For the reaction `CO(g)+(1)/(2)O_(2)(g)rarr CO_(2)(g)`
Which one of the statement is correct at constant T and P ?

Options

A. `Delta H = Delta E`
B. `Delta H lt Delta E`
C. `Delta H gt Delta E`
D. `Delta H` is independent
of physical state of reactants

Answer

To solve the question regarding the reaction \( CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \) and determine which statement is correct at constant temperature and pressure, we will analyze the changes in enthalpy and internal energy.

### Step-by-Step Solution:

1. **Identify the Reaction Components**:
- We have reactants: \( CO(g) \) and \( \frac{1}{2}O_2(g) \).
- We have the product: \( CO_2(g) \).

2. **Count the Moles of Gases**:
- In the reactants:
- \( CO(g) \) contributes 1 mole.
- \( \frac{1}{2}O_2(g) \) contributes 0.5 moles.
- Total moles of reactants = \( 1 + 0.5 = 1.5 \) moles.
- In the products:
- \( CO_2(g) \) contributes 1 mole.
- Total moles of products = 1 mole.

3. **Calculate the Change in Moles of Gas (\( \Delta N_G \))**:
- \( \Delta N_G = \text{moles of products} - \text{moles of reactants} \)
- \( \Delta N_G = 1 - 1.5 = -0.5 \).

4. **Apply the First Law of Thermodynamics**:
- According to the first law of thermodynamics, the change in enthalpy (\( \Delta H \)) is related to the change in internal energy (\( \Delta E \)) and the change in the number of moles of gas:
\[ \Delta H = \Delta E + \Delta N_G \cdot RT \]
where \( R \) is the gas constant and \( T \) is the temperature.

5. **Substitute the Values**:
- Substitute \( \Delta N_G = -0.5 \):
\[ \Delta H = \Delta E + (-0.5) \cdot RT \]
- Rearranging gives:
\[ \Delta H - \Delta E = -0.5 \cdot RT \]

6. **Conclusion**:
- Since \( -0.5 \cdot RT \) is negative, it implies that:
\[ \Delta H < \Delta E \]
- Therefore, the correct statement at constant temperature and pressure is that the change in enthalpy (\( \Delta H \)) is less than the change in internal energy (\( \Delta E \)).

### Final Answer:
The correct statement is: \( \Delta H < \Delta E \).