Problem 21 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Calculate the pH of a buffer that is \(0.150 \mathrm{M}\) in lactic acid and \(0.120 M\) in sodium lactate. (b) Calculate the pH of a buffer formed by mixing \(75 \mathrm{~mL}\) of \(0.150 \mathrm{M}\) lactic acid with \(25 \mathrm{~mL}\) of \(0.120 \mathrm{M}\) sodium lactate.

Step-by-Step Solution

Answer

The pH of the buffer that is 0.150 M in lactic acid and 0.120 M in sodium lactate is 3.66, and the pH of the buffer formed by mixing 75 mL of 0.150 M lactic acid with 25 mL of 0.120 M sodium lactate is 2.61.

Step 1: Find pKa for lactic acid

The \(pK_a\) value for lactic acid is 3.86.

Step 2(a): Use the Henderson-Hasselbalch equation for 0.150 M lactic acid and 0.120 M sodium lactate

Plug the concentrations into the equation: \(pH = 3.86 + log_{10}\dfrac{0.120}{0.150}\) Now, calculate the pH: \(pH = 3.86 - 0.204\) \(pH = 3.656\)

Step 3(a): Round the pH value

Round the pH value to two decimal places to get the pH of the buffer solution: \(pH = 3.66\)

Step 2(b): Calculate the new concentrations of lactic acid and sodium lactate by mixing the solutions

Use the given volumes and concentrations to calculate the moles of lactic acid and sodium lactate: Moles of lactic acid = 0.150 M × 0.075 L = 0.01125 mol Moles of sodium lactate = 0.120 M × 0.025 L = 0.00300 mol Now, calculate the new total volume after mixing the solutions: Total volume = 0.075 L + 0.025 L = 0.100 L Determine the new concentrations: [\(HA\)] = (0.01125 mol) / (0.100 L) = 0.1125 M [\(A^-\)] = (0.00300 mol) / (0.100 L) = 0.0300 M

Step 3(b): Use the new concentrations in the Henderson-Hasselbalch equation

Plug the new concentrations into the equation: \(pH = 3.86 + log_{10}\dfrac{0.0300}{0.1125}\) Now, calculate the pH: \(pH = 3.86 - 1.25\) \(pH = 2.61\)

Step 4(b): Round the pH value

Round the pH value to two decimal places to get the pH of the mixed buffer solution: \(pH = 2.61\) In conclusion, the pH of the buffer that is 0.150 M in lactic acid and 0.120 M in sodium lactate is 3.66, and the pH of the buffer formed by mixing 75 mL of 0.150 M lactic acid with 25 mL of 0.120 M sodium lactate is 2.61.

Key Concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a simple yet powerful tool used in chemistry to calculate the pH of a buffer solution. It relates the pH to the pKa (acid dissociation constant) and the concentrations of the acid

• The equation is: \[pH = pK_a + \log_{10}\left(\frac{[A^-]}{[HA]}\right)\]
• In this equation:
  • \(pK_a\) is the negative log of the acid dissociation constant, a measure of acid strength
  • \([A^-]\) represents the concentration of the conjugate base
  • \([HA]\) is the concentration of the acid

By using this equation, students are able to calculate the pH of buffer solutions accurately. The beauty of the Henderson-Hasselbalch equation is in its simplicity.
It ties together important concepts such as acid strength and concentration ratios in a way that is easy to grasp.

pH calculation

Calculating the pH of a buffer involves a few straightforward steps once you understand the ingredients of the equation. Let’s walk through:

• First, identify the acid and base in your buffer system. In this case, lactic acid is the acid and sodium lactate is the conjugate base.
• Find the pKa value for the acid. For lactic acid, pKa is 3.86.
• Plug the concentrations of your acid and base into the Henderson-Hasselbalch equation.
  • For instance, if lactic acid concentration is 0.150 M and sodium lactate is 0.120 M, the setup is: \[pH = 3.86 + \log_{10}\left(\frac{0.120}{0.150}\right)\]
  • Calculate the logarithmic term to find the pH.
  • Finally, round off the results to get the desired number of decimal places.

This method allows you to understand the balance between the acid and its conjugate base in a solution, providing insight into how buffering capacities work.

lactic acid buffer

A lactic acid buffer is a type of chemical buffer solution that uses lactic acid and its conjugate base, sodium lactate, to maintain a stable pH level. Buffers are important in many chemical and biological processes because they help resist drastic changes in pH.
Here are some features of the lactic acid buffer:

• **Components:**
  • Lactic acid (\([HA]\)): An organic acid, which donates \(H^+\) ions in solution.
  • Sodium lactate (\([A^-]\)): It accepts \(H^+\) ions, balancing the \(pH\) by forming lactic acid in return.
• **Buffer Action:** When a small amount of acid or base is added to the buffer solution, the reaction between \([HA]\) and \([A^-]\) keeps the pH relatively stable.
• **Applications:** Such a buffer can be utilized in food preservation, sports drinks, and certain pharmaceutical products to ensure they remain effective over a range of conditions.

Using lactic acid buffers helps in maintaining a controlled environment, especially in biological systems where precise pH control is crucial.