NEET Thermodynamics — Set 11

Question 1

For $ H_2O(l) \rightarrow H_2(g) + \frac{1}{2}O_2(g) $, $ \Delta H = 285.80 \, \text{kJ/mol} $ at 298 K. What is $ \Delta U $? ($ R = 8.314 \, \text{J/mol·K} $)

Accepted Answer

For $ \Delta n_g = 1.5 - 0 = 1.5 $, $ RT = 8.314 \times 298 \times 10^{-3} = 2.4776 \, \text{kJ} $. Using $ \Delta H = \Delta U + \Delta n_g RT $, $ \Delta U = 285.80 - 1.5 \times 2.4776 = 285.80 - 3.7164 = 282.08 \, \text{kJ/mol} $.

Question 2

For an ideal gas ($\gamma = 1.5$) expanding adiabatically from 10 L to 25 L at 600 K, what is the final temperature?

Accepted Answer

$T_2 = T_1 (V_1/V_2)^{\gamma-1} = 600 \times (10/25)^{0.5} = 600 \times (0.4)^{0.5} = 600 \times 0.632 = 379.2 \, \text{K}$.

Question 3

For a reaction with $ \Delta H = -80.00 \, \text{kJ/mol} $ and $ \Delta S = -200.0 \, \text{J/K·mol} $, what is $ \Delta G $ at 300 K?

Accepted Answer

$ \Delta G = \Delta H - T\Delta S = -80.00 - 300 \times (-0.2000) = -80.00 + 60.00 = -20.00 \, \text{kJ/mol} $. The negative $ \Delta G $ indicates spontaneity at 300 K.

NEET Chemistry: Thermodynamics — Practice Set 11

Q1. For \( H_2O(l) \rightarrow H_2(g) + \frac{1}{2}O_2(g) \), \( \Delta H = 285.80 \, \text{kJ/mol} \) at 298 K. What is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q2. For an ideal gas (\(\gamma = 1.5\)) expanding adiabatically from 10 L to 25 L at 600 K, what is the final temperature?

Q3. For a reaction with \( \Delta H = -80.00 \, \text{kJ/mol} \) and \( \Delta S = -200.0 \, \text{J/K·mol} \), what is \( \Delta G \) at 300 K?

Q4. For the process \( 2NO_2(g) \rightarrow N_2O_4(g) \), \( \Delta H = -57.20 \, \text{kJ/mol} \) at 298 K, what is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q5. Calculate \(\Delta S\) for the fusion of 36 g of ice at 273 K if \(\Delta H_{fus} = 6.01 \, \text{kJ/mol}\). (Molar mass of \(H_2O = 18 \, \text{g/mol}\))

Q6. For which process is \(\Delta H = \Delta U\)?

Q7. Calculate the heat absorbed when 27 g of aluminum is heated from 25°C to 125°C at constant volume. (\(C_v = 22.4 \, \text{J/mol·K}\), molar mass = 27 g/mol)

Q8. Calculate \(\Delta G^\circ\) for a reaction with \(K = 1.5 \times 10^{-4}\) at 298 K. (\(R = 8.314 \, \text{J/mol·K}\))

Q9. For a reaction with \(K = 0.01\) at 298 K, calculate \(\Delta G^\circ\). (\(R = 8.314 \, \text{J/mol·K}\))

Q10. For an adiabatic process, which condition must be satisfied?