NEET Thermodynamics — Set 3

Question 1

A system absorbs 1500 J of heat and expands by 0.6 L against 3 atm at constant pressure. What is $ \Delta U $? (1 atm·L = 101.325 J)

Accepted Answer

Work done: $ w = -P\Delta V = -3 \times 0.6 \times 101.325 = -181.985 \, \text{J} $. Heat absorbed: $ q = 1500 \, \text{J} $. Using the first law, $ \Delta U = q + w = 1500 - 181.985 = 1318.0 \, \text{J} $.

Question 2

For a reaction with $ \Delta G^\circ = 13.8 \, \text{kJ/mol} $ at 298 K, what is the equilibrium constant $ K $? ($ R = 8.314 \, \text{J/mol·K} $)

Accepted Answer

Using $ \Delta G^\circ = -RT \ln K $, we get $ 13.8 \times 10^3 = -8.314 \times 298 \times \ln K $. Thus, $ \ln K = -\frac{13.8 \times 10^3}{8.314 \times 298} = -5.57 $, and $ K = e^{-5.57} \approx 0.0038 $.

Question 3

Using bond enthalpies ($C-H = 413 \, \text{kJ/mol}$, $O=O = 498 \, \text{kJ/mol}$, $C=O = 803 \, \text{kJ/mol}$, $O-H = 467 \, \text{kJ/mol}$), calculate $\Delta H$ for $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$.

Accepted Answer

Bonds broken: $4(C-H) + 2(O=O) = 4 \times 413 + 2 \times 498 = 1652 + 996 = 2648 \, \text{kJ}$. Bonds formed: $2(C=O) + 4(O-H) = 2 \times 803 + 4 \times 467 = 1606 + 1868 = 3474 \, \text{kJ}$. $\Delta H = 2648 - 3474 = -826 \, \text{kJ/mol}$.

NEET Chemistry: Thermodynamics — Practice Set 3

Q1. A system absorbs 1500 J of heat and expands by 0.6 L against 3 atm at constant pressure. What is \( \Delta U \)? (1 atm·L = 101.325 J)

Q2. For a reaction with \( \Delta G^\circ = 13.8 \, \text{kJ/mol} \) at 298 K, what is the equilibrium constant \( K \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q3. Using bond enthalpies (\(C-H = 413 \, \text{kJ/mol}\), \(O=O = 498 \, \text{kJ/mol}\), \(C=O = 803 \, \text{kJ/mol}\), \(O-H = 467 \, \text{kJ/mol}\)), calculate \(\Delta H\) for \(CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)\).

Q4. What is the work done during the free expansion of an ideal gas into a vacuum?

Q5. For a reaction with \(\Delta H = 60 \, \text{kJ/mol}\) and \(\Delta S = 150 \, \text{J/K}\), what is \(\Delta G\) at 400 K?

Q6. For a reaction with \(\Delta H = 100 \, \text{kJ/mol}\) and \(\Delta S = 200 \, \text{J/K}\), at what temperature does \(\Delta G = 0\)?

Q7. For a reaction with \(\Delta H = 75 \, \text{kJ}\) and \(\Delta S = 150 \, \text{J/K}\), above what temperature is it spontaneous?

Q8. Calculate the heat absorbed when 36 g of ice melts at 0°C. (\(\Delta H_{fus} = 6.01 \, \text{kJ/mol}\), molar mass of \(H_2O = 18 \, \text{g/mol}\))

Q9. Calculate the heat absorbed when 50 g of copper is heated from 25°C to 125°C at constant volume. (\(C_v = 22.6 \, \text{J/mol·K}\), molar mass = 63.5 g/mol)

Q10. Calculate the heat absorbed when 40 g of iron is heated from 20°C to 100°C at constant pressure. (\(C_p = 25.1 \, \text{J/mol·K}\), molar mass = 56 g/mol)