In which of the following reactions, `Delta H` is greater than `Delta U` ?

Options

A. `N_(2(g))+3 H_(2(g)) to 2 NH_(3(g))`
B. `PCl_(5(g)) to PCl_(3(g))+Cl_(2(g))`
C. `CH_(4(g))+2 O_(2(g)) to CO_(2(g))+2 H_2 O_((l))`
D. `HCl_((aq))+NaOH_((aq)) to NaCl_((aq))+H_2 O_((aq))`

Answer

To determine in which of the given reactions the change in enthalpy (ΔH) is greater than the change in internal energy (ΔU), we need to analyze the relationship between ΔH and ΔU. The relationship can be expressed as:

ΔH = ΔU + ΔnG RT

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

From this equation, we can derive the following conditions:
1. If ΔnG = 0, then ΔH = ΔU (they are equal).
2. If ΔnG > 0, then ΔH > ΔU (ΔH is greater than ΔU).
3. If ΔnG < 0, then ΔH < ΔU (ΔH is less than ΔU).

To find the correct reaction where ΔH is greater than ΔU, we need to calculate ΔnG for each option provided.

### Step-by-Step Solution:

1. **Option A:**
- Reaction: \(3H_2 + N_2 \rightarrow 2NH_3\)
- Moles of gaseous products = 2 (from 2 moles of NH3)
- Moles of gaseous reactants = 3 (from 3 moles of H2) + 1 (from 1 mole of N2) = 4
- ΔnG = 2 - 4 = -2 (ΔnG < 0)
- Conclusion: ΔH < ΔU (not our answer)

2. **Option B:**
- Reaction: \(Cl_2(g) + PCl_3(g) \rightarrow PCl_5(g)\)
- Moles of gaseous products = 1 (from 1 mole of PCl5)
- Moles of gaseous reactants = 1 (from 1 mole of Cl2) + 1 (from 1 mole of PCl3) = 2
- ΔnG = 1 - 2 = -1 (ΔnG < 0)
- Conclusion: ΔH < ΔU (not our answer)

3. **Option C:**
- Reaction: \(2H_2O(l) + CH_4(g) + 2O_2(g) \rightarrow 2CO_2(g)\)
- Moles of gaseous products = 1 (from 1 mole of CO2)
- Moles of gaseous reactants = 1 (from 1 mole of CH4) + 2 (from 2 moles of O2) = 3
- ΔnG = 1 - 3 = -2 (ΔnG < 0)
- Conclusion: ΔH < ΔU (not our answer)

4. **Option D:**
- Reaction: \(HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(aq)\)
- Moles of gaseous products = 0 (no gases)
- Moles of gaseous reactants = 0 (no gases)
- ΔnG = 0 - 0 = 0 (ΔnG = 0)
- Conclusion: ΔH = ΔU (not our answer)

### Final Conclusion:
After analyzing all options, we find that none of the reactions have ΔnG > 0. Therefore, it seems there might have been an error in the options provided, as we were looking for a reaction where ΔH > ΔU.