NEET Behaviour of Perfect Gas and Kinetic Theory — Set 19

Question 1

A gas occupies 16.8 litres at STP. How many moles are present? (Molar volume at STP = 22.4 litres)

Accepted Answer

Number of moles ($\mu$) = $\frac{\text{Volume}}{\text{Molar volume}}$. $\mu = \frac{16.8}{22.4} = 0.75 \, \text{mol}$.

Question 2

A gas at 3 atm and 600 K has a density of $1.44 \, \text{kg m}^{-3}$. 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

$P = \frac{\rho R T}{M}$, $M = \frac{\rho R T}{P}$. $P = 3 \times 1.01 \times 10^5 = 3.03 \times 10^5 \, \text{Pa}$. $M = \frac{1.44 \times 8.31 \times 600}{3.03 \times 10^5} = 0.0237 \, \text{kg/mol} \approx 23.7 \, \text{g/mol} \approx 24 \, \text{g/mol}$.

Question 3

The rms speed of oxygen molecules is 482 m/s at 300 K. What is the rms speed of helium molecules at the same temperature? (Molecular mass: $O_2 = 32 \, \text{u}$, He = 4 u)

Accepted Answer

$v_{\text{rms}} \propto \frac{1}{\sqrt{m}}$, $\frac{v_{\text{He}}}{v_{\text{O}_2}} = \sqrt{\frac{m_{\text{O}_2}}{m_{\text{He}}}}$. $\frac{v_{\text{He}}}{482} = \sqrt{\frac{32}{4}} = \sqrt{8} \approx 2.828$. $v_{\text{He}} = 482 \times 2.828 \approx 1363 \, \text{m/s}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 19

Q1. A gas occupies 16.8 litres at STP. How many moles are present? (Molar volume at STP = 22.4 litres)

Q2. A gas at 3 atm and 600 K has a density of \(1.44 \, \text{kg m}^{-3}\). 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. The rms speed of oxygen molecules is 482 m/s at 300 K. What is the rms speed of helium molecules at the same temperature? (Molecular mass: \(O_2 = 32 \, \text{u}\), He = 4 u)

Q4. What is the volume of 0.2 moles of an ideal gas at 1.5 atm and 227°C? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q5. A gas mixture contains 6 g of hydrogen and 48 g of oxygen. What is the ratio of their partial pressures?

Q6. A gas mixture has 2 g of helium and 16 g of oxygen. What is the ratio of their partial pressures?

Q7. A gas mixture contains 10 g of neon and 40 g of argon. What is the ratio of their partial pressures? (Atomic mass: Ne = 20.2 u, Ar = 39.9 u)

Q8. A solid has a molar specific heat capacity of \(26.5 \, \text{J mol}^{-1} \text{K}^{-1}\). How many degrees of freedom per atom does it have? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q9. A gas has a \(C_p\) of \(28.8 \, \text{J mol}^{-1} \text{K}^{-1}\). What is its \(C_v\)? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q10. A gas at 2 atm and 300 K has a volume of 5 litres. If the temperature rises to 600 K at constant pressure, what is the new volume?