Question #44160

Consider the complete dissociation of $1\text{ mole}$ of \ce{O2(g)} into \ce{O(g)}. According to Molecular Orbital Theory (MOT), let $x$ be the number of unpaired electrons in an \ce{O2} molecule. Let $y$ be the number of unpaired electrons in an \ce{O} atom in its ground state.

A sample of $1\text{ mole}$ of \ce{O2(g)} initially at $300\text{ K}$ and volume $V_0$ undergoes the following sequence of steps: Step 1: Reversible isothermal expansion to a volume $V_1$ such that the magnitude of work done is $|W_1| = (y - \frac{x}{2}) \times 3.486\text{ kJ}$. Step 2: Complete dissociation into \ce{O(g)} at constant volume $V_1$ and constant temperature $300\text{ K}$. Step 3: Reversible isothermal compression of the product gas back to the original volume $V_0$.

Given the standard enthalpy of dissociation of \ce{O2(g)} at $300\text{ K}$ is $\Delta H^\circ = 498.49\text{ kJ/mol}$. Assume ideal gas behavior for all species. (Use $R = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$, $\ln 2 = 0.7$)

Which of the following options correctly represents the net work done ($W_{net}$) and the net heat absorbed ($q_{net}$) by the system in the entire process? (Use standard IUPAC sign convention)