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Ch.15 - Chemical Equilibrium
All textbooksBrown 14th EditionCh.15 - Chemical EquilibriumProblem 56b
Chapter 15, Problem 56b

At 80Β°C, 𝐾𝑐 = 1.87Γ—10βˆ’3 for the reaction PH3BCl3(𝑠) β‡Œ 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 80Β°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?

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1
Write the expression for the equilibrium constant, Kc, for the reaction: PH3BCl3(s) β‡Œ PH3(g) + BCl3(g). Since the solid does not appear in the expression, Kc = [PH3][BCl3].
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.
At equilibrium, the concentrations will be [PH3] = x and [BCl3] = x. Substitute these into the equilibrium expression: Kc = x^2.
Solve the equation Kc = x^2 for x to find the equilibrium concentrations of PH3 and BCl3. Remember that Kc = 1.87Γ—10^βˆ’3 at 80Β°C.
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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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) β‡Œ PH₃(g) + BCl₃(g), Kc = [PH₃][BCl₃] / [PH₃BCl₃]. A small Kc value, like 1.87Γ—10⁻³, indicates that at equilibrium, the concentration of reactants is much greater than that of products.
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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.
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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.
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Related Practice
Textbook Question

At 218Β°C, 𝐾𝑐 = 1.2Γ—10βˆ’4 for the equilibrium NH4SH(𝑠) β‡Œ NH3(𝑔) + H2S(𝑔) Calculate the equilibrium concentrations of NH3 and H2S if a sample of solid NH4SH is placed in a closed vessel at 218Β°C and decomposes until equilibrium is reached.

Textbook Question

At 80Β°C, 𝐾𝑐 = 1.87Γ—10βˆ’3 for the reaction PH3BCl3(𝑠) β‡Œ 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 80Β°C and decomposes until equilibrium is reached.

Textbook Question

At 25Β°C, the reaction CaCrO4(𝑠) β‡Œ Ca2+(π‘Žπ‘ž) + CrO42βˆ’(π‘Žπ‘ž) has an equilibrium constant 𝐾𝑐 = 7.1Γ—10βˆ’4. What are the equilibrium concentrations of Ca2+ and CrO42βˆ’ in a saturated solution of CaCrO4?