Calculate the temperature at which each of the following reactions becomes spontaneous.
PCl5(g) equilibrium reaction arrow PCl3(g) + Cl2(g)

To calculate the temperature at which a reaction becomes spontaneous, we need to use **Gibbs free energy** (\( \Delta G \)) and the relationship between enthalpy (\( \Delta H \)), entropy (\( \Delta S \)), and temperature (\( T \)):

\[
\Delta G = \Delta H - T \Delta S
\]

For a reaction to be spontaneous, \( \Delta G \) must be negative. Therefore, the reaction becomes spontaneous when:

\[
\Delta G = 0
\]

This gives us the condition:

\[
T = \frac{\Delta H}{\Delta S}
\]

Where:
- \( \Delta H \) is the change in enthalpy of the reaction (usually given in \( \text{kJ/mol} \)),
- \( \Delta S \) is the change in entropy of the reaction (usually given in \( \text{J/mol·K} \)).

**Steps:**
1. Find the values for \( \Delta H \) and \( \Delta S \) for the reaction:
   \[
   \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)
   \]
   These values are typically available in thermodynamic tables.

2. Convert \( \Delta H \) to \( \text{J/mol} \) if it's given in \( \text{kJ/mol} \) (since \( \Delta S \) is usually in \( \text{J/mol·K} \)).

3. Apply the equation \( T = \frac{\Delta H}{\Delta S} \).

Once you have the values, you can plug them into the formula to determine the temperature at which the reaction becomes spontaneous.

Do you have the values for \( \Delta H \) and \( \Delta S \)? If not, I can help explain how to look them up.

---

**Would you like a detailed explanation of the next steps?**

Here are 5 related questions to expand the discussion:
1. What role does entropy play in determining spontaneity?
2. How does the sign of \( \Delta H \) affect the spontaneity of a reaction?
3. What is the significance of the equilibrium constant in relation to Gibbs free energy?
4. How would the spontaneity change if \( \Delta S \) were negative instead of positive?
5. Can a reaction be non-spontaneous at one temperature and spontaneous at another?

**Tip:** A reaction with positive \( \Delta H \) and positive \( \Delta S \) tends to be spontaneous at higher temperatures!

Calculate the temperature at which each of the following reactions becomes spontaneous: PCl5(g) equilibrium reaction arrow PCl3(g) + Cl2(g)

Discover how to calculate the temperature at which the reaction PCl5(g) ⇌ PCl3(g) + Cl2(g) becomes spontaneous using Gibbs Free Energy. This problem involves thermodynamic concepts such as enthalpy, entropy, and Gibbs free energy. Perfect for students at the advanced high school or college level.

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