For the decomposition reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), K_p = 381 at 600 K and K_c = 46.9 at 700 K. (a) Is the reaction endothermic or exothermic? Explain. Does your answer agree with what you would predict based on bond energies?

Verified step by step guidance

1. insert step 1> Start by understanding the relationship between Kp and Kc at different temperatures. The equilibrium constant K changes with temperature, and this change can indicate whether a reaction is endothermic or exothermic.
2. insert step 2> Use the van 't Hoff equation to analyze the temperature dependence of the equilibrium constant: \( \ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H^\circ}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \). Here, \( K_1 \) and \( K_2 \) are the equilibrium constants at temperatures \( T_1 \) and \( T_2 \), respectively.
3. insert step 3> Note that the equilibrium constant decreases from 381 at 600 K to 46.9 at 700 K. According to the van 't Hoff equation, if \( K \) decreases with an increase in temperature, the reaction is exothermic.
4. insert step 4> Consider bond energies to verify this conclusion. In an exothermic reaction, the energy released from forming new bonds is greater than the energy required to break the initial bonds. Compare the bond energies of PCl₅ with those of PCl₃ and Cl₂.
5. insert step 5> Conclude that the reaction is exothermic, as the decrease in \( K \) with increasing temperature and the bond energy considerations both support this conclusion.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. In the context of temperature changes, if a reaction is endothermic, increasing the temperature will favor the formation of products, while decreasing the temperature will favor the reactants. This principle helps predict how changes in temperature affect the equilibrium constant (K) and the direction of the reaction.

Enthalpy and Reaction Type

Enthalpy is a measure of the total heat content of a system, and it plays a crucial role in determining whether a reaction is endothermic or exothermic. An endothermic reaction absorbs heat from the surroundings, resulting in a positive change in enthalpy (ΔH > 0), while an exothermic reaction releases heat, leading to a negative change in enthalpy (ΔH < 0). Understanding the enthalpy change helps in predicting the behavior of the reaction with respect to temperature changes.

Bond Energies

Bond energies refer to the amount of energy required to break a bond between two atoms. In a chemical reaction, the difference in bond energies of the reactants and products can indicate whether the reaction is endothermic or exothermic. If the energy required to break the bonds in the reactants is greater than the energy released when forming the bonds in the products, the reaction is endothermic, which aligns with predictions based on bond energies.