choose the reaction in which `DeltaH` is not equal to `DeltaU`

Options

A. `C_(gra ph ite)`` +O_(2(g))rarrCO_(2(g))`
B. `C_2H_(4(g))``+H_(2(g))rarrC_2H_(6(g))`
C. `N_(2(g))+O_(2(g))rarr2NO_((g))`
D. `H_(2(g))+I_(2(g)) rarr2HI_((g))`

Answer

To determine which reaction has a change in enthalpy (ΔH) that is not equal to the change in internal energy (ΔU), we will use the relationship:

\[ \Delta H = \Delta U + \Delta N_G RT \]

where:
- ΔH = change in enthalpy
- ΔU = change in internal energy
- ΔN_G = change in the number of moles of gaseous products minus gaseous reactants
- R = gas constant
- T = temperature

### Step-by-Step Solution:

1. **Identify the Reactions**: We have four reactions to analyze. We need to calculate ΔN_G for each reaction.

2. **Calculate ΔN_G for Each Reaction**:
- **Reaction 1**:
\[ \text{C (s)} + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \]
- Products: 1 mole of CO₂ (g)
- Reactants: 1 mole of O₂ (g) and 1 mole of C (s) (only count gaseous reactants)
- ΔN_G = 1 (products) - 1 (reactants) = 0

- **Reaction 2**:
\[ \text{C}_2\text{H}_6 (g) \rightarrow \text{C}_2\text{H}_4 (g) + \text{H}_2 (g) \]
- Products: 1 mole of C₂H₄ (g) + 1 mole of H₂ (g) = 2 moles
- Reactants: 1 mole of C₂H₆ (g)
- ΔN_G = 2 (products) - 1 (reactants) = 1

- **Reaction 3**:
\[ \text{2NO (g)} \rightarrow \text{O}_2 (g) \]
- Products: 1 mole of O₂ (g)
- Reactants: 2 moles of NO (g)
- ΔN_G = 1 (products) - 2 (reactants) = -1

- **Reaction 4**:
\[ \text{H}_2 (g) + \text{I}_2 (g) \rightarrow \text{2HI (g)} \]
- Products: 2 moles of HI (g)
- Reactants: 1 mole of H₂ (g) + 1 mole of I₂ (g) = 2 moles
- ΔN_G = 2 (products) - 2 (reactants) = 0

3. **Determine ΔH and ΔU Relationships**:
- For **Reaction 1**: ΔN_G = 0 → ΔH = ΔU
- For **Reaction 2**: ΔN_G = 1 → ΔH ≠ ΔU
- For **Reaction 3**: ΔN_G = -1 → ΔH ≠ ΔU
- For **Reaction 4**: ΔN_G = 0 → ΔH = ΔU

4. **Conclusion**: The reaction where ΔH is not equal to ΔU is **Reaction 2**.

### Final Answer:
**Reaction 2** is the reaction in which ΔH is not equal to ΔU.