For the reaction, `N_2[g] + 3H_2[g] hArr 2NH_3[g] , Delta H = …`

Options

A. `DeltaU - 2RT`
B. `DeltaU + 2RT`
C. `DeltaU + RT`
D. `DeltaU - RT`.

Explanation

To solve the problem regarding the reaction \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \) and to find the relationship between \( \Delta H \) and \( \Delta U \), we can follow these steps:

### Step 1: Identify the reaction and its components
The given reaction is:
\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]
We need to analyze the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta U \)) for this reaction.

### Step 2: Understand the relationship between \( \Delta H \) and \( \Delta U \)
The relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta U \)) is given by the equation:
\[ \Delta H = \Delta U + \Delta n_g RT \]
where:
- \( \Delta n_g \) is the change in the number of moles of gas,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 3: Calculate \( \Delta n_g \)
To find \( \Delta n_g \), we need to calculate the difference between the moles of gaseous products and the moles of gaseous reactants.

- **Products**: \( 2 \) moles of \( NH_3 \)
- **Reactants**: \( 1 \) mole of \( N_2 \) + \( 3 \) moles of \( H_2 \) = \( 4 \) moles

Now, we can calculate \( \Delta n_g \):
\[ \Delta n_g = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 4 = -2 \]

### Step 4: Substitute \( \Delta n_g \) into the equation
Now that we have \( \Delta n_g = -2 \), we can substitute this value into the relationship between \( \Delta H \) and \( \Delta U \):
\[ \Delta H = \Delta U + (-2)RT \]
This simplifies to:
\[ \Delta H = \Delta U - 2RT \]

### Step 5: Final expression
Thus, the final expression relating \( \Delta H \) and \( \Delta U \) for the given reaction is:
\[ \Delta H = \Delta U - 2RT \]

### Conclusion
The relationship between the change in enthalpy and the change in internal energy for the reaction \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \) is:
\[ \Delta H = \Delta U - 2RT \]

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