The following reactions carried in open vessel. The reaction for which `Delta H = Delta U` will be

Options

A. `PCI_(5)(g) rightarrow PCI_(3)(g) + CI_(2)(g)`
B. `2CO(g) + O_(2)(g) rightarrow 2CO_(2)(g)`
C. `N_(2)(g) + 3H_(2)(g) rightarrow 2NH_(3)(g)`
D. `H_(2)(g) + I_(2)(g) rightarrow 2HI(g)`

Answer

To determine the reaction for which ΔH = ΔU when carried out in an open vessel, we need to understand the relationship between enthalpy (ΔH) and internal energy (ΔU). The key equation we will use is:

\[ \Delta H = \Delta U + P \Delta V \]

In an open vessel, the pressure (P) is constant, and we can express the change in volume (ΔV) in terms of the change in the number of moles of gas (Δn):

\[ \Delta V = \Delta n \cdot R \cdot T \]

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

From the equation, we can rewrite ΔH as:

\[ \Delta H = \Delta U + \Delta n \cdot R \cdot T \]

For ΔH to equal ΔU, the term ΔnRT must be zero:

\[ \Delta H = \Delta U \implies \Delta n \cdot R \cdot T = 0 \]

This condition occurs when Δn = 0, meaning the number of moles of gas in the products is equal to the number of moles of gas in the reactants.

### Step-by-Step Solution:

1. **Identify the reactions**: Look at the given reactions and write down the number of moles of gaseous reactants and products for each reaction.

2. **Calculate Δn for each reaction**: For each reaction, calculate Δn using the formula:
\[ \Delta n = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]

3. **Check for Δn = 0**: Determine which reaction has Δn equal to zero. This means that the number of moles of gaseous products is equal to the number of moles of gaseous reactants.

4. **Conclusion**: The reaction for which Δn = 0 will be the reaction for which ΔH = ΔU.

### Example Calculation:

Assuming we have the following reactions:

1. A(g) + B(g) → C(g) (Δn = 1 - 2 = -1)
2. 2D(g) → E(g) + F(g) (Δn = 2 - 2 = 0)
3. G(g) + H(g) → I(g) + J(g) (Δn = 2 - 2 = 0)
4. K(g) → L(g) + M(g) (Δn = 1 - 1 = 0)

From the above reactions, we see that reactions 2, 3, and 4 have Δn = 0. Therefore, for these reactions, ΔH = ΔU.

### Final Answer:

The reactions for which ΔH = ΔU are those where Δn = 0.