Problem 98 - Chemistry and Chemical Reactivity

Question

Chloroacetic acid, \(\mathrm{ClCH}_{2} \mathrm{CO}_{2} \mathrm{H},\) is a moderately weak acid \(\left(K_{\mathrm{a}}=1.40 \times 10^{-3}\right) .\) If you dissolve \(94.5 \mathrm{mg}\) of the acid in water to give \(125 \mathrm{mL}\) of solution, what is the pH of the solution?

Step-by-Step Solution

Answer

The pH of the solution is approximately 2.47.

Step 1: Convert mass to moles

Given the mass of chloroacetic acid is 94.5 mg, convert this to grams (0.0945 g). Use its molar mass (94.50 g/mol) to calculate moles: \[ \text{moles} = \frac{0.0945 \text{ g}}{94.50 \text{ g/mol}} = 0.001000 \text{ mol} \]

Step 2: Determine concentration of the acid

Convert 125 mL of solution to liters (0.125 L). Calculate molarity (\(M\)), which is moles per liter:\[ M = \frac{0.001000 \text{ mol}}{0.125 \text{ L}} = 0.00800 \text{ M} \]

Step 3: Set up the ionization equation

Write the ionization of chloroacetic acid in water: \[ \text{ClCH}_2\text{CO}_2\text{H} \rightleftharpoons \text{CH}_2\text{CO}_2^- + \text{H}^+ \]Let \(x\) be the concentration of \(\text{H}^+\). The equilibrium concentrations in terms of \(x\) are:\[ \text{[CH}_2\text{CO}_2^-\text{]} = x, \quad \text{[H}^+\text{]} = x, \quad \text{[ClCH}_2\text{CO}_2\text{H]} = 0.00800 - x \]

Step 4: Apply the acid dissociation constant

Plug into the formula for the acid dissociation constant:\[ K_a = \frac{x^2}{0.00800 - x} \approx 1.40 \times 10^{-3} \]Assuming \(x\) is small, simplify to:\[ x^2 = 1.40 \times 10^{-3} \times 0.00800 \approx 1.12 \times 10^{-5} \]So,\[ x = \sqrt{1.12 \times 10^{-5}} \approx 3.35 \times 10^{-3} \]

Step 5: Calculate pH

The pH is calculated using the formula:\[ \text{pH} = -\log(x) = -\log(3.35 \times 10^{-3}) \approx 2.47 \]

Key Concepts

Chloroacetic Acid

Chloroacetic acid (\( \text{ClCH}_2\text{CO}_2\text{H} \)) is a type of carboxylic acid where a chlorine atom replaces one of the hydrogens in acetic acid. It is known for being a moderately weak acid compared to strong acids like hydrochloric acid but stronger than its parent, acetic acid.
This is due to the electronegative chlorine atom, which stabilizes the conjugate base through an inductive effect, pulling electron density away from the carboxylate ion. This process makes chloroacetic acid more likely to donate a proton when dissolved in water.

• This gives chloroacetic acid its moderately high acid dissociation constant (\( K_a = 1.40 \times 10^{-3} \)).
• The slightly higher value of \( K_a \) compared to acetic acid (\( K_a = 1.8 \times 10^{-5} \)) signifies that chloroacetic acid dissociates to give more \( \text{H}^+ \) ions.

This property is crucial for understanding how chloroacetic acid behaves in solutions and how it affects the \( \text{pH} \).

pH Calculation

Calculating the pH of chloroacetic acid involves determining how much the acid dissociates in a solution to produce hydrogen ions (\( \text{H}^+ \)). The pH scale indicates the acidity or basicity of a solution, with lower values representing more acidic solutions.
To calculate the pH:

• Determine the molarity of chloroacetic acid in the solution. In our example, the conversion from moles to a concentration of \( 0.00800 \, \text{M} \) sets the stage.
• Use the acid dissociation constant (\( K_a \)) to find the concentration of hydrogen ions produced (\( x \)).
• For weak acids like chloroacetic acid, the assumption that \( x \) is small compared to the initial concentration simplifies calculations.
• The equilibrium hydrogen ion concentration \( x \) was calculated as \( 3.35 \times 10^{-3} \). Using the formula \( \text{pH} = -\log(x) \), this gives a pH of approximately \( 2.47 \), indicating an acidic solution.

Acid Dissociation Constant (Ka)

The acid dissociation constant (\( K_a \)) is a measure of how well an acid can donate its protons to the solvent, typically water. It reflects the extent to which the acid molecules ionize in solution. Chloroacetic acid's \( K_a \) value of \( 1.40 \times 10^{-3} \) positions it in the range of weak acids but on the stronger side within this category.

• The equation used for \( K_a \) is \( K_a = \frac{[\text{CH}_2\text{CO}_2^-][\text{H}^+]}{[\text{ClCH}_2\text{CO}_2\text{H}]} \).
• The dissociation creates equilibrium between non-dissociated chloroacetic acid and its ions (\( \text{CH}_2\text{CO}_2^- \) and \( \text{H}^+ \)).
• In mathematical terms, \( K_a \) allows us to predict the concentration of \( \text{H}^+ \) ions in solution and subsequently the \( \text{pH} \).

Understanding \( K_a \) is vital for acid-base chemistry, helping determine the strength and behavior of acids in various chemical and biological contexts.