyle's temperature (TB). Derive the expression for TB in terms of van der Waals constants a and b.
(b) Explain what happens to a real gas when it is at:
(i) T = TB
(ii) T > TB
(iii) T < TB
(c) The van der Waals constants for CO₂ are a = 3.59 L²·atm/mol² and b = 0.0427 L/mol. Calculate the Boyle's temperature for CO₂.
Numerical / Application-Based Problems
Q16. One mole of CO₂ gas occupies 0.4 L at 300 K and 40 atm.
(a) Calculate the compressibility factor Z.
(b) Compare this with the volume predicted by the ideal gas equation. What does the value of Z tell you about the behaviour of CO₂ under these conditions?
(c) Calculate the pressure using the van der Waals equation. (a = 3.59 L²·atm/mol², b = 0.0427 L/mol)
(d) Which pressure value (from ideal gas equation or van der Waals equation) is closer to the actual pressure of 40 atm? What does this tell you?
Q17. The following data shows the compressibility factor Z for N₂ gas at 0°C:
| P (atm) | Z |
|---|---|
| 1 | 1.000 |
| 100 | 1.069 |
| 200 | 1.138 |
| 400 | 1.276 |
| 600 | 1.414 |
| 800 | 1.552 |
| 1000 | 1.690 |
a) Plot a graph of Z vs P.
(b) At what pressure range does N₂ show the least deviation from ideal behaviour?
(c) Explain why Z > 1 at high pressures for N₂ at 0°C.
(d) If the temperature is lowered to –100°C, would you expect Z to be greater than or less than 1 at moderate pressures? Explain.
Q18. In India, understanding real gas behaviour is important for industrial applications:
(a) Natural gas (mainly methane) is transported through pipelines at high pressures. Explain why the ideal gas equation cannot be used accurately for calculating the amount of gas in the pipeline. What corrections are needed?
(b) A CNG cylinder is filled with methane at 200 atm and 27°C. The cylinder volume is 60 L. Calculate the mass of methane using:
(i) The ideal gas equation
(ii) The van der Waals equation (a = 2.25 L²·atm/mol², b = 0.0428 L/mol)
Compare the two results and calculate the percentage deviation.
(c) In the production of liquid oxygen for hospitals, O₂ gas is cooled and compressed. Explain why O₂ deviates significantly from ideal behaviour during liquefaction.
(d) A student argues that since air is mostly N₂ and O₂, it can be treated as an ideal gas for all practical purposes. Is this reasoning valid for all conditions? Give examples where this approximation would fail.