If you need to prepare 250.0 mL of a pH 5.00 buffer tha
t has a total buffer concentration of acetic acid +
sodium acetate of 0.050 M, how many moles of each will you need to prepare the solution? Given solutions
of acetic acid and sodium acetate with concentrations of 0.10 M and pKa= 4.76, describe how to pre
pare this
buffer.
I saw this question posted on this site but there was no final answer and I dont understand the math that needs to be done to get to it
To prepare the pH 5.00 buffer solution with a total buffer concentration of acetic acid and sodium acetate of 0.050 M, you need to calculate the number of moles of each component required.
The Henderson-Hasselbalch equation can be used to determine the ratio of the acid (acetic acid) and its conjugate base (sodium acetate) needed to achieve the desired pH.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log ([salt]/[acid])
pH is the desired pH (5.00 in this case),
pKa is the acid dissociation constant (-log Ka) for acetic acid (4.76 in this case),
[salt] is the concentration of the salt (sodium acetate), and
[acid] is the concentration of the acid (acetic acid).
Rearranging the equation to solve for the ratio [salt]/[acid]:
[salt]/[acid] = 10^(pH - pKa)
Substituting the given values:
[salt]/[acid] = 10^(5.00 - 4.76)
[salt]/[acid] = 10^0.24
[salt]/[acid] = 1.580
This means that the ratio of the concentration of sodium acetate to acetic acid should be 1.580.
Since the total buffer concentration is given as 0.050 M, we can set up the following equation:
0.050 M = [salt] + [acid]
Let's assume the volume of the buffer solution is V (in liters), which is given as 250.0 mL or 0.250 L.
Using the ratio calculated earlier, we can express the concentrations of sodium acetate and acetic acid in terms of the ratio:
[salt] = 1.580 [acid]
Plugging this into the equation:
0.050 M = 1.580 [acid] + [acid]
0.050 M = 2.580 [acid]
Solving for [acid]:
[acid] = 0.050 M / 2.580
[acid] ≈ 0.019 M
Now that we have the concentration of acetic acid, we can calculate the moles of acetic acid needed:
moles of acetic acid = concentration × volume
moles of acetic acid = 0.019 mol/L × 0.250 L
moles of acetic acid = 0.00475 mol
Since the ratio of [salt] to [acid] is 1.580, the moles of sodium acetate required can be calculated:
moles of sodium acetate = ratio × moles of acetic acid
moles of sodium acetate = 1.580 × 0.00475 mol
moles of sodium acetate ≈ 0.00752 mol
Therefore, to prepare the pH 5.00 buffer solution with a total buffer concentration of 0.050 M, you will need approximately 0.00475 moles of acetic acid and 0.00752 moles of sodium acetate.
To prepare the buffer solution:
1. Measure 0.00475 moles of acetic acid.
2. Dissolve the acetic acid in a portion of the 250.0 mL (0.250 L) total volume.
3. Measure 0.00752 moles of sodium acetate.
4. Dissolve the sodium acetate in the remaining portion of the 250.0 mL (0.250 L) total volume.
5. Mix the two solutions thoroughly to ensure homogeneity.
6. Check the pH of the buffer solution using a pH meter or pH indicator paper, and adjust if necessary by adding small amounts of acetic acid or sodium acetate solution.
Note: It is important to handle chemicals safely and accurately measure volumes and masses.