NEET Behaviour of Perfect Gas and Kinetic Theory — Set 9

Question 1

A gas at 2.5 atm and 500 K has a volume of 12 litres. If the pressure increases to 5 atm at constant temperature, what is the new volume?

Accepted Answer

Boyle’s law: $P_1 V_1 = P_2 V_2$. $P_1 = 2.5 \, \text{atm}$, $V_1 = 12 \, \text{litres}$, $P_2 = 5 \, \text{atm}$. $V_2 = \frac{P_1 V_1}{P_2} = \frac{2.5 \times 12}{5} = 6 \, \text{litres}$.

Question 2

A gas mixture contains 16 g of oxygen and 4 g of hydrogen. What is the ratio of their partial pressures?

Accepted Answer

$P = \frac{\mu RT}{V}$, $\frac{P_{\text{O}_2}}{P_{\text{H}_2}} = \frac{\mu_{\text{O}_2}}{\mu_{\text{H}_2}}$. $\mu_{\text{O}_2} = \frac{16}{32} = 0.5 \, \text{mol}$, $\mu_{\text{H}_2} = \frac{4}{2} = 2 \, \text{mol}$. Ratio = $\frac{0.5}{2} = 1:4$.

Question 3

How much heat is required to raise the temperature of 0.15 moles of a triatomic gas by 25 K at constant volume, with no vibrational modes? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

Triatomic gas: 6 degrees of freedom, $C_v = 3 R$. $Q = \mu C_v \Delta T = 0.15 \times 3 \times 8.31 \times 25 = 93.4875 \, \text{J} \approx 93.5 \, \text{J}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 9

Q1. A gas at 2.5 atm and 500 K has a volume of 12 litres. If the pressure increases to 5 atm at constant temperature, what is the new volume?

Q2. A gas mixture contains 16 g of oxygen and 4 g of hydrogen. What is the ratio of their partial pressures?

Q3. How much heat is required to raise the temperature of 0.15 moles of a triatomic gas by 25 K at constant volume, with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q4. A monatomic gas has a molar specific heat at constant pressure of \(20.8 \, \text{J mol}^{-1} \text{K}^{-1}\). What is the value of \(C_v\)?

Q5. A gas mixture has equal volumes of helium and argon at the same temperature and pressure. What is the ratio of their rms speeds? (Atomic mass: He = 4 u, Ar = 39.9 u)

Q6. At what temperature is the rms speed of argon molecules 860 m/s? (Atomic mass of Ar = 39.9 u, \(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q7. How much heat is required to raise the temperature of 0.3 moles of a triatomic gas by 15 K at constant volume, ignoring vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q8. What is the average translational kinetic energy of a nitrogen molecule at 1000 K? (\(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q9. A gas mixture contains 8 g of helium and 64 g of oxygen. What is the ratio of their partial pressures?

Q10. A mixture of 0.3 moles of nitrogen and 0.7 moles of argon is at 350 K in a 20-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))