Question

Write the equilibrium law for the following reactions in aqueous solution. $$ \begin{array}{l} \text { (a) } \mathrm{HClO}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}+(a q)^{+} \mathrm{ClO}^{-}(a q) \\ \text { (b) } \mathrm{CO}_{3}^{2-}(a q)+\mathrm{HSO}^{-}(a q) \rightleftharpoons \\ \mathrm{HCO}_{3}^{-}(a q)+\mathrm{SO}_{4}^{2-}(a q) \end{array} $$

Short answer

\[ \text{For reaction (a): } K_{eq} = \frac{[\text{H}_3\text{O}^+][\text{ClO}^-]}{[\text{HClO}]} \quad \text{For reaction (b): } K_{eq} = \frac{[\text{HCO}_3^-][\text{SO}_4^{2-}]}{[\text{CO}_3^{2-}][\text{HSO}^-]} \]

Step-by-step solution

Identify the reactants and products for Reaction (a)

For the first reaction, the reactants are HClO and H2O, and the products are H3O+ and ClO-.

Write the equilibrium expression for Reaction (a)

The equilibrium constant expression, known as the law of mass action, for reaction (a) is the product of the concentrations of the products raised to the power of their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to the power of their respective stoichiometric coefficients. For this reaction, since all species are in aqueous solution and we assume water's concentration is essentially constant, the expression is: \[ K_{eq} = \frac{[\text{H}_3\text{O}^+][\text{ClO}^-]}{[\text{HClO}]} \] Note that water is not included in the expression because its concentration does not change significantly.

Identify the reactants and products for Reaction (b)

For the second reaction, the reactants are CO3^2- and HSO^-, and the products are HCO3^- and SO4^2-.

Write the equilibrium expression for Reaction (b)

Similarly, the equilibrium constant expression for reaction (b) is given by: \[ K_{eq} = \frac{[\text{HCO}_3^-][\text{SO}_4^{2-}]}{[\text{CO}_3^{2-}][\text{HSO}^-]} \]

Key concepts

Law of Mass Action

The Law of Mass Action is a principle that relates the rate of a chemical reaction to the concentration of the reactants. In the context of chemical equilibrium, it provides the foundation for the equilibrium constant expression. For a generic reaction where reactants A and B react to form products C and D, with stoichiometric coefficients a, b, c, and d respectively, the Law of Mass Action states that at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction.

This balance can be expressed mathematically as: \[ K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]
The equilibrium constant, \( K_{eq} \), is a dimensionless number that gives a sense of the extent to which a reaction proceeds before reaching equilibrium. If \( K_{eq} \) is very large, the products are highly favored at equilibrium. Conversely, if \( K_{eq} \) is very small, the reactants are favored. The concentrations in the expression are usually measured in molarity (mol/L), and the exponents are the stoichiometric coefficients from the balanced chemical equation.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, resulting in no net change in the concentrations of the reactants and products over time. It is a dynamic state, meaning that while the concentrations remain constant, the reactants and products continually convert into each other. Equilibrium can be reached from either direction of a reversible reaction.

Understanding equilibrium is essential for predicting the position of balance and the concentrations of substances in a mixture at equilibrium. The equilibrium constant gives us insight into this balance. It's important to note that equilibrium does not mean the amounts of reactants and products are equal, but that their rates of formation are. External factors like temperature, pressure (for gases), and concentration changes can shift the position of equilibrium, which is described by Le Chatelier's Principle.

Stoichiometric Coefficients

Stoichiometric coefficients are the numbers in front of chemicals in a balanced chemical equation that indicate the relative amounts of reactants and products involved in the reaction. They reflect the principle of the conservation of mass and the conservation of atoms: for every atom going into a reaction, the same number and type of atoms must come out in the products.

The stoichiometric coefficients play a crucial role in the Law of Mass Action. They determine the powers to which the concentrations of the reactants and products are raised in the equilibrium constant expression. For example, in the reaction: \[ aA + bB \leftrightharpoons cC + dD \]
the coefficients a, b, c, and d must be used as exponents in the equilibrium expression: \[ K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]
When writing equilibrium constant expressions, it is important that the chemical equation is balanced correctly, and thus the stoichiometric coefficients are accurate to ensure the proper calculation of the equilibrium constant.