Question

Give the general expression for the equilibrium constant of the follow- ing generic reaction: $$a A+b B \rightleftharpoons c \mathrm{C}+d \mathrm{D}$$

Short answer

For the given reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant \(K\) is expressed as \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\).

Step-by-step solution

Identifying the Reaction Components

First, identify the reactants and products in the given generic reaction along with their stoichiometric coefficients. The reactants are A and B with stoichiometric coefficients a and b, respectively. The products are C and D with stoichiometric coefficients c and d, respectively.

Writing the Expression for the Equilibrium Constant

The equilibrium constant expression (K) for a reaction is given by the product of the concentrations of the products raised to the power of their coefficients, divided by the product of the concentrations of the reactants raised to the power of their coefficients. Each concentration is represented as [species].

Formulating the Equilibrium Constant Expression

For the given reaction, the general expression for the equilibrium constant (K) will be the concentration of C raised to the power of c times the concentration of D raised to the power of d, divided by the concentration of A raised to the power of a times the concentration of B raised to the power of b.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, meaning that the concentrations of reactants and products remain constant over time, although not necessarily equal. This balance between the two processes occurs in closed systems and is dynamic, as reactions continue to occur, but without any net change in the amounts of substances.

To visualize this, imagine a busy street with cars moving equally in both directions at the same rate. There's ongoing movement, but the number of cars on each side remains the same. Similarly, in a chemical reaction at equilibrium, the continuous conversion of reactants to products and vice versa happens at an equal rate, maintaining a constant composition.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is essentially the 'recipe' for a reaction, telling chemists how much of each reactant is needed to produce a given amount of product.

The coefficients in a balanced chemical equation indicate the mole ratio of the substances involved in the reaction; for example, in the equation \(aA + bB \rightleftharpoons cC + dD\), \(a\), \(b\), \(c\), and \(d\) tell us how many moles of each substance react or are produced. This becomes crucial when calculating the equilibrium constant, as these stoichiometric coefficients directly influence the expression.

Reactants and Products

Reactants are the starting materials in a chemical reaction, while products are the substances produced as a result of that reaction. In a balanced equation, the number and type of atoms are conserved from reactants to products, demonstrating the law of conservation of mass.

During a reaction, reactants are consumed to create products until equilibrium is reached. At this point, the reactions do not stop; instead, the conversion rates of reactants to products and vice versa are the same, generating no net change in their concentrations, which is an important aspect when considering reaction dynamics and calculating the equilibrium constant.

Concentration

The concentration of a substance in a mixture, often denoted by square brackets \([ ]\), is a measure of how much of that substance is present in a given volume of the mixture. In the context of equilibrium, concentrations are used to determine the position of equilibrium and calculate the equilibrium constant.

In the equation \(aA + bB \rightleftharpoons cC + dD\), the concentration of each species is raised to the power of its stoichiometric coefficient in the balanced chemical equation. The equilibrium constant expression, therefore, incorporates these concentrations, reflecting the ratio of product concentrations to reactant concentrations, each raised to the power of their respective coefficients, providing insight into the favorability and extent of a reaction.