NEET Thermodynamics — Set 10

Question 1

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} $)

Accepted Answer

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} $.

Question 2

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} $)

Accepted Answer

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} $.

Question 3

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 $C_2H_4(g)$?

Accepted Answer

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 $\Delta H_f^\circ (H_2) = 0$.

NEET Chemistry: Thermodynamics — Practice Set 10

Q1. 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? (\( R = 8.314 \, \text{J/mol·K} \))

Q2. 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 \( C_2H_5OH = 46.07 \, \text{g/mol} \))

Q3. 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 \(C_2H_4(g)\)?

Q4. Calculate \(\Delta H\) for \(C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)\) using bond enthalpies: \(C=C = 610 \, \text{kJ/mol}\), \(H-H = 436 \, \text{kJ/mol}\), \(C-H = 413 \, \text{kJ/mol}\), \(C-C = 346 \, \text{kJ/mol}\).

Q5. 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 \(CH_4 = 16 \, \text{g/mol}\))

Q6. 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 \(\Delta G\)?

Q7. For a reaction with \(\Delta G^\circ = -25.7 \, \text{kJ/mol}\) at 298 K, calculate \(K\). (\(R = 8.314 \, \text{J/mol·K}\))

Q8. Which of the following is true for an endothermic process where \(\Delta S < 0\)?

Q9. 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)

Q10. For an ideal gas (\(\gamma = 1.67\)) compressed adiabatically from 10 L to 2 L at 300 K, what is the final temperature?