To calculate the temperature at which a reaction becomes spontaneous, we use the Gibbs free energy equation:

$\Delta G = \Delta H - T \Delta S$

A reaction is spontaneous when $\Delta G < 0$. At the temperature where the reaction becomes spontaneous, $\Delta G = 0$, so:

$0 = \Delta H - T \Delta S$

This simplifies to:

$T = \frac{\Delta H}{\Delta S}$

Where:

• $\Delta H$ is the enthalpy change of the reaction.
• $\Delta S$ is the entropy change of the reaction.
• $T$ is the temperature (in Kelvin).

Steps:

1. Find $\Delta H$ and $\Delta S$ for the reaction $\text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g)$.
2. Use the equation $T = \frac{\Delta H}{\Delta S}$.

Could you provide the values for $\Delta H$ and $\Delta S$, or would you like me to look them up?

---

Would you like details or have any questions on this process?
Here are 5 related questions to explore further:

1. What is the difference between endothermic and exothermic reactions?
2. How does entropy affect the spontaneity of a reaction?
3. Why does $\Delta G$ need to be negative for a reaction to be spontaneous?
4. What other factors can influence the spontaneity of a chemical reaction?
5. How do you calculate $\Delta G$ at non-standard conditions?

Tip: For reactions that involve gases, remember that increasing temperature generally increases the entropy ($\Delta S$) of the system.