Consider the following equilibrium, for which K_p= 0.0752 at 480°C: 2 Cl₂(g) + 2 H₂O(g) ⇌ 4 HCl(g) + O₂(g) (b) What is the value of K_p for the reaction Cl₂(g) + H₂O(g) ⇌ 2 HCl(g) + 1/2 O2(g)?

검증된 단계별 안내

Understand that the equilibrium constant Kp is dependent on the stoichiometry of the balanced chemical equation. The given reaction is: 2 Cl2(g) + 2 H2O(g) ⇌ 4 HCl(g) + O2(g) with Kp = 0.0752.

Recognize that the new reaction Cl2(g) + H2O(g) ⇌ 2 HCl(g) + 1/2 O2(g) is derived by halving the coefficients of the original reaction. This means the stoichiometry of the reaction has changed.

Recall that when the coefficients of a balanced equation are multiplied by a factor, the equilibrium constant is raised to the power of that factor. In this case, the coefficients are halved, which corresponds to raising Kp to the power of 1/2.

Express the mathematical relationship for the new Kp: Kp(new) = (Kp(original))^(1/2).

Substitute the given Kp value into the equation: Kp(new) = (0.0752)^(1/2). This will give you the equilibrium constant for the new reaction.

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주요 개념

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Equilibrium Constant (Kp)

The equilibrium constant, Kp, 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. It is calculated using the partial pressures of gases involved in the reaction. A Kp value less than 1 indicates that reactants are favored at equilibrium, while a value greater than 1 suggests that products are favored.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationship between the amounts of reactants and products in a chemical reaction, as represented by the balanced chemical equation. In this case, the stoichiometry of the reactions must be carefully considered to relate the Kp values of different but related reactions, as they can be derived from one another by manipulating the coefficients of the balanced equations.

Manipulating Equilibrium Expressions

When dealing with equilibrium constants, it is essential to understand how to manipulate equilibrium expressions. If a reaction is reversed, the new Kp is the reciprocal of the original. If the coefficients of a balanced equation are multiplied by a factor, the Kp is raised to the power of that factor. This principle allows for the calculation of Kp for related reactions based on known values.

Consider the following equilibrium, for which Kp = 0.0752 at 480°C: 2 Cl2(g) + 2 H2O(g) ⇌ 4 HCl(g) + O2(g) (b) What is the value of Kp for the reaction Cl2(g) + H2O(g) ⇌ 2 HCl(g) + 1/2 O2(g)?