Question

If \( \Delta G \) and \( \Delta S \) for the reaction \( A(g) \to B(g) + 2C(g) \) at 2000 K are -40 kJ mol$^{-1}$ and 0.22 kJ K$^{-1}$ mol$^{-1}$, respectively, the change in internal energy for the same reaction approximately (in kJ mol$^{-1}$) is?

• A. 366.7
• B. -366.7
• C. 433.3
• D. -433.3

Hint:

In thermodynamics, the internal energy change \( \Delta U \) can be calculated using the relationship \( \Delta H = \Delta U + P \Delta V \), and for ideal gases, we often neglect \( P \Delta V \) when volume changes are small.

Answer 1

The Correct Option is A

We use the following thermodynamic relation to calculate the change in internal energy: \[ \Delta G = \Delta H - T \Delta S \] Rearrange to solve for \( \Delta H \): \[ \Delta H = \Delta G + T \Delta S \] Next, use the relation \( \Delta H = \Delta U + P\Delta V \), and for ideal gases, we can approximate the change in volume \( \Delta V \). However, the question asks for \( \Delta U \), and since \( P \Delta V \) is negligible in this case (assuming ideal gas behavior), we can approximate: \[ \Delta U = \Delta H \] Now calculate: \[ \Delta H = (-40 \, \text{kJ/mol}) + (2000 \, \text{K})(0.22 \, \text{kJ/K/mol}) \] \[ \Delta H = -40 + 440 = 366.7 \, \text{kJ/mol} \] Thus, the change in internal energy \( \Delta U \) is approximately \( \boxed{366.7} \).