Question

What is the value of \(\Delta H - \Delta U\) for the formation of 2 moles of ammonia from \(H_{2(g)}\) and \(N_{2(g)}\)?

• A. \(-\frac{RT}{2}\)
• B. \(\frac{RT}{2}\)
• C. \(-2RT\)
• D. \(2RT\)

Hint:

\(\Delta H = \Delta U + \Delta n_g RT\). For reactions where number of gas moles decreases, \(\Delta H < \Delta U\) (negative difference).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need \(\Delta H - \Delta U\) for the reaction forming 2 moles of NH\(_3\) from N\(_2\) and H\(_2\).

Step 2: Key Formula or Approach:
For gaseous reactions, \(\Delta H - \Delta U = \Delta n_g RT\), where \(\Delta n_g\) = moles of gaseous products – moles of gaseous reactants.

Step 3: Detailed Explanation:
Reaction: \(N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)\). \(\Delta n_g = 2 - (1+3) = 2 - 4 = -2\). Thus, \(\Delta H - \Delta U = (-2)RT = -2RT\).

Step 4: Final Answer:
Option (C) is correct.