Question

For a reaction \( 2\text{CO (g)} + \text{O}_2 \text{(g)} \rightarrow 2\text{CO}_2 \text{(g)} \), Given: \[ \Delta_r G^\circ = -128 \, \text{kJ}, \quad \Delta_r S^\circ = -40 \, \text{JK}^{-1}, \quad T = 300 \, \text{K} \] Calculate \( \Delta_r U \) (in kJ).

• A. \( -137.5 \, \text{kJ} \)
• B. \( -128 \, \text{kJ} \)
• C. \( -140 \, \text{kJ} \)
• D. \( 126.2 \, \text{kJ} \)

Hint:

Use \( \Delta_r U = \Delta_r H - \Delta n_g RT \). Convert entropy to kJ when using with G.

Answer 1

The Correct Option is A

We know: \[ \Delta_r G = \Delta_r H - T \Delta_r S \Rightarrow \Delta_r H = \Delta_r G + T \Delta_r S \] Substitute: \[ \Delta_r H = -128 \, \text{kJ} + 300 \times (-40 \times 10^{-3}) = -128 - 12 = -140 \, \text{kJ} \] Now, use: \[ \Delta_r U = \Delta_r H - \Delta n_g RT \] For gaseous moles: \[ \Delta n_g = (2) - (2 + 1) = -1 \Rightarrow \Delta_r U = -140 - (-1) \cdot 8.314 \cdot 300 \cdot 10^{-3} = -140 + 2.4942 \approx -137.5 \, \text{kJ} \]