NEET Thermodynamics — Set 16

Question 1

For the vaporization of 72 g of water at 373 K ($ \Delta H_{vap} = 40.79 \, \text{kJ/mol} $, molar mass = 18 g/mol), what is $ \Delta S_{sys} $?

Accepted Answer

Moles = $ 72 / 18 = 4 \, \text{mol} $. For vaporization, $ \Delta S_{sys} = n \times \Delta H_{vap} / T = 4 \times 40790 / 373 \approx 437.48 \, \text{J/K} \approx 437.5 \, \text{J/K} $.

Question 2

For $ 2SO_3(g) \rightarrow 2SO_2(g) + O_2(g) $, $ \Delta H = 197.80 \, \text{kJ/mol} $ at 298 K, what is $ \Delta U $? ($ R = 8.314 \, \text{J/mol·K} $)

Accepted Answer

For $ \Delta n_g = 3 - 2 = 1 $, $ RT = 8.314 \times 298 \times 10^{-3} = 2.4776 \, \text{kJ} $. Using $ \Delta H = \Delta U + \Delta n_g RT $, $ \Delta U = 197.80 - 1 \times 2.4776 = 195.32 \, \text{kJ/mol} $.

Question 3

For an ideal gas ($ \gamma = 1.4 $) expanding adiabatically from 5 L to 10 L at 500 K, calculate the work done if $ C_v = 20.785 \, \text{J/mol·K} $. (1 mol gas)

Accepted Answer

For adiabatic expansion, $ T_2 = 500 \times (5/10)^{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} $.

NEET Chemistry: Thermodynamics — Practice Set 16

Q1. For the vaporization of 72 g of water at 373 K (\( \Delta H_{vap} = 40.79 \, \text{kJ/mol} \), molar mass = 18 g/mol), what is \( \Delta S_{sys} \)?

Q2. For \( 2SO_3(g) \rightarrow 2SO_2(g) + O_2(g) \), \( \Delta H = 197.80 \, \text{kJ/mol} \) at 298 K, what is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q3. For an ideal gas (\( \gamma = 1.4 \)) expanding adiabatically from 5 L to 10 L at 500 K, calculate the work done if \( C_v = 20.785 \, \text{J/mol·K} \). (1 mol gas)

Q4. Calculate the work done when 1 mol of an ideal gas expands irreversibly against a constant external pressure of 2 atm from 5 L to 10 L. (1 atm·L = 101.3 J)

Q5. For \( CH_4(g) + Cl_2(g) \rightarrow CH_3Cl(g) + HCl(g) \), \( \Delta H = -103.00 \, \text{kJ/mol} \) at 298 K. What is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q6. For a reaction, \(\Delta H = -150 \, \text{kJ}\) and \(\Delta S = -0.5 \, \text{kJ/K}\). Below what temperature is it spontaneous?

Q7. For the process \(N_2(g) \rightarrow 2N(g)\), what are the signs of \(\Delta H\) and \(\Delta S\)?

Q8. Which property is intensive?

Q9. Calculate \(\Delta H\) for \(C_2H_2(g) + 2H_2(g) \rightarrow C_2H_6(g)\) using: \(\Delta H_f^\circ (C_2H_2,g) = 226.7 \, \text{kJ/mol}\), \(\Delta H_f^\circ (C_2H_6,g) = -84.7 \, \text{kJ/mol}\).

Q10. The enthalpy of vaporization of a liquid is 32.00 kJ/mol at 350 K. What is \( \Delta U \) if \( \Delta n_g = 1 \)? (\( R = 8.314 \, \text{J/mol·K} \))