Question

For which reaction \( \Delta H \neq \Delta U \)?

• A. \( H_2(g) + I_2(g) \longrightarrow 2HI(g) \)
• B. \( 2NO(g) \longrightarrow N_2(g) + O_2(g) \)
• C. \( N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g) \)
• D. \( C(s) + O_2(g) \longrightarrow CO_2(g) \)

Hint:

Use the equation \( \Delta H = \Delta U + \Delta n_g RT \) to check if \( \Delta H \) differs from \( \Delta U \).

Answer 1

The Correct Option is C

Step 1: Relation Between \( \Delta H \) and \( \Delta U \) The enthalpy change \( \Delta H \) and internal energy change \( \Delta U \) are related by: \[ \Delta H = \Delta U + \Delta n_g RT \] where: - \( \Delta n_g \) is the change in the number of moles of gas, - \( R \) is the universal gas constant, - \( T \) is the temperature in Kelvin. Step 2: Computing \( \Delta n_g \) for Each Reaction - (A) \( H_2 + I_2 \rightarrow 2HI \) \( \Delta n_g = 2 - (1 + 1) = 0 \) \( \Delta H = \Delta U \). - (B) \( 2NO \rightarrow N_2 + O_2 \) \( \Delta n_g = (1 + 1) - 2 = 0 \) \( \Delta H = \Delta U \). - (C) \( N_2 + 3H_2 \rightarrow 2NH_3 \) \( \Delta n_g = 2 - (1 + 3) = -2 \) \( \Delta H \neq \Delta U \). - (D) \( C(s) + O_2 \rightarrow CO_2 \) \( \Delta n_g = 1 - 1 = 0 \) \( \Delta H = \Delta U \). Conclusion Thus, the correct answer is: \[ N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g) \]