A student is asked to prepare 1.0 L of Buffer at pH 4.55 using 0.10 M of acetic acid and 0.10 M of sodium acetate. Calculate

Question

A student is asked to prepare 1.0 L of Buffer at pH 4.55 using 0.10 M of acetic acid and 0.10 M of sodium acetate. Calculate what volume of the two buffers the student would need to mix to obtain a buffer of the required pH.

Answer 1

Henderson Hasselbalch equation: pH = pKa + log [salt]/[acid]

So, first off, you need to know the pKa for acetic acid. Looking it up in a reference book, I find it to be 4.76

4.55 = 4.76 + log [salt]/[acid]

4.55 = 4.76 + log [salt]/[acid]

log [salt]/[acid] = 4.55 - 4.76 = -0.21

Taking antilogs ... [salt]/[acid] = 0.6166

To prepare 1 liter, and obtain a ratio of sodium acetate : acetic acid of 0.62 : 1, ....

[salt] + [acid] = 0.1 mol/L

[salt]/[acid] = 0.62/1

0.62[acid] + [acid] = 0.1

1.62[acidi] = 0.1

[acid] = 0.062 mole/L

[salt] = 0.62 x [acid] = 0.62 x 0.062 = 0.038 mol/L

Thus, to prepare 1 liter of the desired buffer you would use 620 ml of 0.1 M acetic acid + 380 ml of 0.1 M sodium acetate.

Check: moles acetic acid = 0.62 L x 0.1 mol/L = 0.062 moles

moles sodium acetate = 0.038 L x 0.1 mol/L = 0.038 moles

ratio salt/acid = 0.038/0.062 = 0.61 = desired ratio

Check for pH: pH = pKa + log [salt]/[acid] = 4.76 + log 0.61 = 4.76 + (-0.21) = 4.55 = desired pH