Thermodynamics Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Calculate \( \Delta S_{sys} \) for the vaporization of 36 g of ethanol at 351 K if \( \Delta H_{vap} = 38.6 \, \text{kJ/mol} \). (Molar mass of \( C_2H_5OH = 46.07 \, \text{g/mol} \))

Moles = \( 36 / 46.07 \approx 0.7812 \, \text{mol} \). For vaporization, \( \Delta S_{sys} = n \times \Delta H_{vap} / T = 0.7812 \times 38.6 \times 10^3 / 351 \approx 86.0 \, \text{J/K} \).

110.0 J/K
38.6 J/K
86.0 J/K
43.0 J/K
3

For an ideal gas (\(\gamma = 1.67\)) compressed adiabatically from 10 L to 2 L at 300 K, what is the final temperature?

\(T_2 = T_1 (V_1/V_2)^{\gamma-1} = 300 \times (10/2)^{0.67} = 300 \times 5^{0.67} = 300 \times 2.63 = 789 \, \text{K}\).

60 K
526 K
789 K
1500 K
3

Calculate the heat absorbed when 54 g of water is heated from 20°C to 80°C at constant pressure. (\(C_p = 75.3 \, \text{J/mol·K}\), molar mass = 18 g/mol)

Moles = \(54 / 18 = 3 \, \text{mol}\), \(\Delta T = 80 - 20 = 60 \, \text{K}\), \(q_p = nC_p\Delta T = 3 \times 75.3 \times 60 = 13554 \, \text{J} = 13.55 \, \text{kJ}\).

4.52 kJ
75.3 kJ
9.03 kJ
13.55 kJ
4

The enthalpy change for vaporization of 1 mol of water at 373 K is 40.79 kJ/mol. What is \( \Delta U \) if water vapor behaves as an ideal gas? (\( R = 8.314 \, \text{J/mol·K} \))

For \( H_2O(l) \rightarrow H_2O(g) \), \( \Delta n_g = 1 \). Using \( \Delta H = \Delta U + \Delta n_g RT \), where \( RT = 8.314 \times 373 \times 10^{-3} = 3.1012 \, \text{kJ} \), \( \Delta U = 40.79 - 3.1012 = 37.69 \, \text{kJ/mol} \).

40.79 kJ/mol
37.7 kJ/mol
43.9 kJ/mol
34.6 kJ/mol
2

For \(H_2(g) + Br_2(g) \rightarrow 2HBr(g)\), \(\Delta H = -72.6 \, \text{kJ/mol}\), \(\Delta S = 114 \, \text{J/K}\) at 298 K. What is \(\Delta G\)?

\(\Delta G = \Delta H - T\Delta S = -72.6 - 298 \times 0.114 = -72.6 - 33.97 = -106.57 \, \text{kJ/mol}\).

72.6 kJ/mol
-33.97 kJ/mol
106.57 kJ/mol
-106.6 kJ/mol
4

Calculate \(\Delta H\) for \(C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)\) using bond enthalpies: \(C=C = 610 \, \text{kJ/mol}\), \(H-H = 436 \, \text{kJ/mol}\), \(C-H = 413 \, \text{kJ/mol}\), \(C-C = 346 \, \text{kJ/mol}\).

Bonds broken: \(C=C (610) + H-H (436) = 1046 \, \text{kJ}\). Bonds formed: \(C-C (346) + 2 \times C-H (2 \times 413 = 826) = 1172 \, \text{kJ}\). \(\Delta H = 1046 - 1172 = -126 \, \text{kJ/mol}\).

126 kJ/mol
610 kJ/mol
-126 kJ/mol
-436 kJ/mol
3

For a reaction with \(\Delta G^\circ = -25.7 \, \text{kJ/mol}\) at 298 K, calculate \(K\). (\(R = 8.314 \, \text{J/mol·K}\))

\(\Delta G^\circ = -RT \ln K\), \(-25.7 \times 10^3 = -8.314 \times 298 \times \ln K\), \(\ln K = 10.37\), \(K = e^{10.37} \approx 31800\).

0.00318
10
1000
31800
4

The enthalpy of combustion of methane is -890 kJ/mol. What is the heat released when 8 g of methane is burnt? (Molar mass of \(CH_4 = 16 \, \text{g/mol}\))

Moles of \(CH_4 = 8 / 16 = 0.5 \, \text{mol}\). Heat released = \(0.5 \times 890 = 445 \, \text{kJ}\).

890 kJ
445 kJ
1780 kJ
222.5 kJ
2

The standard enthalpy change for \(2C(s) + 2H_2(g) \rightarrow C_2H_4(g)\) is 52.3 kJ/mol. What is \(\Delta H_f^\circ\) of \(C_2H_4(g)\)?

The reaction forms 1 mol of \(C_2H_4(g)\) from its elements in standard states, so \(\Delta H = \Delta H_f^\circ (C_2H_4) = 52.3 \, \text{kJ/mol}\), as \(\Delta H_f^\circ (C) = 0\) and \(\Delta H_f^\circ (H_2) = 0\).

52.3 kJ/mol
26.15 kJ/mol
-52.3 kJ/mol
104.6 kJ/mol
1

Which of the following is true for an endothermic process where \(\Delta S < 0\)?

For an endothermic process, \(\Delta H > 0\). If \(\Delta S < 0\), then \(T\Delta S < 0\), and \(\Delta G = \Delta H - T\Delta S > 0\), making the process non-spontaneous at all temperatures.

\(\Delta G > 0\)
\(\Delta G < 0\)
\(\Delta U = 0\)
\(\Delta H < 0\)
1

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