Assume each reaction is carried out in an open container. For which reaction will `DeltaH` = `DeltaE` ?

Options

A. `H_(2)(g) + Br_(2)(g) → 2HBr(g)`
B. `C(s) + 2H_(2)O(g) → 2H_(2)(g) + CO_(2)(g)`
C. `PCl_(5)(g)→ PCl_(3)(g) + Cl_(2)(g)`
D. `2CO(g)+O_(2)(g)to2CO_(2)(g)`

Explanation

To determine for which reaction ΔH = ΔE, we need to analyze the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔE). The relationship is given by the equation:

\[ \Delta H = \Delta E + \Delta N_{g} RT \]

Where:
- ΔN_g = moles of gaseous products - moles of gaseous reactants
- R = universal gas constant
- T = temperature in Kelvin

For ΔH to equal ΔE, the term ΔN_g RT must be zero. This implies that:

\[ \Delta N_{g} = 0 \]

This means that the number of moles of gaseous products must equal the number of moles of gaseous reactants.

### Step-by-step Solution:

1. **Identify the reactions**: We need to examine each reaction provided to determine the moles of gaseous reactants and products.

2. **Calculate ΔN_g for each reaction**:
- **Reaction A**:
- Reactants: 2 moles of H2O (g) + 2 moles of HBr (g) → Total = 2 + 2 = 4 moles (reactants)
- Products: (Assuming products are also gaseous)
- ΔN_g = moles of gaseous products - moles of gaseous reactants = 0 (if products are also 4 moles)

- **Reaction B**:
- Reactants: 2 moles of H2O (g) + 2 moles of HBr (g) → Total = 2 + 2 = 4 moles (reactants)
- Products: 2 moles of H2O (g) + 1 mole of HBr (g) → Total = 2 + 1 = 3 moles (products)
- ΔN_g = 3 - 4 = -1

- **Reaction C**:
- Reactants: PCl5 (g) → Total = 1 mole (reactants)
- Products: 2 moles of Cl2 (g) → Total = 2 moles (products)
- ΔN_g = 2 - 1 = 1

- **Reaction D**:
- Reactants: 3 moles of gaseous reactants → Total = 3 moles (reactants)
- Products: 2 moles of gaseous products → Total = 2 moles (products)
- ΔN_g = 2 - 3 = -1

3. **Determine which reaction has ΔN_g = 0**:
- From the calculations:
- Reaction A has ΔN_g = 0.
- Reactions B, C, and D do not have ΔN_g = 0.

4. **Conclusion**: The only reaction for which ΔH = ΔE is Reaction A.

### Final Answer:
The reaction for which ΔH = ΔE is **Reaction A**.