Question

Identify from following reactions that it takes place with \(\Delta H=\Delta U\).

• A. \(\text{CO}_{2}(g)+\text{H}_{2}(g)\rightarrow \text{CO}(g)+\text{H}_{2}\text{O}(g)\)
• B. \(\text{N}_{2}(g)+3\text{H}_{2}(g)\rightarrow 2\text{NH}_{3}(g)\)
• C. \(\text{CO}(g)+\frac{1}{2}\text{O}_{2}(g)\rightarrow \text{CO}_{2}(g)\)
• D. \(\text{H}_{2}(g)+\frac{1}{2}\text{O}_{2}(g)\rightarrow \text{H}_{2}\text{O}(l)\)

Hint:

The two are equal only when the number of moles of gas does not change.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
\(\Delta H = \Delta U + \Delta n_g RT\). So \(\Delta H = \Delta U\) only when \(\Delta n_g = 0\).

Step 2: Calculate for each reaction
First: \(\Delta n_g = 2-2 = 0\). Second: \(2-4 = -2\). Third: \(1-1.5 = -0.5\). Fourth: \(0-1.5 = -1.5\), because water is a liquid.

Step 3: Compare the options
Only the first reaction has \(\Delta n_g = 0\).

Final Answer:
The reaction of CO2 with H2 to give CO and H2O(g) has equal enthalpy and internal energy changes. \[ \boxed{\text{(A) }\text{CO}_{2}(g)+\text{H}_{2}(g)\rightarrow \text{CO}(g)+\text{H}_{2}\text{O}(g)} \]