Determine the volumes of 1 M acetic acid and 1 M NaOH required to make a 200mL 0.1 M buffer with a pH of 5.5. (Assume the pKa of acetic acid is 4.76).
You want 200 mL x 0.1M buffer which means 20 millimoles. For the buffer to be 01M, that means acid (HAc) + base (Ac^-) = 0.1M
Since mL x M = mmoles, we want to start with 20 mL of 1M base to start with 20 mmoles. For final pH = 5.5, we can calculate the base/acid ratio as
5.5 = 4.76 + log (b/a)
b/a = 5.5 or
Ac = 5.5*HAc
Solve these two equations simultaneously as
B + A = 0.1M
B/A = 5.5
You should confirm but I get approximately 0.015M for acid and 0.085M for base. Convert to mmoles gives
200 x 0.015 = about 3 mmoles HAc
200 x 0.085 = about 17 mmoles for Ac
..............HAc + OH^- ==> Ac^- + H2O
initial.......20.....0.........0......0
add..................x..................
change.........-x....-x.........x.....x
equil..........3......0.........17
Thus x = 17 mmoles and you will need to add 17 mL of 1M NaOH to provide 17 mmoles NaAc and leave 3 mmoles Ac^-. Check all of this work. Note that you will need to add enough water to make the final volume 200 mL.
Rachel--As I posted my response above it occurred to me that I've worked several of these buffer problems for you before the 2012 New Year's holidays. You need to learn how to do these yourself. If you care to go into detail about why you still have trouble with them perhaps I can help you over the tight spots.
To determine the volumes of acetic acid and NaOH required to make a 0.1 M buffer with a pH of 5.5, we need to use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
pH = desired pH of the buffer (5.5)
pKa = dissociation constant of acetic acid (4.76)
[A-] = concentration of the conjugate base (acetate ion)
[HA] = concentration of the acid (acetic acid)
We also need to consider the ionic strength effect. The ionic strength of a buffer is given by the equation:
I = (1/2)([A-] + [HA])
We want the ionic strength to be low, so we assume the concentration of the buffer components ([A-] and [HA]) are approximately equal. Hence, we can simplify the equation to:
I = [A-]
Now, let's calculate the concentration of acetic acid ([HA]) and the concentration of sodium acetate ([A-]) needed to prepare the buffer.
Step 1: Calculate the concentration of acetic acid ([HA]):
We know that the total volume of the buffer is 200 mL, and the desired concentration of acetic acid ([HA]) is 0.1 M.
[HA] = 0.1 M * (volume of acetic acid / total volume of buffer)
To find the volume of acetic acid, we assume the volume of sodium hydroxide (NaOH) added to the buffer is negligible. Therefore, the volume of acetic acid is the same as the total volume of buffer.
[HA] = 0.1 M * (200 mL / 200 mL)
[HA] = 0.1 M
Step 2: Calculate the concentration of sodium acetate ([A-]):
Using the relationship I = [A-], we have:
I = [A-] = 0.1 M
Therefore, we need a 0.1 M concentration of sodium acetate.
Step 3: Calculate the volumes of 1 M acetic acid and 1 M NaOH needed:
Since the total volume of the buffer is 200 mL, and we know the concentration of acetic acid ([HA]) is 0.1 M, and the concentration of sodium acetate ([A-]) is also 0.1 M, we can calculate the volumes as:
Volume of acetic acid = [HA] * total volume of buffer
Volume of acetic acid = 0.1 M * 200 mL
Volume of acetic acid = 20 mL
Volume of NaOH = [A-] * total volume of buffer
Volume of NaOH = 0.1 M * 200 mL
Volume of NaOH = 20 mL
Therefore, to make a 200 mL 0.1 M buffer with a pH of 5.5, you would need 20 mL of 1 M acetic acid and 20 mL of 1 M NaOH.