Answer:
The correct answer is 190.5 mL of 1.00 M KH₂PO₄
Explanation:
A phosphate buffer is composed by phosphate acid (KH₂PO₄) and its conjugated base (K₂HPO₄). To obtain the relation between the concentrations of base and acid to add, we use Henderson-Hasselbach equation:
pH= pKa + log
We have: pH= 6.97 and pKa= 7.21. So, we replace the values in the equation:
6.97= 7.21 + log
6.97-7.21= log
-0.24= log
=
0.575 =
=
It means that you have to mix a volume 0.575 times of conjugated base and 1 volume of acid. If we assume a total buffer concentration of 1 M, we have:
base + acid = 1
base= 1 - acid
We replace in the previous equation:
0.575=
0.575 acid= 1 - acid
0.575 acid + 1 acid= 1
1.575 acid = 1
acid= 1/1,575
acid= 0.635
base= 1 - acid = 1 - 0.635 = 0.365
For a total volume of 300 ml, the volumes of both acid and base will be:
300 ml x 0.635 M = 190.5 ml of acid (KH₂PO₄)
300 ml x 0.365 M= 109.5 ml of base (K₂HPO₄)
We can corroborate our calculations as follows:
190.5 ml + 109.5 ml = 300 ml
109.5 ml / 190.5 ml = 0.575