For a reaction, `A(g) to A(l), Delta H = -3RT`
The correct statement for the reaction is :

Options

A. `Delta H = Delta U = 0`
B. `|DeltaH| lt |DeltaU|`
C. `|DeltaH| gt |DeltaU|`
D. `Delta H = Delta U ne 0`

Answer

To solve the problem, we need to analyze the given reaction and the relationships between the enthalpy change (ΔH) and the internal energy change (ΔU).

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction given is:
\[ A(g) \rightarrow A(l) \]
This indicates that one mole of gas A is converting into liquid A.

2. **Given Data**:
The change in enthalpy (ΔH) for this reaction is given as:
\[ \Delta H = -3RT \]

3. **Using the Thermodynamic Relationship**:
We know the relationship between enthalpy change and internal energy change:
\[ \Delta H = \Delta U + P \Delta V \]
where \(P\) is the pressure and \(\Delta V\) is the change in volume.

4. **Calculating Change in Volume (ΔV)**:
Since we are converting from gas to liquid, the volume of the gas will decrease significantly. For one mole of gas turning into a liquid, we can consider:
\[ \Delta n_g = n_{products} - n_{reactants} = 0 - 1 = -1 \]
Thus, the change in volume (ΔV) is negative.

5. **Relating ΔH and ΔU**:
From the ideal gas law, we can express \(P \Delta V\) as:
\[ P \Delta V = \Delta n_g RT \]
Substituting \(\Delta n_g = -1\):
\[ P \Delta V = -RT \]
Now, substituting this into the equation for ΔH:
\[ \Delta H = \Delta U - RT \]

6. **Substituting the Value of ΔH**:
Now we substitute the value of ΔH:
\[ -3RT = \Delta U - RT \]
Rearranging gives:
\[ \Delta U = -3RT + RT = -2RT \]

7. **Comparing ΔH and ΔU**:
Now we have:
\[ \Delta H = -3RT \quad \text{and} \quad \Delta U = -2RT \]
To compare the magnitudes:
\[ |\Delta H| = 3RT \quad \text{and} \quad |\Delta U| = 2RT \]
Therefore, we find that:
\[ |\Delta H| > |\Delta U| \]

8. **Conclusion**:
The correct statement for the reaction is that the magnitude of ΔH is greater than the magnitude of ΔU.

### Final Answer:
The correct statement for the reaction is:
**The magnitude of ΔH is greater than the magnitude of ΔU.**

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