At 80°C, 𝐾_𝑐 = 1.87×10⁻³ for the reaction PH₃BCl₃(𝑠) ⇌ PH₃(𝑔) + BCl₃(𝑔) (a) Calculate the equilibrium concentrations of PH₃ and BCl₃ if a solid sample of PH₃BCl₃ is placed in a closed vessel at 80°C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH₃BCl₃(𝑠) that must be added to the flask to achieve equilibrium?

Verified step by step guidance

1. Write the expression for the equilibrium constant, Kc, for the reaction: PH3BCl3(s) ⇌ PH3(g) + BCl3(g). Since the solid does not appear in the expression, Kc = [PH3][BCl3].
2. Set up an ICE (Initial, Change, Equilibrium) table. Assume initially there are no gases, so [PH3] = 0 and [BCl3] = 0. Let x be the change in concentration for both PH3 and BCl3 as the solid decomposes.
3. At equilibrium, the concentrations will be [PH3] = x and [BCl3] = x. Substitute these into the equilibrium expression: Kc = x^2.
4. Solve the equation Kc = x^2 for x to find the equilibrium concentrations of PH3 and BCl3. Remember that Kc = 1.87×10^−3 at 80°C.
5. For part (b), use the ideal gas law PV = nRT to find the number of moles of gas at equilibrium, which is 2x (since x moles of PH3 and x moles of BCl3 are produced). Calculate the mass of PH3BCl3 needed to produce these moles, using its molar mass.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction PH₃BCl₃(s) ⇌ PH₃(g) + BCl₃(g), Kc = [PH₃][BCl₃] / [PH₃BCl₃]. A small Kc value, like 1.87×10⁻³, indicates that at equilibrium, the concentration of reactants is much greater than that of products.

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 this case, adding PH₃BCl₃(s) will shift the equilibrium towards the products, PH₃(g) and BCl₃(g), until a new balance is achieved.

Stoichiometry and Concentration Calculations

Stoichiometry involves using the coefficients of a balanced chemical equation to relate the amounts of reactants and products. To find the equilibrium concentrations of PH₃ and BCl₃, one must set up an ICE (Initial, Change, Equilibrium) table based on the stoichiometry of the reaction and the initial amount of PH₃BCl₃(s) added, considering the volume of the flask to convert moles to concentrations.