At constant `T`and`P`,Which of the following statements is correct for the reaction,
`CO(G)+(1)/(2)O_(2)(g)rarrCO_(2)(g)`,

Options

A. `triangleH` is independent of the physical state of the reactants of that compound
B. `triangleH gt triangleE`
C. `triangleH lt triangleE`
D. `triangleH=triangleE`

Answer

To solve the question regarding the reaction \( CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \) at constant temperature and pressure, we will analyze the relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta E \)).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction given is:
\[ CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \]

2. **Determine the Change in Number of Moles (\( \Delta N_g \))**:
- **Products**: 1 mole of \( CO_2 \) (gaseous)
- **Reactants**: 1 mole of \( CO \) + 0.5 mole of \( O_2 \) = 1.5 moles (gaseous)
- Therefore, the change in the number of moles of gas (\( \Delta N_g \)) is calculated as:
\[ \Delta N_g = \text{moles of products} - \text{moles of reactants} = 1 - 1.5 = -0.5 \]

3. **Use the Relationship Between \( \Delta H \) and \( \Delta E \)**:
The relationship between the change in enthalpy and the change in internal energy at constant temperature and pressure is given by:
\[ \Delta H = \Delta E + \Delta N_g RT \]
where \( R \) is the universal gas constant and \( T \) is the temperature.

4. **Substitute \( \Delta N_g \) into the Equation**:
Substituting \( \Delta N_g = -0.5 \):
\[ \Delta H = \Delta E + (-0.5)RT \]
This simplifies to:
\[ \Delta H = \Delta E - 0.5RT \]

5. **Analyze the Relationship**:
From the equation \( \Delta H = \Delta E - 0.5RT \), we can conclude that:
\[ \Delta E = \Delta H + 0.5RT \]
This implies that \( \Delta E \) is greater than \( \Delta H \) because \( 0.5RT \) is a positive term.

6. **Conclusion**:
Thus, the correct statement regarding the relationship between \( \Delta H \) and \( \Delta E \) for the given reaction at constant temperature and pressure is:
\[ \Delta E > \Delta H \]

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