For which of the following change `DeltaH ne DeltaE` ?
(Where `DeltaH` is change in enthaply , `DeltaE` is change in internal energy ).

Options

A. `H_2(g)+I_2(g)rarr2HI(g)`
B. `HCl(aq)+NaOH(aq)rarrNaCl(aq)+H_2O(l)`
C. `C(s)+O_2(g)rarrCO_2(g)`
D. `N_2(g)+3H_2(g)rarr2NH_2(g)`

Answer

To determine when the change in enthalpy (ΔH) is not equal to the change in internal energy (ΔE), we need to analyze the relationship between these two thermodynamic quantities.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Enthalpy (H)** is defined as \( H = U + PV \), where \( U \) is the internal energy, \( P \) is the pressure, and \( V \) is the volume.
- **Internal Energy (U)** is the total energy contained within the system.

2. **Change in Enthalpy and Internal Energy**:
- The change in enthalpy can be expressed as:
\[ \Delta H = \Delta U + \Delta (PV) \]
- For ideal gases, we can express \( PV \) as \( nRT \) (where \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature).
- Thus, we can rewrite the change in enthalpy:
\[ \Delta H = \Delta U + \Delta(nRT) \]

3. **Considering the Change in Moles of Gas**:
- The change in the number of moles of gas (\( \Delta n_g \)) is crucial. It is defined as:
\[ \Delta n_g = n_{products} - n_{reactants} \]
- If there is a change in the number of moles of gas during a reaction, it will affect the enthalpy change.

4. **When ΔH ≠ ΔU**:
- If there is a change in the number of moles of gas (\( \Delta n_g \neq 0 \)), then:
\[ \Delta H = \Delta U + \Delta n_g RT \]
- In this case, \( \Delta H \) will not be equal to \( \Delta U \) because of the term \( \Delta n_g RT \).

5. **Conclusion**:
- Therefore, ΔH is not equal to ΔU when there is a change in the number of moles of gaseous products or reactants during a reaction.