`(Delta H - Delta U)` for the formation of carbon monoxide `(CO)` from its elements at `298K` is
`(R = 8.314 K^(-1)mol^(-1))`

Options

A. `-1238.78J "mol"^(-1)`
B. `123.78J " mol"^(-1)`
C. `-2477.57 J "mol"^(-1)`
D. `2477.57J"mol"^(-1)`

Answer

To solve the problem of finding `(Delta H - Delta U)` for the formation of carbon monoxide `(CO)` from its elements at `298K`, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Reaction**:
The formation of carbon monoxide from its elements can be represented as:
\[ \text{C (s) + } \frac{1}{2} \text{O}_2 \text{ (g)} \rightarrow \text{CO (g)} \]

2. **Identify the Change in Moles of Gas**:
In the reaction, we have:
- Reactants: 1 mole of solid carbon (C) and 0.5 moles of gaseous oxygen (O₂), totaling 0.5 moles of gas.
- Products: 1 mole of gaseous carbon monoxide (CO).
Therefore, the change in the number of moles of gas (`Delta N_g`) is:
\[ \Delta N_g = \text{Moles of products} - \text{Moles of reactants} = 1 - 0.5 = 0.5 \]

3. **Use the Formula for Delta H - Delta U**:
The relationship between the change in enthalpy (Delta H) and the change in internal energy (Delta U) is given by:
\[ \Delta H - \Delta U = \Delta N_g \cdot R \cdot T \]
Where:
- \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \) (gas constant)
- \( T = 298 \, \text{K} \)

4. **Substitute the Values**:
Now substituting the values into the formula:
\[ \Delta H - \Delta U = 0.5 \cdot 8.314 \cdot 298 \]

5. **Calculate the Result**:
First, calculate \( 8.314 \cdot 298 \):
\[ 8.314 \cdot 298 = 2477.572 \, \text{J/mol} \]
Now, multiply by 0.5:
\[ \Delta H - \Delta U = 0.5 \cdot 2477.572 = 1238.786 \, \text{J/mol} \]

6. **Final Answer**:
Therefore, the value of \( \Delta H - \Delta U \) for the formation of carbon monoxide from its elements at 298 K is approximately:
\[ \Delta H - \Delta U \approx 1238.78 \, \text{J/mol} \]