Question

In general terms, what does the equilibrium constant for a reaction represent? What is the algebraic form of the equilibrium constant for a typical reaction? What do square brackets indicate when we write an equilibrium constant?

Short answer

The equilibrium constant (K) represents the ratio of the concentrations of the products and reactants when a reaction reaches equilibrium, indicating the extent of the reaction and the relative proportions of products and reactants. Its algebraic form for a general reaction, \(aA + bB \rightleftharpoons cC + dD\), can be written as \(K = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}\), where the molar concentrations of the substances at equilibrium are denoted by square brackets, such as [A], and the coefficients from the balanced chemical equation are represented by a, b, c, and d.

Step-by-step solution

Equilibrium Constant Definition

The equilibrium constant (K) for a reaction represents the ratio of the concentrations of the products and reactants when the reaction reaches equilibrium. At equilibrium, the rates of the forward and reverse reactions are equal, meaning that there's no net change in the concentrations of products and reactants. The equilibrium constant, therefore, gives us an idea of the extent of the reaction and the relative proportions of products and reactants at equilibrium. A high value of K indicates that the products are favored, while a low value indicates that the reactants are favored.

Algebraic Form of the Equilibrium Constant

The algebraic form of the equilibrium constant for a general chemical reaction can be written using the following equation: \(K = \dfrac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}\) Let's consider a general chemical reaction with reactants A and B, and products C and D: \(aA + bB \rightleftharpoons cC + dD\) The equilibrium constant (K) for this reaction can be written as: \(K = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}\) In this equation, [A], [B], [C], and [D] represent the molar concentrations of the respective substances at equilibrium, and a, b, c, and d are the coefficients from the balanced chemical equation.

Significance of Square Brackets

In the context of an equilibrium constant expression, square brackets, [ ], are used to represent the molar concentration of a substance. For example, [A] represents the molar concentration of substance A at equilibrium. The use of square brackets simplifies the notation and makes it easier to write the expressions for equilibrium constants.