For which of the following reactions, `DeltaH = DeltaU` ?

Options

A. `H_2(g) + l_2(g) rightarrow 2Hl(g)`
B. `N_2(g) + 3H_2(g) rightarrow 2NH_3(g)`
C. `C(s) + H_2O(g) rightarrow CO(g) + H_2(g)
D. `CH_4(g) + H_2O(g) rightarrow CO(g) + 3H_2(g)`

Answer

To determine for which of the given reactions ΔH = ΔU, we need to analyze the relationship between enthalpy change (ΔH) and internal energy change (ΔU) using the formula:

\[ \Delta H = \Delta U + \Delta N_g RT \]

Where:
- ΔH = change in enthalpy
- ΔU = change in internal energy
- ΔN_g = change in the number of moles of gaseous products minus the number of moles of gaseous reactants
- R = gas constant
- T = temperature (assumed constant)

### Step 1: Understand ΔN_g
ΔN_g is defined as:
\[ \Delta N_g = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]
For ΔH to equal ΔU, ΔN_g must be zero:
\[ \Delta H = \Delta U \quad \text{if} \quad \Delta N_g = 0 \]

### Step 2: Analyze each option for ΔN_g

1. **Option 1**:
- Products: 2 moles of gas
- Reactants: 1 mole of gas + 1 mole of gas = 2 moles
- ΔN_g = 2 - 2 = 0

2. **Option 2**:
- Products: 2 moles of gas
- Reactants: 3 moles of gas + 1 mole of gas = 4 moles
- ΔN_g = 2 - 4 = -2

3. **Option 3**:
- Products: 1 mole of gas + 1 mole of solid (solids are not counted)
- Reactants: 1 mole of gas
- ΔN_g = 2 - 1 = 1

4. **Option 4**:
- Products: 3 moles of gas + 1 mole of gas = 4 moles
- Reactants: 1 mole of gas + 1 mole of gas = 2 moles
- ΔN_g = 4 - 2 = 2

### Step 3: Conclusion
From the above analysis, we find that ΔN_g is zero only in **Option 1**. Therefore, for this reaction:

\[ \Delta H = \Delta U \]

### Final Answer
The correct option for which ΔH = ΔU is **Option 1**.

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