At 218°C, 𝐾_𝑐= 1.2×10⁻⁴ for the equilibrium NH₄SH(𝑠) ⇌ 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 218°C and decomposes until equilibrium is reached.

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Write the equilibrium expression for the reaction: For the decomposition of ammonium hydrosulfide, the equilibrium constant expression (Kc) is given by Kc = [NH3][H2S], where [NH3] and [H2S] are the molar concentrations of ammonia and hydrogen sulfide, respectively.

Set up the expression using initial concentrations and changes at equilibrium: Assume the initial concentrations of NH3 and H2S are 0 M. Let x be the change in concentration of NH3 and H2S at equilibrium. Since the stoichiometry of NH3 and H2S in the balanced equation is 1:1, the concentration of each at equilibrium will be x M.

Substitute the equilibrium concentrations into the Kc expression: Substitute x for [NH3] and [H2S] in the equilibrium expression, resulting in Kc = x^2.

Solve for x: Rearrange the equation to solve for x. Since Kc = 1.2×10^(-4), set up the equation x^2 = 1.2×10^(-4). Solve for x to find the equilibrium concentrations of NH3 and H2S.

Check the units and make sure they are consistent throughout the problem to ensure the correctness of the calculation.

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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 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 changing the conditions (such as concentration, temperature, or pressure), the system will adjust to counteract the disturbance and restore a new equilibrium. In this case, the decomposition of solid NH₄SH into gaseous products will shift the equilibrium position to favor the formation of NH₃ and H₂S until the equilibrium concentrations are established.

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 of the gaseous products based on the initial amount of solid NH₄SH and the value of Kc.

At 218°C, 𝐾𝑐 = 1.2×10−4 for the equilibrium NH4SH(𝑠) ⇌ 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 218°C and decomposes until equilibrium is reached.