At 218°C, 𝐾 𝑐 = 1.2×10 −4 for the equilibrium NH 4 SH(𝑠) ⇌ NH 3 (𝑔) + H 2 S(𝑔) (a) Calculate the equilibrium concentrations of NH 3 and H 2 S if a sample of solid NH 4 SH is placed in a closed vessel at 218°C and decomposes until equilibrium is reached.

Hello everyone. Today we have the following problem. The equilibrium constant for the following decomposition reaction at 212°C is 1.2. What are the equilibrium concentrations of chlorine, chlorine and oxygen gas? If a sample of our calcium hypochlorite is put inside a closed container at two, 12°C and allowed to reach equilibrium. So what we first want to do it's right are equal expression. But we must take into account some things. We're gonna only include Aquarius and gaseous species in this equal expression, solids and liquids are ignored. And another thing we want to focus on is the fact that coefficient, so coefficients are going to be our exponents in the expression. And then we're gonna use brackets to indicate concentration. So writing out our equilibrium expression, equilibrium expression, it's going to be the concentration of our products over our reactant. Since both of our, our reactant are solids, we are not going to include them. So we're just gonna include our products, which is our chlorine gas and our oxygen gas. So based on solid geometry principles, the concentrations of these two are going to be the same. So we're going to let X represent the concentration of our chlorine gas, which is going to be equal to the concentration of oxygen gas. If we let X represent that our expression can be as follows, we will have our K C equal to X times X which is X squared. Furthermore, We know that our KC expression is 1.2 or the equilibrium constant. So we're gonna do 1.2 is equal to X squared. We're gonna take the square root of both sides. And that's gonna give us X equaling 1.1 molar as our final answer. So these are the equilibrium concentrations of both of our products. And 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 51a

Chapter 15, Problem 51a

At 218°C, 𝐾_𝑐= 1.2×10⁻⁴ for the equilibrium NH₄SH(𝑠) ⇌ NH₃(𝑔) + H₂S(𝑔) (a) Calculate the equilibrium concentrations of NH₃ and H₂S if a sample of solid NH₄SH is placed in a closed vessel at 218°C and decomposes until equilibrium is reached.

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Identify the equilibrium expression for the reaction: NH_4SH(s) ⇌ NH_3(g) + H_2S(g). Since NH_4SH is a solid, it does not appear in the equilibrium expression. Therefore, K_c = [NH_3][H_2S].

Let x be the equilibrium concentration of NH_3 and H_2S. Since the stoichiometry of the reaction is 1:1, [NH_3] = x and [H_2S] = x at equilibrium.

Substitute the equilibrium concentrations into the equilibrium expression: K_c = x * x = x^2.

Set the equilibrium constant equal to the expression: 1.2 \times 10^{-4} = x^2.

Solve for x by taking the square root of both sides to find the equilibrium concentrations of NH_3 and H_2S.

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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 NH₄SH(s) ⇌ NH₃(g) + H₂S(g), Kc = [NH₃][H₂S] / [NH₄SH]. Since NH₄SH is a solid, its concentration does not appear in the expression, simplifying the calculation of equilibrium concentrations.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will adjust to counteract the disturbance and restore a new equilibrium. In this case, the introduction of solid NH₄SH will shift the equilibrium position to favor the formation of NH₃ and H₂S until the concentrations stabilize according to the Kc value.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. For the decomposition of NH₄SH, the stoichiometry indicates that one mole of NH₄SH produces one mole of NH₃ and one mole of H₂S. This relationship is crucial for calculating the equilibrium concentrations based on the initial amount of solid NH₄SH and the changes that occur as the system reaches equilibrium.