Problem 89 - Chemistry: The Central Science

Question

How many microliters of \(1.000 \mathrm{M} \mathrm{NaOH}\) solution must be added to \(25.00 \mathrm{~mL}\) of a \(0.1000 \mathrm{M}\) solution of lactic acid \(\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right.\) or \(\left.\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\right]\) to produce \(\mathrm{a}\) buffer with \(\mathrm{pH}=3.75 ?\)

Step-by-Step Solution

Answer

To create a buffer with a pH of 3.75, approximately 1580 μL of 1.000 M NaOH solution must be added to 25.00 mL of 0.1000 M lactic acid solution.

Step 1: Determine the pKa value of lactic acid

We are given the desired pH of 3.75. We need first to find the pKa of lactic acid. The Ka of lactic acid is \(1.4 \times 10^{-4}\). Therefore, the pKa value can be calculated by: \(pKa = -\log_{10}(Ka) = -\log_{10}(1.4 \times 10^{-4}) \approx 3.85\)

Step 2: Use the Henderson-Hasselbalch equation to find the ratio of [A⁻]/[HA]

We can now plug the pKa, and pH values into the Henderson-Hasselbalch equation: \(3.75 = 3.85 + \log\frac{[A^{-}]}{[HA]}\) Rearrange the equation to find the ratio of the conjugate base to the weak acid: \(\frac{[A^{-}]}{[HA]} = 10^{3.75 - 3.85} \approx 0.63\)

Step 3: Calculate the amount of moles of lactic acid

Now, we can calculate the moles of lactic acid present in the 25.00 mL of 0.1000 M solution: moles of lactic acid = concentration × volume = 0.1000 mol/L × 0.025 L ≈ 0.0025 mol

Step 4: Determine the moles of NaOH required

Using the previously computed ratio, we can now find the required moles of NaOH: moles of NaOH = moles of lactic acid × \(\frac{[A^{-}]}{[HA]}\) = 0.0025 mol × 0.63 ≈ 0.00158 mol

Step 5: Calculate the volume of the NaOH solution

Finally, we can find the volume of the NaOH solution needed to achieve the desired pH by dividing the amount of NaOH moles by its concentration: Volume (in liters) = \(\frac{\text{moles of NaOH}}{\text{concentration of NaOH}}\) = \(\frac{0.00158 \text{ mol}}{1.000 \text{ M}}\) ≈ 0.00158 L To convert the volume to microliters, multiply it by \(10^6\): Volume (in microliters) = 0.00158 L × \(10^6\) ≈ 1580 μL Therefore, approximately 1580 μL of 1.000 M NaOH solution must be added to the 25.00 mL 0.1000 M lactic acid solution to produce a buffer with a pH of 3.75.

Key Concepts

Understanding Buffer Solutions

A buffer solution is a special type of solution that resists changes in pH even when small amounts of acid or base are added. This is particularly important in many chemical and biological processes where maintaining a stable pH is crucial. In a buffer solution, there is a mixture of a weak acid and its conjugate base.

• The weak acid can neutralize added bases.
• The conjugate base can neutralize added acids.

For example, in the case of lactic acid being used to create a buffer solution, it acts as the weak acid, while its conjugate base, lactate, acts to neutralize any additional acid introduced to the solution. This mechanism helps the solution maintain a stable pH, which is necessary for many reactions and processes.
Understanding this concept can be especially helpful when solving exercises involving buffers, such as calculating how much of a particular component is needed to achieve a desired pH.

The Role of pKa Value in Buffers

The pKa value of an acid is a critical concept in understanding buffer solutions. It is essentially the negative logarithm of the acid dissociation constant (Ka) and indicates how strongly an acid dissociates into its ions in a solution. The lower the pKa value, the stronger the acid.

• pKa is used to predict the pH of the buffer solution.
• It helps to determine the optimal pH range for buffer action.

In the problem we are dealing with, the pKa of lactic acid is calculated based on its known Ka value, which is given as \(1.4 \times 10^{-4}\). Using the formula \(pKa = -\log_{10}(Ka)\), we calculated the pKa to be approximately 3.85.
This information allows us to set up the Henderson-Hasselbalch equation, which relates the pH, the pKa, and the ratio of the concentrations of the conjugate base and the weak acid in the buffer. Understanding pKa is fundamental to solving buffer solution problems.

Calculating Moles for Chemical Solutions

Moles calculation is a fundamental step in many chemistry problems, including buffer preparation. To understand this concept better, it is essential to know that a mole represents \(6.022 \times 10^{23}\) units of any given substance, such as atoms, molecules, or ions.
When preparing buffer solutions, knowing the number of moles involved helps to determine quantities necessary for achieving the desired concentrations and pH. For example:

• Moles of lactic acid are calculated by multiplying its concentration (in mol/L) by the volume (in L).
• We found that 0.0025 mol of lactic acid is present in 25.00 mL of a 0.1000 M solution.

These calculated moles are then used in subsequent calculations, like finding the correct amount of NaOH needed to achieve the desired buffer pH, as outlined in the original problem.
Mastering moles calculation facilitates accurate preparation and adjustments in chemical experiments and solutions.

Grasping the Titration Process

Titration is a common laboratory technique used to determine the concentration of a solution by gradually adding a titrant until the reaction reaches its endpoint. To perform a titration effectively, several key components and steps must be understood:

• The titrant is a solution of known concentration, used to react with the solution of unknown concentration.
• An indicator or a pH meter is used to determine when the endpoint of the titration is reached.

In the context of our problem, we titrate the lactic acid solution with a sodium hydroxide solution to create a buffer with specific pH. Using the Henderson-Hasselbalch equation during titration allows us to determine how much NaOH must be added to achieve the desirable buffer pH. This requires calculating the moles of each component involved in the reaction.
Titration is essential in many fields of chemistry, and learning this technique can boost your understanding in various scientific applications. Understanding the role of titration in buffer solutions can help immensely in accurately carrying out such reactions.