Which statement is ture for reaction ? `2H_(2) (g) + O_(2) (g) rarr 2H_(2) O (g)`

Options

A. `S = +ve`
B. `H gt U`
C. `-H lt U`
D. H = U

Answer

To determine which statement is true for the reaction \(2H_2(g) + O_2(g) \rightarrow 2H_2O(g)\), we will analyze the thermodynamic properties involved in the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction given is \(2H_2(g) + O_2(g) \rightarrow 2H_2O(g)\). This is a combustion reaction where hydrogen gas reacts with oxygen gas to form water vapor.

2. **Use the Formula for Enthalpy and Internal Energy**: The relationship between enthalpy change (\(\Delta H\)) and internal energy change (\(\Delta U\)) is given by the equation:
\[ \Delta H = \Delta U + n_{z}RT \]
where \(n_{z}\) is the change in the number of moles of gas.

3. **Calculate \(n_{z}\)**: To find \(n_{z}\), we need to determine the change in the number of moles of gas from reactants to products:
- Moles of gaseous reactants: \(2 \, (H_2) + 1 \, (O_2) = 3\)
- Moles of gaseous products: \(2 \, (H_2O)\)
- Therefore, \(n_{z} = \text{moles of products} - \text{moles of reactants} = 2 - 3 = -1\).

4. **Substitute \(n_{z}\) into the Equation**: Now substituting \(n_{z}\) into the enthalpy-internal energy relationship:
\[ \Delta H = \Delta U + (-1)RT \]
This simplifies to:
\[ \Delta H = \Delta U - RT \]

5. **Analyze the Relationship**: From the equation \(\Delta H = \Delta U - RT\), we can conclude that:
\[ \Delta H < \Delta U \]
This indicates that the enthalpy change is less than the internal energy change.

6. **Evaluate the Options**: Based on our analysis:
- Option A: Entropy will be positive.
- Option B: Enthalpy is greater than internal energy.
- Option C: Negative of enthalpy is less than internal energy.
- Option D: Internal energy is equal to enthalpy.

Since we have established that \(\Delta H < \Delta U\), we can eliminate options B, C, and D. Thus, the only statement that can be true is option A, which states that the entropy will be positive.

7. **Conclusion**: Therefore, the correct answer is:
\[ \text{Option A: Entropy will be positive.} \]