Your boss wants you to make some buffesr using the acetic acid/acetate buffering

Question

Your boss wants you to make some buffesr using the acetic acid/acetate buffering system. You find 0.100 M stock solutions of Na acetate and acetic acid on the shelf. Use your resources to find the pKa for this system and calculate the amount in mL of each you would have to use to make 500 mL of the following buffers

Desired pH mL Na acetate mL acetic acid

4.00

4.80

6.30

5.25

I figured ou the pKa using the molar mass of Na acetate (0.100M Na acetate) / (82.03 g/mol) and doing the same thing with acetic acid and getting the equation   

pKa = pH + log(acid/base) -> 4.00 + log (0.0017 M Na acetate/ 0.0012 M acetic acid) = 4.15

but I don't know how to get the ration for mL from this, please help!

Explanation / Answer

Use the Henderson Hasselbalch equation to find the ratio of A- to HA.

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

4 = 4.15 + log [A- ] / [HA]

-0.15 = log [A- ] / [HA]

0.70796 = [A- ] / [HA]

Calculate the decimal fraction (part/whole) of each buffer component.

A- = 0.70796 / (1.00 + 0.70796 ) = 0.70796 / 1.70796 = 0.4145

HA = 1.00 / 1.70796 = 0.5855

Let us consider the buffer molarity as 0.1M

Find the molarity (M) of each component in the buffer by simply multiplying the molarity of the buffer by the decimal fraction of each component.

MA- = 0.01M x 0. 4145=  4.145 x 10-3 M

MHA = 0.01M x 0. 5855= 5.855x 10-3 M

Calculate the moles of each component in the buffer.

Moles = Molarity x Liters of buffer

molesA- = 0.004145M x 0.5L = 2.0725x 10-3 moles

molesHA = 0.005855M x 0.01L = 2.9275x 10-3 moles

Calculate the volume of each stock solution required to make the buffer

Liters of stock = moles of the buffer component / Molarity of the

stock A- = 2.0725x 10-3 moles/ 0.1 M = 20.725 x 10-3 L = 20.7 ml

         HA = 2.9275x 10-3 moles / 0.1 M = 29.275x 10-3 L = 29.3 ml

mL Na acetate = 20.7 ml mL acetic acid = 29.3 ml

Similarly we can calculate for rest all

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