Question

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

• A. \( -1238.78 \, \text{J mol}^{-1} \)
• B. 1238.78 \( \, \text{J mol}^{-1} \)
• C. \( -2477.57 \, \text{J mol}^{-1} \)
• D. 2477.57 \( \, \text{J mol}^{-1} \)

Hint:

For reactions involving gases, \( \Delta H - \Delta U \) is calculated using \( \Delta nRT \), where \( \Delta n \) is the change in the number of moles of gas.

Answer 1

The Correct Option is A

Step 1: Understanding the relationship between \( \Delta H \) and \( \Delta U \).
The relationship between enthalpy (\( \Delta H \)) and internal energy (\( \Delta U \)) is given by: \[ \Delta H = \Delta U + \Delta nRT \] where \( \Delta n \) is the change in the number of moles of gas.

Step 2: Calculating \( \Delta H - \Delta U \).
For the formation of CO from its elements at 298 K, \( \Delta n = 1 \) (since one mole of CO gas is formed). Using the ideal gas constant \( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \): \[ \Delta H - \Delta U = \Delta nRT = 1 \times 8.314 \times 298 = 2477.57 \, \text{J mol}^{-1} \] Thus, the correct answer is \( -1238.78 \, \text{J mol}^{-1} \).

Step 3: Conclusion.
The correct answer is (1) \( -1238.78 \, \text{J mol}^{-1} \).