A mixture of `2` moles of `CO` and `1` mole of `O_(2)`, in a closed vessele is ignited to convert the `CO` to `CO_(2)` if `Delta H` is the enthalpy change and `Delta U` is the change in internal energy then:

Options

A. `Delta H = Delta cup`
B. `Delta H gt Delta cup`
C. `Delta H lt Delta cup`
D. The relationship depends upon the capacity of vessel

Answer

To solve the problem, we need to analyze the reaction and the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) for the combustion of carbon monoxide (CO) in the presence of oxygen (O₂) to form carbon dioxide (CO₂).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction can be written as:
\[ 2 \text{CO} (g) + \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) \]
Here, we have 2 moles of CO reacting with 1 mole of O₂ to produce 2 moles of CO₂.

2. **Calculate the Change in Moles (Δn)**:
We need to determine the change in the number of moles of gas during the reaction:
\[ \Delta n = \text{(moles of products)} - \text{(moles of reactants)} \]
- Moles of products = 2 (from CO₂)
- Moles of reactants = 2 (from CO) + 1 (from O₂) = 3
\[ \Delta n = 2 - 3 = -1 \]

3. **Use the Relationship Between ΔH and ΔU**:
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) is given by the equation:
\[ \Delta H = \Delta U + \Delta n RT \]
Where:
- R = Universal gas constant
- T = Temperature in Kelvin

4. **Substitute Δn into the Equation**:
From our earlier calculation, we know that Δn = -1. Substituting this into the equation gives:
\[ \Delta H = \Delta U + (-1)RT \]
Simplifying this, we get:
\[ \Delta H = \Delta U - RT \]

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

6. **Conclusion**:
Therefore, the correct answer is:
\[ \Delta H < \Delta U \]
This corresponds to option C.