Chemical Thermodynamics Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A spontaneous process is characterized by:

For a spontaneous process under constant \(T\) and \(p\), Gibbs free energy decreases (\(\Delta G < 0\)).

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

A system at constant pressure releases 800 J of heat and contracts by 0.3 L against 2 atm. What is \( \Delta U \)? (1 atm·L = 101.325 J)

Work done: \( w = -P\Delta V = -2 \times (-0.3) \times 101.325 = 60.795 \, \text{J} \). Given \( q = -800 \, \text{J} \), \( \Delta U = q + w = -800 + 60.795 = -739.21 \approx -739.2 \, \text{J} \).

-800 J
-739.2 J
-860.8 J
-678.4 J
2

What is the standard enthalpy of formation of \(O_2(g)\) at 298 K?

The standard enthalpy of formation of an element in its standard state (e.g., \(O_2(g)\) at 1 bar, 298 K) is zero by definition.

0 kJ/mol
33.2 kJ/mol
-285.8 kJ/mol
90 kJ/mol
1

Calculate the bond enthalpy of \(H-H\) in \(H_2(g)\) given \(\Delta H_f (H,g) = 218 \, \text{kJ/mol}\).

For \(H_2(g) \rightarrow 2H(g)\), \(\Delta H = 2 \times \Delta H_f (H) - \Delta H_f (H_2) = 2 \times 218 - 0 = 436 \, \text{kJ/mol}\), which is the bond enthalpy.

218 kJ/mol
109 kJ/mol
872 kJ/mol
436 kJ/mol
4

A gas absorbs 1200 J of heat at constant pressure, and its volume increases by 0.5 L against 2 atm. What is \( \Delta U \)? (1 atm·L = 101.325 J)

Work done: \( w = -P\Delta V = -2 \times 0.5 \times 101.325 = -101.325 \, \text{J} \). Given \( q = 1200 \, \text{J} \), \( \Delta U = q + w = 1200 - 101.325 = 1098.68 \approx 1098.7 \, \text{J} \).

1200 J
1098.7 J
1301.3 J
998.7 J
2

Which of the following is true for an ideal gas undergoing an irreversible adiabatic expansion against constant external pressure?

For an irreversible adiabatic expansion (\(q = 0\)), \(\Delta U = w = -P_{ext} \Delta V\). Since \(\Delta V > 0\), \(w < 0\), and thus \(\Delta U < 0\).

\(\Delta U < 0\)
\(\Delta H = 0\)
\(\Delta S = 0\)
\(q > 0\)
1

A system undergoes a process where 500 J of heat is released, and 300 J of work is done by the system. What is the change in internal energy (\(\Delta U\))?

\(\Delta U = q + w\). Here, \(q = -500 \, \text{J}\) (heat released), \(w = -300 \, \text{J}\) (work done by system), so \(\Delta U = -500 - 300 = -800 \, \text{J}\).

-800 J
800 J
-200 J
200 J
1

For an ideal gas (\( \gamma = 1.4 \)) compressed adiabatically from 20 L to 5 L at 400 K, calculate \( \Delta U \) if \( C_v = 20.785 \, \text{J/mol·K} \). (1 mol gas)

For adiabatic compression, \( T_2 = 400 \times (20/5)^{0.4} \approx 400 \times 1.741 = 696.4 \, \text{K} \). Then, \( \Delta T = 696.4 - 400 = 296.4 \, \text{K} \). Internal energy change: \( \Delta U = nC_v\Delta T = 1 \times 20.785 \times 296.4 \approx 6160 \, \text{J} \).

-6160 J
3080 J
6160 J
0 J
3

For an ideal gas (\( \gamma = 1.4 \)) expanding adiabatically from 6 L to 12 L at 500 K, calculate the work done if \( C_v = 20.785 \, \text{J/mol·K} \). (1 mol gas)

For adiabatic expansion, \( T_2 = 500 \times (6/12)^{0.4} \approx 500 \times 0.7579 = 378.9 \, \text{K} \). Then, \( \Delta T = 378.9 - 500 = -121.1 \, \text{K} \). Work done: \( w = nC_v\Delta T = 1 \times 20.785 \times (-121.1) \approx -2516 \, \text{J} \).

2516 J
-1258 J
-2516 J
0 J
3

For a reaction with \( \Delta H = 75.00 \, \text{kJ/mol} \) and \( \Delta S = 250.0 \, \text{J/K} \), what is \( \Delta G \) at 350 K?

Using \( \Delta G = \Delta H - T\Delta S \), \( \Delta G = 75.00 - 350 \times 0.2500 = 75.00 - 87.50 = -12.50 \, \text{kJ/mol} \).

87.5 kJ/mol
75 kJ/mol
12.5 kJ/mol
-12.5 kJ/mol
4

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