NEET Thermodynamics — Set 12

Question 1

Calculate the bond enthalpy of $O=O$ in $O_2(g)$ given: $\Delta H_f^\circ (H_2O,g) = -241.8 \, \text{kJ/mol}$, $H-H = 436 \, \text{kJ/mol}$, $O-H = 463 \, \text{kJ/mol}$.

Accepted Answer

For $H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(g)$, $\Delta H = -241.8 \, \text{kJ}$. Bonds broken: $H-H (436) + \frac{1}{2}O=O$. Bonds formed: $2(O-H) = 2 \times 463 = 926$. $\Delta H = (436 + \frac{1}{2}O=O) - 926 = -241.8$, $\frac{1}{2}O=O = 248.2$, $O=O = 496.4 \, \text{kJ/mol}$.

Question 2

Which of the following statements is true for a reversible adiabatic expansion of an ideal gas?

Accepted Answer

In a reversible adiabatic process ($q = 0$), $\Delta U = w$. For an ideal gas, $\Delta U = nC_v\Delta T$, and since expansion cools the gas, $\Delta T < 0$, making $\Delta U < 0$.

Question 3

For an ideal gas expanding irreversibly against a constant external pressure of 1 atm from 2 L to 5 L, calculate the work done. (1 atm·L = 101.3 J)

Accepted Answer

$w = -P_{ext} \Delta V = -1 \times (5 - 2) \times 101.3 = -1 \times 3 \times 101.3 = -303.9 \, \text{J}$.

NEET Chemistry: Thermodynamics — Practice Set 12

Q1. Calculate the bond enthalpy of \(O=O\) in \(O_2(g)\) given: \(\Delta H_f^\circ (H_2O,g) = -241.8 \, \text{kJ/mol}\), \(H-H = 436 \, \text{kJ/mol}\), \(O-H = 463 \, \text{kJ/mol}\).

Q2. Which of the following statements is true for a reversible adiabatic expansion of an ideal gas?

Q3. For an ideal gas expanding irreversibly against a constant external pressure of 1 atm from 2 L to 5 L, calculate the work done. (1 atm·L = 101.3 J)

Q4. For \( N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \), \( \Delta H = -92.20 \, \text{kJ/mol} \) at 298 K. What is \( \Delta U \)? (\( R = 8.314 \, \text{J/mol·K} \))

Q5. Calculate \(\Delta S_{total}\) when 2 mol of water vapor condenses at 373 K if \(\Delta H_{vap} = 40.79 \, \text{kJ/mol}\).

Q6. A reaction has \(\Delta H = -200 \, \text{kJ/mol}\) and \(\Delta S = -250 \, \text{J/K}\). At what temperature does it cease to be spontaneous?

Q7. Calculate the bond enthalpy of \( N≡N \) in \( N_2(g) \) given: \( \Delta H_f^\circ (NH_3,g) = -46.10 \, \text{kJ/mol} \), \( N-H = 391.0 \, \text{kJ/mol} \), \( \Delta H_a (H,g) = 218.0 \, \text{kJ/mol} \).

Q8. The heat released when 12 g of carbon is burnt in excess oxygen is: (\(\Delta H_c = -393.5 \, \text{kJ/mol}\), molar mass of \(C = 12 \, \text{g/mol}\))

Q9. For an ideal gas (\( \gamma = 1.67 \)) compressed adiabatically from \(V_1 = 12\,\text{L}\) to \(V_2 = 3\,\text{L}\), starting at \(T_1 = 300\,\text{K}\), calculate the work done on the gas if \( C_v = 12.47 \, \text{J mol}^{-1}\text{K}^{-1} \). (Assume \(n=1\) mol.)

Q10. For the reaction \(N_2(g) + 2O_2(g) \rightarrow 2NO_2(g)\), \(\Delta H = 66.4 \, \text{kJ/mol}\) at 298 K, what is \(\Delta U\)? (\(R = 8.314 \, \text{J/mol·K}\))