For which of the following `DeltaE = DeltaH`

Options

A. `N_(2)O_(4)(g) iff 2NO_(2)(g)`
B. `2SO_(2)(g)+O_(2)(g)iff2SO_(3)(g)`
C. `H_(2)(g)+Cl_(2)(g)iff2HCl(g)`
D. `H_(2)(g)+(1)/(2)O_(2)(g)iffH_(2)O(l)`

Explanation

To determine when \(\Delta E = \Delta H\), we need to understand the relationship between the change in internal energy (\(\Delta E\)) and the change in enthalpy (\(\Delta H\)).

### Step-by-Step Solution:

1. **Understand the Definitions**:
- \(\Delta E\) (Change in Internal Energy) is the total energy change of a system.
- \(\Delta H\) (Change in Enthalpy) is the heat content change of a system at constant pressure.

2. **Use the Relationship**:
The relationship between \(\Delta H\) and \(\Delta E\) can be expressed as:
\[ \Delta H = \Delta E + \Delta nRT \]
where \(\Delta n\) is the change in the number of moles of gas during the reaction, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin.

3. **Identify Conditions**:
For \(\Delta E\) to equal \(\Delta H\), the term \(\Delta nRT\) must be zero. This occurs when:
- There is no change in the number of moles of gas (\(\Delta n = 0\)).
- This typically happens in reactions where the number of gaseous reactants equals the number of gaseous products.

4. **Conclusion**:
Therefore, \(\Delta E = \Delta H\) when there is no change in the number of moles of gas during the reaction.