NEET Behaviour of Perfect Gas and Kinetic Theory — Set 4

Question 1

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

Accepted Answer

$P = \frac{\mu RT}{V}$, $\frac{P_{\text{He}}}{P_{\text{O}_2}} = \frac{\mu_{\text{He}}}{\mu_{\text{O}_2}}$. $\mu_{\text{He}} = \frac{8}{4} = 2 \, \text{mol}$, $\mu_{\text{O}_2} = \frac{8}{32} = 0.25 \, \text{mol}$. Ratio = $\frac{2}{0.25} = 8:1$.

Question 2

A gas at 3 atm and 600 K has a density of $0.96 \, \text{kg m}^{-3}$. What is its molecular mass? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$, 1 atm = $1.01 \times 10^5 \, \text{Pa}$)

Accepted Answer

$P = \frac{\rho R T}{M}$, $M = \frac{\rho R T}{P}$. $P = 3 \times 1.01 \times 10^5 = 3.03 \times 10^5 \, \text{Pa}$. $M = \frac{0.96 \times 8.31 \times 600}{3.03 \times 10^5} = 0.0158 \, \text{kg/mol} \approx 15.8 \, \text{g/mol} \approx 16 \, \text{g/mol}$.

Question 3

A gas at 2 atm and 400 K has a volume of 10 litres. If the temperature decreases to 100 K at constant pressure, what is the new volume?

Accepted Answer

Charles’ law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$. $V_1 = 10 \, \text{litres}$, $T_1 = 400 \, \text{K}$, $T_2 = 100 \, \text{K}$. $V_2 = V_1 \times \frac{T_2}{T_1} = 10 \times \frac{100}{400} = 2.5 \, \text{litres}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 4

Q1. A gas mixture contains 8 g of helium and 8 g of oxygen. What is the ratio of their partial pressures?

Q2. A gas at 3 atm and 600 K has a density of \(0.96 \, \text{kg m}^{-3}\). What is its molecular mass? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), 1 atm = \(1.01 \times 10^5 \, \text{Pa}\))

Q3. A gas at 2 atm and 400 K has a volume of 10 litres. If the temperature decreases to 100 K at constant pressure, what is the new volume?

Q4. A gas at 2.5 atm and 500 K has a density of \(0.96 \, \text{kg m}^{-3}\). What is its molecular mass? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), 1 atm = \(1.01 \times 10^5 \, \text{Pa}\))

Q5. What is the heat required to raise the temperature of 0.2 moles of a triatomic gas by 10 K at constant volume? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), no vibrational modes)

Q6. A solid has a molar specific heat capacity of \(25.5 \, \text{J mol}^{-1} \text{K}^{-1}\). How many degrees of freedom per atom does it have? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q7. A gas occupies 5.6 litres at STP. How many moles of the gas are present? (Molar volume at STP = 22.4 litres)

Q8. A gas at 1 atm and 273 K has a volume of 8 litres. If the pressure increases to 4 atm at constant temperature, what is the new volume?

Q9. A mixture of 0.2 moles of helium and 0.8 moles of oxygen is at 300 K in a 10-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q10. A gas at 1 atm and 300 K has a volume of 10 litres. If the volume is reduced to 5 litres at constant temperature, what is the new pressure?