For which of the following reactions, `DeltaH` is equal to `DeltaU` ?

Options

A. `N_(2) (g) + 3 H_(2) (g) to 2 N H _(3) (g)`
B. `2 H I (g) to H_(2) (g) + I_(2) (g)`
C. `2 N O_(2) (g) to N_(2) O_(4) (g)`
D. `2 S O _(2) + O_(2) (g) to 2 S O _(3) (g)`

Explanation

To determine for which of the following reactions the change in enthalpy (ΔH) is equal to the change in internal energy (ΔU), we need to analyze the relationship between these two thermodynamic quantities.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The relationship between ΔH and ΔU can be expressed as:
\[ \Delta H = \Delta U + \Delta N_g \cdot R \cdot T \]
where ΔN_g is the change in the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

2. **Condition for ΔH = ΔU**:
For ΔH to be equal to ΔU, the term ΔN_g must be equal to zero:
\[ \Delta N_g = 0 \]
This means that the number of moles of gaseous products must equal the number of moles of gaseous reactants.

3. **Analyzing Each Reaction**:
We will analyze the given reactions to find ΔN_g for each.

- **Reaction 1**: \( N_2 + 3H_2 \rightarrow 2NH_3 \)
- Moles of gaseous products = 2 (from 2 NH3)
- Moles of gaseous reactants = 4 (1 N2 + 3 H2)
- ΔN_g = 2 - 4 = -2 (not equal to 0)

- **Reaction 2**: \( 2HI \rightarrow H_2 + I_2 \)
- Moles of gaseous products = 2 (1 H2 + 1 I2)
- Moles of gaseous reactants = 2 (2 HI)
- ΔN_g = 2 - 2 = 0 (equal to 0)

- **Reaction 3**: \( 2H_2 \rightarrow 2H \)
- Moles of gaseous products = 2 (2 H)
- Moles of gaseous reactants = 2 (2 H2)
- ΔN_g = 2 - 2 = 0 (equal to 0)

- **Reaction 4**: \( 2SO_2 \rightarrow 2SO_3 \)
- Moles of gaseous products = 2 (2 SO3)
- Moles of gaseous reactants = 2 (2 SO2)
- ΔN_g = 2 - 2 = 0 (equal to 0)

4. **Conclusion**:
The reactions for which ΔH is equal to ΔU are those where ΔN_g = 0. Based on our analysis, the reactions that satisfy this condition are:
- **Reaction 2**: \( 2HI \rightarrow H_2 + I_2 \)
- **Reaction 3**: \( 2H_2 \rightarrow 2H \)
- **Reaction 4**: \( 2SO_2 \rightarrow 2SO_3 \)

### Final Answer:
The reaction for which ΔH is equal to ΔU is:
- **2HI → H2 + I2** (and also the other reactions with ΔN_g = 0).