Question

A \(0.100 \mathrm{M}\) solution of bromoacetic acid \(\left(\mathrm{BrCH}_{2} \mathrm{COOH}\right)\) is \(13.2 \%\) ionized. Calculate \(\left[\mathrm{H}^{+}\right],\left[\mathrm{BrCH}_{2} \mathrm{COO}^{-}\right]\), and \(\left[\mathrm{BrCH}_{2} \mathrm{COOH}\right]\)

Short answer

The concentrations of the bromoacetic acid solution are: \[ [H^+] = 0.0132\,\text{M} \] \[ [\mathrm{BrCH}_{2} \mathrm{COO}^-] = 0.0132\,\text{M} \] \[ [\mathrm{BrCH}_{2} \mathrm{COOH}] = 0.0868\,\text{M} \]

Step-by-step solution

Calculate the concentration of ionized bromoacetic acid

We can calculate the concentration of ionized bromoacetic acid using the given percentage ionization and its initial concentration. Percentage ionization = 13.2% Initial concentration (C) = 0.100 M Ionized concentration = Percentage ionization × Initial concentration = \(0.132 \times 0.100\) M Ionized concentration = 0.0132 M

Calculate the concentration of H⁺ and BrCH₂COO⁻ ions

Since both H⁺ and BrCH₂COO⁻ ions are produced in equimolar amounts during the ionization of bromoacetic acid, their concentration would be the same as the concentration of ionized bromoacetic acid. \[ [H⁺] = [\mathrm{BrCH}_{2} \mathrm{COO}^-] = 0.0132\,\text{M} \]

Calculate the concentration of un-ionized BrCH₂COOH

To find the concentration of un-ionized bromoacetic acid, we can subtract the ionized concentration from the initial concentration. \[ [\mathrm{BrCH}_{2} \mathrm{COOH}] = \text{Initial concentration} \,-\, \text{Ionized concentration} \] \[ [\mathrm{BrCH}_{2} \mathrm{COOH}] = 0.100\,\text{M} \,-\, 0.0132\,\text{M} \] Concentration of un-ionized BrCH₂COOH = 0.0868 M Thus, the concentrations are as follows: \[ [H^+] = 0.0132\,\text{M} \] \[ [\mathrm{BrCH}_{2} \mathrm{COO}^-] = 0.0132\,\text{M} \] \[ [\mathrm{BrCH}_{2} \mathrm{COOH}] = 0.0868\,\text{M} \]

Key concepts

Acid-Base Equilibrium

Acid-base equilibrium is a fundamental concept in chemistry, particularly in the study of reaction mechanisms involving acids and bases. An acid is a substance that can donate a proton (H⁺ ion), while a base is a substance that can accept a proton. When an acid is placed in an aqueous solution, it tends to donate protons to water, resulting in the formation of hydronium ions ((H_3O^+)) and the concurrent generation of anion counterparts called conjugate bases.

The dynamic state where the rate of the forward reaction (the ionization of the acid to produce H⁺ ions and its conjugate base) equals the rate of the reverse reaction (the recombination of H⁺ ions with the conjugate base to form the non-ionized acid) is called an acid-base equilibrium. At equilibrium, the concentrations of reactants and products remain constant over time.

• The strength of an acid is dictated by its tendency to donate protons; the stronger the acid, the more it ionizes in solution.
• Weak acids, such as bromoacetic acid in the exercise ((BrCH_2COOH)), do not completely dissociate in water, creating a balance between their ionized and non-ionized forms.
• Acid dissociation constants ((K_a)) help quantify the equilibrium, representing the ratio of the concentration of the products to the concentration of the reactants.

Chemical Concentration

Chemical concentration is a measure of the amount of a solute that is dissolved in a given quantity of solvent. It's a crucial concept in chemistry, as reactions depend on the concentration of reactants. Concentration can be expressed in several ways, such as molarity (M), which is moles of solute per liter of solution, and percentage concentration.

In the context of our textbook exercise, molarity is used to describe the concentration of bromoacetic acid in the solution. Understandably, the chemical concentration greatly influences the extent of acid ionization and thereby, the equilibrium state of the acid in solution.

• Increase in concentration typically leads to an increase in the number of ions produced, thus affecting the equilibrium.
• Dilution (decreasing concentration) will shift the equilibrium to generate more ions to maintain a constant ion product, in accordance with Le Chatelier's principle.
• Calculating the concentration of ionized and non-ionized species is essential to understanding the acid's behavior in solution and predicting the pH, which is a scale used to determine the acidity or basicity of the solution.

Percentage Ionization

Percentage ionization is a term used to quantify the extent of ionization of an acid or base in solution. It's calculated by taking the concentration of ionized acid, dividing by the initial concentration of the acid, and then multiplying by 100 to obtain a percentage.

This concept is a powerful tool for comparing the strength of weak acids or bases. A higher percentage ionization indicates a stronger acid or base. In our exercise, the percentage ionization provided tells us how much of the bromoacetic acid ((BrCH_2COOH)) has ionized in the aqueous solution.

• Understanding the percentage ionization helps in deducing the pH of the solution and in characterizing the nature of the solute as a weak or strong acid/base.
• Conditions such as temperature and common ion effect can influence the percentage ionization, thus requiring a consideration of the surrounding circumstances when interpreting results.
• For bromoacetic acid with a 13.2% ionization, we can discern that it is a weak acid since it does not fully ionize in solution. Such information is critical in various applications, including the formulation of buffer solutions and the titration of acids and bases.