An acetic acid buffer solution is required to have a pH of 5.27. You have a solution that contains 0.01 mol of acetic acid. How many moles of sodium acetate will you need to add to the solution? The pKa of acetic acid is 4.74. Show all calculations in your answer.

To calculate the number of moles of sodium acetate needed to add to the acetic acid solution, we need to use the Henderson-Hasselbalch equation:

pH = pKa + log10([A-]/[HA])

Given:
pH = 5.27
pKa = 4.74
[HA] = 0.01 mol (acetic acid)

Rearranging the Henderson-Hasselbalch equation, we have:

[A-]/[HA] = 10^(pH - pKa)

[A-]/0.01 = 10^(5.27 - 4.74)

[A-]/0.01 = 10^0.53

[A-] = 0.01 * 10^0.53

[A-] = 0.01 * 3.548

[A-] = 0.0355 mol

The moles of sodium acetate needed will be the same as the moles of [A-]. So, you will need to add 0.0355 moles of sodium acetate to the solution.

To determine the number of moles of sodium acetate needed to create an acetic acid buffer solution with a pH of 5.27, we follow these steps:

Step 1: Calculate the ratio of acetic acid (HA) to sodium acetate (A-) required for a buffer with the desired pH.

The Henderson-Hasselbalch equation describes the relationship between the pH, pKa, and the ratio of the conjugate acid-base pair:

pH = pKa + log([A-]/[HA])

Given that the desired pH is 5.27 and the pKa of acetic acid is 4.74, we can rearrange the equation to solve for [A-]/[HA]:

5.27 = 4.74 + log([A-]/[HA])
0.53 = log([A-]/[HA])

Since log([A-]/[HA]) is approximately equal to log([NaAc]/[AcH]), where NaAc is sodium acetate and AcH is acetic acid, we can simplify the equation to:

0.53 = log([NaAc]/[AcH])

Step 2: Calculate the ratio of moles of sodium acetate (NaAc) to moles of acetic acid (AcH) required for a buffer with the desired pH.

To calculate the ratio of moles instead of concentrations, we need to convert the given number of moles of acetic acid (0.01 mol) to concentration. Assume we have a total volume of 1 liter (L):

[AcH] = (0.01 mol) / (1 L) = 0.01 M

Now we can rearrange the simplified Henderson-Hasselbalch equation to solve for [NaAc]/[AcH]:

0.53 = log([NaAc]/0.01)
Antilog(0.53) = [NaAc]/0.01
3.514 = [NaAc]/0.01

The ratio [NaAc]/0.01 indicates that for every mole of acetic acid, we need 3.514 moles of sodium acetate.

Step 3: Calculate the number of moles of sodium acetate (NaAc) needed.

Since we have 0.01 mol of acetic acid, we multiply this value by the ratio we calculated in step 2 to find the number of moles of sodium acetate required:

(0.01 mol AcH) * (3.514 mol NaAc / 1 mol AcH) = 0.03514 mol NaAc

Therefore, you will need to add 0.03514 moles of sodium acetate to the solution.

Technically, the Henderson-Hasselbalch equation requires concentrations in mols/L; however, since the L will cancel we can use mols only as a short cut.

pH = pKa + log (base)/(acid)
YOu have pH and pKa, base is the unknown (in mols) and plug in 0.01 mol for acid.
Show your work if you get stuck.