Behaviour of Perfect Gas and Kinetic Theory Chapter-Wise Test 4

Correct answer Carries: 4.

Wrong Answer Carries: -1.

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?

Charles’ law: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\).

\(V_1 = 10 \, \text{litres}\), \(T_1 = 400 \, \text{K}\), \(T_2 = 100 \, \text{K}\).

\(V_2 = V_1 \times \frac{T_2}{T_1} = 10 \times \frac{100}{400} = 2.5 \, \text{litres}\).

2.5 litres
5.0 litres
7.5 litres
10.0 litres
1

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 = \(1.01 \times 10^5 \, \text{Pa}\))

\(P = \frac{\rho R T}{M}\), \(M = \frac{\rho R T}{P}\).

\(P = 2.5 \times 1.01 \times 10^5 = 2.525 \times 10^5 \, \text{Pa}\).

\(M = \frac{0.96 \times 8.31 \times 500}{2.525 \times 10^5} = 0.0158 \, \text{kg/mol} \approx 15.8 \, \text{g/mol} \approx 16 \, \text{g/mol}\).

12 g/mol
16 g/mol
20 g/mol
24 g/mol
2

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?

Boyle’s law: \(P_1 V_1 = P_2 V_2\).

\(P_1 = 1 \, \text{atm}\), \(V_1 = 8 \, \text{litres}\), \(P_2 = 4 \, \text{atm}\).

\(V_2 = \frac{P_1 V_1}{P_2} = \frac{1 \times 8}{4} = 2 \, \text{litres}\).

2 litres
4 litres
6 litres
8 litres
1

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?

Boyle’s law: \(P_1 V_1 = P_2 V_2\).

\(P_1 = 1 \, \text{atm}\), \(V_1 = 10 \, \text{litres}\), \(V_2 = 5 \, \text{litres}\).

\(P_2 = \frac{P_1 V_1}{V_2} = \frac{1 \times 10}{5} = 2 \, \text{atm} \).

0.5 atm
1.0 atm
1.5 atm
2.0 atm
4

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? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

\(PV = \mu R T\), \(P = \frac{\mu R T}{V}\).

Total moles = \(0.2 + 0.8 = 1.0\), \(V = 10 \times 10^{-3} \, \text{m}^3\).

\(P = \frac{1.0 \times 8.31 \times 300}{10 \times 10^{-3}} = 2.493 \times 10^5 \, \text{Pa} \approx 2.49 \, \text{atm}\).

1.50 atm
2.00 atm
2.49 atm
3.00 atm
3

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? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

\(C = f \times \frac{R}{2}\), \(25.5 = f \times \frac{8.31}{2}\).

\(f = \frac{25.5 \times 2}{8.31} \approx 6.14 \approx 6\).

4
5
6
7
3

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

Number of moles (\(\mu\)) = \(\frac{\text{Volume}}{\text{Molar volume}}\).

\(\mu = \frac{5.6}{22.4} = 0.25 \, \text{mol}\).

0.15 mol
0.25 mol
0.50 mol
1.00 mol
2

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

\(P = \frac{\mu RT}{V}\), \(\frac{P_{\text{He}}}{P_{\text{O}_2}} = \frac{\mu_{\text{He}}}{\mu_{\text{O}_2}}\).

\(\mu_{\text{He}} = \frac{8}{4} = 2 \, \text{mol}\), \(\mu_{\text{O}_2} = \frac{8}{32} = 0.25 \, \text{mol}\).

Ratio = \(\frac{2}{0.25} = 8:1\).

1:4
1:1
4:1
8:1
4

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)

Triatomic gas: 6 degrees of freedom (3 translational + 3 rotational).

\(C_v = 3R\), \(Q = \mu C_v \Delta T = 0.2 \times 3 \times 8.31 \times 10 = 49.86 \, \text{J} \).

33.24 J
49.86 J
66.48 J
83.10 J
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 = \(1.01 \times 10^5 \, \text{Pa}\))

\(P = \frac{\rho R T}{M}\), \(M = \frac{\rho R T}{P}\).

\(P = 3 \times 1.01 \times 10^5 = 3.03 \times 10^5 \, \text{Pa}\).

\(M = \frac{0.96 \times 8.31 \times 600}{3.03 \times 10^5} = 0.0158 \, \text{kg/mol} \approx 15.8 \, \text{g/mol} \approx 16 \, \text{g/mol}\).

12 g/mol
16 g/mol
20 g/mol
24 g/mol
2

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