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.

검증된 단계별 안내

Write the balanced chemical equation for the reaction: PH3BCl3(s) ⇌ PH3(g) + BCl3(g).

Set up an ICE (Initial, Change, Equilibrium) table. Since PH3BCl3 is a solid, its concentration does not appear in the expression for Kc. Assume initial concentrations of PH3 and BCl3 to be 0 M.

Let x be the change in concentration of PH3 and BCl3 as PH3BCl3 decomposes. At equilibrium, the concentrations of PH3 and BCl3 will both be x M.

Write the expression for the equilibrium constant, Kc, in terms of x: Kc = [PH3][BCl3]. Substitute the equilibrium concentrations into this expression to get Kc = x^2.

Solve the equation Kc = x^2 for x to find the equilibrium concentrations of PH3 and BCl3. Use the given value of Kc = 1.87×10−3 to find the value of x.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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]. Since solids do not appear in the expression, Kc only involves the gaseous 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 to counteract the change and restore a new equilibrium. In this case, if PH₃BCl₃ decomposes, the system will shift to produce more PH₃ and BCl₃ until the concentrations reach a state that satisfies the equilibrium constant.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations, the changes in concentrations, and the equilibrium concentrations of reactants and products in a chemical reaction. For this reaction, the initial concentration of PH₃BCl₃ is known, and as it decomposes, the changes in concentrations of PH₃ and BCl₃ can be calculated to find their equilibrium concentrations using the Kc value.

At 80°C, 𝐾𝑐 = 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.