Consider the following reaction :
`CO_((g))+(1)/(2)O_(2(g)) rarr CO_(2(g))`
How are `Delta U` and `DeltaH` related for the reaction ?

Options

A. (a) `DeltaH = DeltaU-0.5RT`
B. (b) `DeltaH=DeltaU-RT`
C. (c) `DeltaH=DeltaU+0.5RT`
D. (d) `DeltaH=DeltaU-1.5RT`

Explanation

To determine the relationship between ΔU (change in internal energy) and ΔH (enthalpy change) for the reaction:

\[ \text{CO}_{(g)} + \frac{1}{2} \text{O}_{2(g)} \rightarrow \text{CO}_{2(g)} \]

we can follow these steps:

### Step 1: Understand the relationship between ΔH and ΔU
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) for a reaction can be expressed by the equation:

\[ \Delta H = \Delta U + \Delta N_g RT \]

where:
- ΔN_g = change in the number of moles of gas (moles of products - moles of reactants)
- R = universal gas constant
- T = temperature in Kelvin

### Step 2: Calculate ΔN_g for the reaction
In the given reaction:

- Reactants: 1 mole of CO and 0.5 moles of O2
- Products: 1 mole of CO2

Now, we can calculate ΔN_g:

\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 1 - (1 + 0.5) = 1 - 1.5 = -0.5 \]

### Step 3: Substitute ΔN_g into the equation
Now that we have ΔN_g, we can substitute it back into the relationship between ΔH and ΔU:

\[ \Delta H = \Delta U + (-0.5)RT \]

This simplifies to:

\[ \Delta H = \Delta U - 0.5RT \]

### Conclusion
Thus, the relationship between ΔU and ΔH for the given reaction is:

\[ \Delta H = \Delta U - 0.5RT \]