NEET Behaviour of Perfect Gas and Kinetic Theory — Set 10

Question 1

A gas at 1 atm and 273 K has a density of $1.43 \, \text{kg m}^{-3}$. 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

$P = \frac{\rho R T}{M}$, $M = \frac{\rho R T}{P}$. $M = \frac{1.43 \times 8.31 \times 273}{1.01 \times 10^5} = 0.0321 \, \text{kg/mol} \approx 32.1 \, \text{g/mol}$.

Question 2

A gas has a $C_v$ of $21.0 \, \text{J mol}^{-1} \text{K}^{-1}$. What is its $C_p$? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

$C_p = C_v + R$. $C_p = 21.0 + 8.31 = 29.31 \, \text{J mol}^{-1} \text{K}^{-1} \approx 29.3 \, \text{J mol}^{-1} \text{K}^{-1}$.

Question 3

What is the time between collisions for a gas molecule with a mean free path of $4.5 \times 10^{-7} \, \text{m}$ and average speed of 450 m/s?

Accepted Answer

$\tau = \frac{l}{ } = \frac{4.5 \times 10^{-7}}{450} = 1.0 \times 10^{-9} \, \text{s}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 10

Q1. A gas at 1 atm and 273 K has a density of \(1.43 \, \text{kg m}^{-3}\). What is its molecular mass? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), 1 atm = \(1.01 \times 10^5 \, \text{Pa}\))

Q2. A gas has a \(C_v\) of \(21.0 \, \text{J mol}^{-1} \text{K}^{-1}\). What is its \(C_p\)? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q3. What is the time between collisions for a gas molecule with a mean free path of \(4.5 \times 10^{-7} \, \text{m}\) and average speed of 450 m/s?

Q4. How much heat is required to raise the temperature of 0.5 moles of neon by 25 K at constant volume? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q5. How many degrees of freedom does a diatomic molecule have if its vibrational mode is active?

Q6. What is the average translational kinetic energy of a neon atom at 800 K? (\(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q7. What is the collision frequency of a gas molecule if its mean free path is \(2 \times 10^{-7} \, \text{m}\) and average speed is 500 m/s?

Q8. A gas mixture has equal masses of neon and nitrogen at 300 K. What is the ratio of their rms speeds? (Atomic mass: Ne = 20.2 u, \(N_2 = 28 \, \text{u}\))

Q9. A gas occupies 33.6 litres at STP. How many molecules are present? (\(N_A = 6.02 \times 10^{23} \, \text{mol}^{-1}\), molar volume at STP = 22.4 litres)

Q10. A vessel contains 1 mole of a diatomic gas at 300 K. What is its total internal energy if vibrational modes are not excited? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))