Behavior Of Perfect Gas And Kinetic Theory Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

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

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

\(\mu = \frac{16.8}{22.4} = 0.75 \, \text{mol}\).

0.50 mol
0.75 mol
1.00 mol
1.25 mol
2

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)

\(P = \frac{\mu RT}{V}\), \(\frac{P_{\text{Ne}}}{P_{\text{Ar}}} = \frac{\mu_{\text{Ne}}}{\mu_{\text{Ar}}}\).

\(\mu_{\text{Ne}} = \frac{10}{20.2} \approx 0.495 \, \text{mol}\), \(\mu_{\text{Ar}} = \frac{40}{39.9} \approx 1.0025 \, \text{mol}\).

Ratio = \(\frac{0.495}{1.0025} \approx 0.494 \approx 1:2\).

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

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

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

\(\mu_{\text{H}_2} = \frac{6}{2} = 3 \, \text{mol}\), \(\mu_{\text{O}_2} = \frac{48}{32} = 1.5 \, \text{mol}\).

Ratio = \(\frac{3}{1.5} = 2:1\).

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

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

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

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

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

1:4
1:2
1:1
2:1
3

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?

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

\(V_1 = 5 \, \text{litres}\), \(T_1 = 300 \, \text{K}\), \(T_2 = 600 \, \text{K}\).

\(V_2 = V_1 \times \frac{T_2}{T_1} = 5 \times \frac{600}{300} = 10 \, \text{litres}\).

2.5 litres
5.0 litres
7.5 litres
10.0 litres
4

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

\(C = f \times \frac{R}{2}\), \(26.5 = f \times \frac{8.31}{2}\).

\(f = \frac{26.5 \times 2}{8.31} \approx 6.38 \approx 6\).

4
5
6
7
3

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

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

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

\(M = \frac{1.44 \times 8.31 \times 600}{3.03 \times 10^5} = 0.0237 \, \text{kg/mol} \approx 23.7 \, \text{g/mol} \approx 24 \, \text{g/mol}\).

20 g/mol
24 g/mol
28 g/mol
32 g/mol
2

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)

\(v_{\text{rms}} \propto \frac{1}{\sqrt{m}}\), \(\frac{v_{\text{He}}}{v_{\text{O}_2}} = \sqrt{\frac{m_{\text{O}_2}}{m_{\text{He}}}}\).

\(\frac{v_{\text{He}}}{482} = \sqrt{\frac{32}{4}} = \sqrt{8} \approx 2.828\).

\(v_{\text{He}} = 482 \times 2.828 \approx 1363 \, \text{m/s}\).

964 m/s
1200 m/s
1363 m/s
1500 m/s
3

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

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

\(T = 227 + 273 = 500 \, \text{K}\), \(P = 1.5 \times 1.01 \times 10^5 = 1.515 \times 10^5 \, \text{Pa}\).

\(V = \frac{0.2 \times 8.31 \times 500}{1.515 \times 10^5} = 5.485 \times 10^{-3} \, \text{m}^3 \approx 5.49 \, \text{litres}\).

4.50 litres
5.49 litres
6.00 litres
7.50 litres
2

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

\(C_v = C_p - R\).

\(C_v = 28.8 - 8.31 = 20.49 \, \text{J mol}^{-1} \text{K}^{-1} \approx 20.5 \, \text{J mol}^{-1} \text{K}^{-1}\).

20.5 J mol⁻¹ K⁻¹
24.9 J mol⁻¹ K⁻¹
27.1 J mol⁻¹ K⁻¹
29.3 J mol⁻¹ K⁻¹
1

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