(b) Calculate the pH of a buffer formed by mixing 85 mL of 0.13 M lactic acid with 95 mL of 0.15 M sodium lactate.

Verified step by step guidance

1. Step 1: Understand the concept of a buffer solution. A buffer solution resists changes in pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base.
2. Step 2: Identify the components of the buffer. In this problem, lactic acid (CH₃CH(OH)COOH) is the weak acid, and sodium lactate (CH₃CH(OH)COONa) is the conjugate base.
3. Step 3: Use the Henderson-Hasselbalch equation to calculate the pH of the buffer. The equation is: ${\mathrm{pH}}_{}={\mathrm{pK}}_{}a+log\left(\frac{\mathrm{[A}]-}{\mathrm{[HA]}}\right)$, where [A⁻] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.
4. Step 4: Calculate the concentrations of lactic acid and sodium lactate in the buffer solution. Use the formula $C=\frac{n}{V}$, where C is concentration, n is the number of moles, and V is the volume in liters. First, calculate the moles of each component using their initial concentrations and volumes, then find the final concentrations in the total volume of the buffer.
5. Step 5: Substitute the calculated concentrations and the known pKa value of lactic acid into the Henderson-Hasselbalch equation to find the pH of the buffer solution.

Key Concepts

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, lactic acid (weak acid) and sodium lactate (conjugate base) form a buffer that helps maintain a stable pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is essential for determining the pH of the buffer in the given problem.

Dilution and Concentration Calculations

When mixing solutions, the final concentrations of the components must be calculated based on their initial concentrations and volumes. The total volume after mixing affects the concentrations of lactic acid and sodium lactate, which are necessary for applying the Henderson-Hasselbalch equation. Understanding dilution principles is crucial for accurate pH calculations in buffer solutions.