Question

What is the change in internal energy for $2\text{CO}_{(g)} + \text{O}_{2(g)} \rightarrow 2\text{CO}_{2(g)}$ at $25^\circ\text{C}$ ?
( $\text{R} = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$, $\Delta H = -560 \text{ kJ}$ )}

• A. $-557.5 \text{ kJ}$
• B. $-530.0 \text{ kJ}$
• C. $510.0 \text{ kJ}$
• D. $656.9 \text{ kJ}$

Hint:

Formula: $\Delta U = \Delta H - \Delta n_g RT$

Answer 1

The Correct Option is A

Concept: \[ \Delta H = \Delta U + \Delta n_g RT \Rightarrow \Delta U = \Delta H - \Delta n_g RT \]

Step 1: Calculate $\Delta n_g$. \[ \Delta n_g = \text{products} - \text{reactants} = 2 - (2+1) = -1 \]

Step 2: Substitute values. \[ \Delta U = -560 - [(-1) \times 8.314 \times 298] \] \[ = -560 + (8.314 \times 298) \]

Step 3: Calculate. \[ 8.314 \times 298 \approx 2476 \text{ J} = 2.476 \text{ kJ} \] \[ \Delta U = -560 + 2.476 \approx -557.5 \text{ kJ} \]

Step 4: Conclusion.
$\Delta U = -557.5 \text{ kJ}$ Final Answer: Option (A)