n is the combustion of carbon monoxide:

$$ 2\text{CO} + \text{O}_2 \rightarrow 2\text{CO}_2 $$

We know that this reaction occurs in a closed vessel, which implies a constant volume process. The relationship between enthalpy change and internal energy change for a reaction can be described by the equation:

$$ \Delta H = \Delta E + \Delta n_gRT $$

Where:

$$\Delta H$$ is the enthalpy change
$$\Delta E$$ is the internal energy change
$$\Delta n_g$$ is the change in the number of moles of gases
$$R$$ is the universal gas constant
$$T$$ is the temperature in Kelvin

To determine $$\Delta n_g$$, we need to look at the number of moles of gas before and after the reaction:

Before the reaction: 2 moles of CO and 1 mole of $$\text{O}_2$$, totaling 3 moles of gas.
After the reaction: 2 moles of $$\text{CO}_2$$.

Hence, $$\Delta n_g$$ can be calculated as:

$$ \Delta n_g = n_{\text{final}} - n_{\text{initial}} = 2 - 3 = -1 $$

Substituting $$\Delta n_g = -1$$ into the enthalpy-internal energy relationship:

$$ \Delta H = \Delta E + (-1)RT $$

$$ \Delta H = \Delta E - RT $$

Since $$RT$$ is always a positive quantity, it means that:

$$ \Delta H < \Delta E $$

Therefore, the correct answer is:

Option B: $$\Delta H < \Delta U$$

Thermodynamics

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