`DeltaH` and `DeltaU` are the same of the reaction, `N_(2)(g)+O_(2)(g)iff2NO(g)`,
All reactants and products are gases where all gases are ideal.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To determine whether ΔH (change in enthalpy) and ΔU (change in internal energy) are the same for the reaction \( N_2(g) + O_2(g) \rightarrow 2NO(g) \), we can follow these steps:

### Step 1: Identify the reaction and its components
The reaction given is:
\[ N_2(g) + O_2(g) \rightarrow 2NO(g) \]

### Step 2: Calculate the change in the number of moles of gas (Δn)
To find Δn, we need to count the number of moles of gaseous reactants and products:
- Reactants:
- \( N_2 \) has 1 mole
- \( O_2 \) has 1 mole
- Total moles of reactants = 1 + 1 = 2 moles

- Products:
- \( 2NO \) has 2 moles
- Total moles of products = 2 moles

Now, we can calculate Δn:
\[ \Delta n = \text{moles of products} - \text{moles of reactants} = 2 - 2 = 0 \]

### Step 3: Use the relationship between ΔH and ΔU
The relationship between ΔH and ΔU is given by the equation:
\[ \Delta H = \Delta U + \Delta n \cdot R \cdot T \]
Where:
- \( R \) is the ideal gas constant
- \( T \) is the temperature in Kelvin

Since we found that Δn = 0, we can substitute this into the equation:
\[ \Delta H = \Delta U + 0 \cdot R \cdot T \]
This simplifies to:
\[ \Delta H = \Delta U \]

### Step 4: Conclusion
Since we have shown that ΔH equals ΔU for the given reaction, we conclude that the first statement is correct.

### Step 5: Verify the conditions
The second statement mentions that all reactants and products are gases and that they behave as ideal gases. This condition is necessary for the relationship to hold true, as it ensures that the change in the number of moles of gas (Δn) is accurately represented.

### Final Answer
Thus, both statements are correct:
1. ΔH and ΔU are the same for the reaction.
2. All reactants and products are gases where all gases are ideal.

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