The reaction PCl₃(g) + Cl₂(g) ⇌ PCl₅(g) has Kp = 0.0870 at 300 _x001F_C. A flask is charged with 0.50 atm PCl₃, 0.50 atm Cl₂, and 0.20 atm PCl₅ at this temperature. (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of Cl₂ in the equilibrium mixture?

Verified step by step guidance

1. Identify that the reaction is exothermic, meaning heat is released as a product. According to Le Chatelier's principle, increasing the temperature will shift the equilibrium to favor the endothermic direction, which is the reverse reaction in this case.
2. Recognize that shifting the equilibrium towards the reactants (PCl₃ and Cl₂) will increase their concentrations at equilibrium.
3. Understand that the mole fraction of a component in a mixture is the ratio of its partial pressure to the total pressure of the system. Therefore, an increase in the partial pressure of Cl₂ will increase its mole fraction.
4. Consider the initial conditions: 0.50 atm PCl₃, 0.50 atm Cl₂, and 0.20 atm PCl₅. As the equilibrium shifts towards the reactants, the partial pressure of Cl₂ will increase, affecting its mole fraction.
5. Conclude that increasing the temperature will increase the mole fraction of Cl₂ in the equilibrium mixture, as the equilibrium shifts towards the reactants.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. In the context of temperature changes, if the reaction is exothermic, increasing the temperature shifts the equilibrium position to favor the endothermic direction, which in this case would be the formation of reactants.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) for a reaction at a given temperature quantifies the ratio of the partial pressures of products to reactants at equilibrium. For the reaction PCl₃(g) + Cl₂(g) ⇌ PCl₅(g), Kp = 0.0870 indicates that at equilibrium, the concentration of PCl₅ is relatively low compared to the reactants. Changes in temperature can alter the value of Kp, affecting the equilibrium position.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components. In this reaction, the mole fraction of Cl₂ will change as the equilibrium shifts in response to temperature changes, impacting the overall composition of the gas mixture in the flask.