Question:
For which reaction \( \Delta H \neq \Delta U \)?
For which reaction \( \Delta H \neq \Delta U \)?
Show Hint
Use the equation \( \Delta H = \Delta U + \Delta n_g RT \) to check if \( \Delta H \) differs from \( \Delta U \).
Updated On: Mar 18, 2026
- \( H_2(g) + I_2(g) \longrightarrow 2HI(g) \)
- \( 2NO(g) \longrightarrow N_2(g) + O_2(g) \)
- \( N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g) \)
- \( C(s) + O_2(g) \longrightarrow CO_2(g) \)
Show Solution
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The Correct Option is C
Solution and Explanation
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:
\[
N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g)
\]
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