Behaviour of Perfect Gas and Kinetic Theory Chapter-Wise Test 9

Correct answer Carries: 4.

Wrong Answer Carries: -1.

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

Triatomic gas: 6 degrees of freedom, \(C_v = 3 R\).

\(Q = \mu C_v \Delta T = 0.15 \times 3 \times 8.31 \times 25 = 93.4875 \, \text{J} \approx 93.5 \, \text{J}\).

62.3 J
93.5 J
124.7 J
155.8 J
2

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

Triatomic gas: 6 degrees of freedom, \(C_v = 3R\).

\(Q = \mu C_v \Delta T = 0.3 \times 3 \times 8.31 \times 15 = 112.185 \, \text{J} \approx 112.2 \, \text{J}\).

74.8 J
112.2 J
149.6 J
187.0 J
2

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)

\(v_{\text{rms}} \propto \frac{1}{\sqrt{m}}\), \(\frac{v_{\text{He}}}{v_{\text{Ar}}} = \sqrt{\frac{m_{\text{Ar}}}{m_{\text{He}}}} = \sqrt{\frac{39.9}{4}} \approx \sqrt{10} \approx 3.16\).

1:3.16
1:1
3.16:1
10:1
3

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

Average translational KE = \(\frac{3}{2} k_B T\).

\(\frac{3}{2} \times 1.38 \times 10^{-23} \times 1000 = 2.07 \times 10^{-20} \, \text{J}\).

\(1.656 \times 10^{-20} \, \text{J}\)
\(1.863 \times 10^{-20} \, \text{J}\)
\(2.07 \times 10^{-20} \, \text{J}\)
\(2.484 \times 10^{-20} \, \text{J}\)
3

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

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

Total moles = \(0.3 + 0.7 = 1.0\), \(V = 20 \times 10^{-3} \, \text{m}^3\).

\(P = \frac{1.0 \times 8.31 \times 350}{20 \times 10^{-3}} = 1.45575 \times 10^5 \, \text{Pa} \approx 1.46 \, \text{atm}\).

1.00 atm
1.46 atm
2.00 atm
2.50 atm
2

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

\(v_{\text{rms}} = \sqrt{\frac{3k_B T}{m}}\), \(m = \frac{39.9 \times 10^{-3}}{6.02 \times 10^{23}} = 6.63 \times 10^{-26} \, \text{kg}\).

\(860^2 = \frac{3 \times 1.38 \times 10^{-23} \times T}{6.63 \times 10^{-26}}\), \(T = \frac{7.396 \times 10^5 \times 6.63 \times 10^{-26}}{4.14 \times 10^{-23}} \approx 1185 \, \text{K}\).

900 K
1200 K
1500 K
1800 K
2

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

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

\(\mu_{\text{He}} = \frac{8}{4} = 2 \, \text{mol}\), \(\mu_{\text{O}_2} = \frac{64}{32} = 2 \, \text{mol}\).

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

1:2
1:1
2:1
4:1
2

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

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

\(\mu_{\text{O}_2} = \frac{16}{32} = 0.5 \, \text{mol}\), \(\mu_{\text{H}_2} = \frac{4}{2} = 2 \, \text{mol}\).

Ratio = \(\frac{0.5}{2} = 1:4\).

1:4
1:2
2:1
4:1
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?

Boyle’s law: \(P_1 V_1 = P_2 V_2\).

\(P_1 = 2.5 \, \text{atm}\), \(V_1 = 12 \, \text{litres}\), \(P_2 = 5 \, \text{atm}\).

\(V_2 = \frac{P_1 V_1}{P_2} = \frac{2.5 \times 12}{5} = 6 \, \text{litres}\).

3 litres
6 litres
9 litres
12 litres
2

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 \(C_v\)?

For an ideal gas: \(C_p - C_v = R\), where \(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\).

\(C_v = C_p - R = 20.8 - 8.31 = 12.49 \, \text{J mol}^{-1} \text{K}^{-1} \approx 12.5 \, \text{J mol}^{-1} \text{K}^{-1} \).

12.5 J mol⁻¹ K⁻¹
16.6 J mol⁻¹ K⁻¹
20.8 J mol⁻¹ K⁻¹
25.0 J mol⁻¹ K⁻¹
1

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