Question

Calculate the \(\mathrm{pH}\) and the equilibrium concentration of \(\mathrm{HClO}\) in a \(0.10 M\) solution of hypochlorous acid. \(K_{\mathrm{a}} \mathrm{HClO}=2.8 \times 10^{-8}\)

Short answer

Question: Calculate the pH of a 0.10 M solution of hypochlorous acid (HClO) and determine the equilibrium concentration of the acid. Given, the Ka value for hypochlorous acid is 2.8 x 10⁻⁸. Answer: The pH of the 0.10 M solution of hypochlorous acid is 4.78 and the equilibrium concentration of HClO is 0.0999833 M.

Step-by-step solution

Write down the balanced chemical equation for the dissociation of HClO

The dissociation of hypochlorous acid (HClO) can be represented as: HClO \(\rightleftharpoons\) H⁺ + ClO⁻

Write down the Kₐ expression

The Kₐ expression for the dissociation of HClO is defined as: Kₐ \(=\frac{[H^+][ClO^-]}{[HClO]}\), where [H⁺], [ClO⁻], and [HClO] are the equilibrium concentrations of the ions and the acid, respectively.

Set up the initial concentrations and the changes during the reaction

Initially, we have 0.10 M HClO. Therefore, the initial concentrations for the equilibrium reaction table are: [HClO] = 0.10 M, [H⁺] = 0, [ClO⁻] = 0 During the dissociation: Δ[HClO] = -x, Δ[H⁺] = +x, Δ[ClO⁻] = +x

Determine the equilibrium concentrations

At equilibrium, the concentrations become: [HClO] = 0.10 - x, [H⁺] = x, [ClO⁻] = x

Substitute the equilibrium concentrations into the Kₐ expression

Inserting the equilibrium concentrations into the Kₐ expression: \(2.8\times10^{-8} =\frac{x\times x}{0.1-x}\)

Solve for x

As Kₐ is very small, we can assume that x is very small compared to 0.1, so 0.1 - x ≈ 0.1. Thus, the equation becomes: \(2.8\times10^{-8} =\frac{x^2}{0.1}\) or \(x^2=2.8\times10^{-9}\), solve for x, we have x = \(H^+\) which equals to: \(1.67\times10^{-5}\) M

Calculate the pH

The δpHδ is defined as the negative logarithm of the molar concentration of H⁺: \(pH = -\log[H^+] = -\log (1.67\times10^{-5})=4.78\)

Calculate the equilibrium concentration of HClO

The equilibrium concentration of HClO can be determined by substituting x back into the equilibrium concentration expressions given in step 4: \([HClO]_{eq}=0.1-x=0.1-(1.67\times10^{-5})=0.0999833M\) The pH of the 0.10 M solution of hypochlorous acid is 4.78 and the equilibrium concentration of HClO is 0.0999833 M.

Key concepts

pH Calculation

Understanding the concept of pH is essential if you're studying chemistry, especially when dealing with acids and bases. pH stands for 'potential of Hydrogen' and represents the acidity or basicity of a solution.

The pH is calculated as the negative logarithm of the concentration of hydrogen ions (\( H^+ \) ions) in a solution. The formula is given by: \[ pH = -\log[H^+] \] where \( [H^+] \) stands for the molarity of the hydrogen ions. In simpler terms, a low pH value indicates a high concentration of hydrogen ions, making the solution acidic, whereas a high pH value signifies a low concentration of hydrogen ions, thus a basic solution.

In the given exercise, we utilize logarithms to find that a hydrogen ion concentration of \( 1.67\times10^{-5} \) M leads to a pH of 4.78, indicating an acidic solution. Remember that the pH scale generally ranges from 0 (very acidic) to 14 (very basic), with 7 being neutral. Calculations like these are fundamental for understanding chemical reactions and the behavior of acids and bases in different conditions.

Equilibrium Concentration

The term 'equilibrium concentration' refers to the concentrations of reactants and products in a chemical reaction when the reaction has reached a state of balance—meaning the rate of the forward reaction equals the rate of the reverse reaction.

For a weak acid like hypochlorous acid (HClO) undergoing dissociation, we set up an equilibrium expression based on the initial concentrations and the changes it undergoes until equilibrium is established. This expression helps us to calculate the exact concentration of each species involved at equilibrium.

In our example, the initial concentration of HClO was 0.10 M, and as it dissociated, it produced equal amounts of \( H^+ \) and ClO⁻ ions. The change in concentration is denoted by 'x.' At equilibrium, the concentration of HClO decreased by x, while the concentrations of \( H^+ \) and ClO⁻ increased by x. Through this process, we were able to determine the equilibrium concentration of HClO, which turned out to be 0.0999833 M.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It essentially tells us how well an acid can donate \( H^+ \) ions when in an aqueous solution. A larger \( K_a \) value indicates a stronger acid, which dissociates more completely.

The \( K_a \) is defined by the equilibrium concentrations of the reactants and products for the dissociation reaction of the acid. The general expression for \( K_a \) is: \[ K_a =\frac{[H^+][A^-]}{[HA]} \] where \( [HA] \) is the concentration of the undissociated acid and \( [H^+] \) and \( [A^-] \) are the concentrations of the dissociated ions.

Employing the value of \( K_a \) for hypochlorous acid and the established equilibrium concentrations, we are able to solve for x, which in turn allowed us to calculate both the pH and the equilibrium concentration of HClO. Given \( K_a = 2.8 \times 10^{-8} \) for HClO, we see that it is a relatively weak acid as it only partially dissociates in water, a conclusion supported by its \( K_a \) value.