What is the acidity constant for the following reaction given that the hydronium ion concentration of a \(0.04 \mathrm{M}\) solution of \(\mathrm{Ni}^{2+}\) solution of nickel(II) perchlorate is \(4.5 \times 10^{-6}\) ? $$ \mathrm{Ni}^{2+}(\text { aq. })+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{Ni}(\mathrm{OH})^{+}(a q .)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) $$ (a) \(2 \times 10^{-12}\) (b) \(4 \times 10^{-6}\) (c) \(5 \times 10^{-12}\) (d) \(5 \times 10^{-10}\)

In the world of chemistry, chemical equilibrium is a central concept that describes the state of a reaction when the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactant and product over time. At this point, it might seem that the reaction has stopped, but in reality, the reactants and products continue to interconvert at a constant rate.

Understanding chemical equilibrium helps us to predict how a reaction will respond to changes in conditions, such as concentration, temperature, or pressure, according to Le Châtelier's Principle. This principle asserts that when an external stress is applied to a system in equilibrium, the system adjusts to minimize that stress.

When tackling problems involving equilibrium, such as the acidity constant calculation for a reaction, it's crucial to grasp that although the concentrations of the substances involved remain constant at equilibrium, they are not necessarily equal to each other. They are defined by the equilibrium constant of the reaction.

The hydronium ion concentration in a solution is a measure of its acidity and is represented by the symbol \( [\mathrm{H_3O}^+] \). It is essentially the concentration of hydrogen ions \( \mathrm{H}^+ \) that have bonded with water molecules to form hydronium ions. In aqueous solutions, the concentration of hydronium ions can range from as high as 10 moles per liter in strong acids to as low as 10^-14 moles per liter in strong bases.The hydronium ion concentration is crucial in determining the pH of a solution, where \( \text{pH} = -\log[\mathrm{H_3O}^+] \). This relationship allows chemists to quickly assess whether a solution is acidic, neutral, or basic. When working with acidity constants, knowing the hydronium ion concentration is necessary to calculate the equilibrium concentrations of all species in a reaction, as demonstrated in the provided exercise.

The equilibrium constant expression for a chemical reaction quantifies the relationship between the concentrations of reactants and products at equilibrium. It is denoted by \( K \) and varies only with temperature, representing a unique value for every reaction at a given temperature.

The general form of the expression for a reaction \(a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}\) is given by: \[ K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \] where \( [\text{A}], [\text{B}], [\text{C}], [\text{D}] \) represent the molar concentrations of the reactants and products, respectively, and \( a, b, c, d \) are the stoichiometric coefficients. It’s important to note that pure solids and liquids do not appear in the expression.

In the context of acid-base reactions, the equilibrium constant is called the acidity constant \( Ka \) and specifically refers to the equilibrium involving the dissociation of an acid into its ions. Calculating the value of \( Ka \) from known concentrations of reactants and products, as in our exercise, enables chemists to understand the strength of an acid and predict the direction of the reaction.