At 80°C, 𝐾 𝑐 = 1.87×10 −3 for the reaction PH 3 BCl 3 (𝑠) ⇌ PH 3 (𝑔) + BCl 3 (𝑔) (a) Calculate the equilibrium concentrations of PH 3 and BCl 3 if a solid sample of PH 3 BCl 3 is placed in a closed vessel at 80°C and decomposes until equilibrium is reached.

Hello everyone. Today, we got the following problem. The equilibrium constant for the following decomposition reaction at 75°C is 2.73. What are the equilibrium concentrations of ammonia and boron try fluoride if a sample of this complex is put inside a closed container at 75°C and allowed to reach equilibrium. So one thing to note when writing our equilibrium expressions is that we are only going to include so we could only include our Aquarius and our gasses, meaning solids and liquids are not included with that. In mind. We see that we do have a solid for the reactant. So we're not going to include that. So when we are writing our expression are equally room expression, it's generally the concentration of products over the concentration of reactant. However, we only have gasses for our products. So our expression is going to be the concentration of ammonia times our concentration of boron try fluoride. So based on geometric principles, we can let x which is a variable equal the concentration of ammonia, which can also equal the concentration of boron try fluoride since there's one mole of each and with that we have our case, the expression which can be represented by X times X or X squared R K C expression. According to the question was 2.73. We're gonna equal that two X squared. And when we square both sides, we're going to get 1.65 moller as our final answer. And so with that, we've answered the question overall, I hope this helped. And until next time.

Ch.15 - Chemical Equilibrium

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Brown 15th Edition

Ch.15 - Chemical Equilibrium

Problem 52a

Chapter 15, Problem 52a

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.

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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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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) ⇌ 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.