Question

\mathrm{~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],\left[\mathrm{BrCH}_{2} \mathrm{COOH}\right]\( and \)K_{a}$ for bromoacetic acid.

Short answer

The equilibrium concentrations of the bromoacetic acid solution are [H⁺] ≈ 0.0132 M, [BrCH₂COO⁻] ≈ 0.0132 M, and [BrCH₂COOH] ≈ 0.0868 M. The Ka value for bromoacetic acid is approximately 2.00 × 10⁻³.

Step-by-step solution

Find the change in concentration due to ionization

We are given that the 0.100 M solution of bromoacetic acid (BrCH₂COOH) is 13.2% ionized. To find the change in concentration due to ionization, we can multiply the initial concentration by the percentage ionized: Change in [BrCH₂COOH] = Initial concentration × % ionization = 0.100 M × 0.132 = 0.0132 M

Calculate the equilibrium concentrations

Since the amount of BrCH₂COOH that ionizes is equal to the amount of H⁺ and BrCH₂COO⁻ formed, we can find the equilibrium concentrations for each species as follows: [BrCH₂COOH]ₑ = Initial [BrCH₂COOH] - Change in [BrCH₂COOH] = 0.100 M - 0.0132 M = 0.0868 M [H⁺]ₑ = [BrCH₂COO⁻]ₑ = Change in [BrCH₂COOH] = 0.0132 M

Calculate the Ka value

Now that we have the equilibrium concentrations for each species, we can calculate the Ka value for bromoacetic acid using the following expression: Ka = \(\frac{[\mathrm{H}^{+}][\mathrm{BrCH}_{2} \mathrm{COO}^{-}]}{[\mathrm{BrCH}_{2} \mathrm{COOH}]}\) Ka = \(\frac{(0.0132)(0.0132)}{(0.0868)}\) Ka ≈ 2.00 × 10⁻³ So, the Ka value for bromoacetic acid is approximately 2.00 × 10⁻³. Thus, the equilibrium concentrations are: [H⁺] ≈ 0.0132 M [BrCH₂COO⁻] ≈ 0.0132 M [BrCH₂COOH] ≈ 0.0868 M and Ka ≈ 2.00 × 10⁻³.

Key concepts

Bromoacetic Acid

Bromoacetic acid, designated as BrCH₂COOH, is an organic compound belonging to the family of halogenated acetic acids. The bromine atom in its structure gives it unique chemical properties compared to its non-halogenated counterparts like acetic acid. The presence of the bromine atom increases the acidity of the carboxylic acid group. This makes bromoacetic acid an interesting subject for studying acid ionization. It is commonly used in various chemical applications and research due to its reactive nature.
Stability and ionization are key characteristics of bromoacetic acid, as they dictate how it behaves when dissolved in a solvent like water. This ionization process is crucial for understanding its chemical behavior and reactions.
When bromoacetic acid ionizes in a solution, it releases protons (H⁺) and forms the bromide acetate ion (BrCH₂COO⁻). These reactions and the resulting equilibrium states are essential for calculating properties like equilibrium concentrations and the acid dissociation constant (Ka).

Equilibrium Concentrations

In a chemical equilibrium involving bromoacetic acid, the solution contains a mixture of undissociated bromoacetic acid molecules, protons (H⁺), and the bromide acetate ions (BrCH₂COO⁻). Calculating equilibrium concentrations is essential for understanding the balance between these different species once equilibrium is reached.
To find these concentrations, you first need the initial concentration and the ionization percentage. For instance, if you start with a 0.100 M solution of bromoacetic acid, and 13.2% of it ionizes, you can determine how much of the acid remains un-ionized in the solution.

• The change in concentration due to ionization can be calculated by multiplying the initial concentration by the ionization percentage.
• The equilibrium concentration of BrCH₂COOH can be found by subtracting the change from the initial concentration.
• The concentrations of H⁺ and BrCH₂COO⁻ at equilibrium are equal to the change in the concentration of BrCH₂COOH.

Understanding these equilibrium concentrations is crucial for further calculations, such as determining the ionization percentage and acid dissociation constant.

Ionization Percentage

The ionization percentage of an acid solution tells you what fraction of the acid molecules have donated a proton to the solution. For bromoacetic acid, this percentage defines how extensively the acid breaks up into its ions in water. Knowing the ionization percentage is important because it influences the solution's pH and the equilibrium concentrations of all species in the reaction.
To find the ionization percentage, you take the amount of acid that has ionized and compare it to the initial concentration. A higher ionization percentage signifies a stronger acid because more molecules split into ions.
In the exercise given, bromoacetic acid is 13.2% ionized. This means that 13.2% of the total initial moles of bromoacetic acid have transformed into H⁺ ions and BrCH₂COO⁻ ions.

• The ionization percentage helps predict the behavior of the acid in different environments and under various conditions.
• It provides insight into the strength and reactivity of bromoacetic acid compared to other acids.

Acid Dissociation Constant (Ka)

The acid dissociation constant, abbreviated as Ka, is a numerical value used to quantify the strength of an acid in solution. It measures the extent to which an acid dissociates into its ions. For bromoacetic acid, a strong acid should have a higher Ka value, indicating that it dissociates more in solution.
You calculate Ka using the formula: \[K_a = \frac{[\text{H}^+][\text{BrCH}_2\text{COO}^-]}{[\text{BrCH}_2\text{COOH}]}\]This formula considers the concentrations of the ions produced (H⁺ and BrCH₂COO⁻) and the remaining concentration of the un-ionized acid (BrCH₂COOH) at equilibrium.

• The higher the Ka value, the stronger the acid, as it indicates a greater extent of ionization.
• In the given exercise, the Ka of bromoacetic acid calculated is approximately 2.00 × 10^-3, suggesting that it is a relatively strong acid.

Understanding Ka is essential for predicting how an acid will behave in different chemical processes and environments. It allows chemists to compare acid strengths and predict reaction outcomes.