What mass of KCN should the student dissolve in the HCN solution

Question

A chemistry graduate student is given 125. mL of a 0.90M hydrocyanic acid (HCN) solution. Hydrocyanic acid is a weak acid with K, = 4.9 x 10^-10. What mass of KCN should the student dissolve in the HCN solution to turn it into a buffer with pH = 8.86? You may assume that the volume of the solution doesn't change when the KCN is dissolved in it. Be sure your answer has a unit symbol, and round it to 2 significant digits

Answer 1

Adding KCN to a solution of HCN will create a buffer solution since it will then contain a weak acid (HCN) and the salt (conjugate base) of that acid (KCN). For a buffer of this nature, we can use the Henderson Hasselbalch equation to find the pH.

pH = pKa + log [salt] / [acid]

pKa = -log Ka = -log 4.9x10-10 = 9.31

8.86 = 9.31 + log [x M KCN] / 0.90 M HCN]

8.86 = 9.31 + log x/0.90

-0.45 = log x/0.90

0.355 = x / 0.90

x = 0.320 M KCN

Molar mass of KCN = 65.1 g / mol

125 ml = 0.125 L x 0.320 mol / L KCN = 0.040 mols KCN needed

0.040 mols KCN x 65.1 g / mol = 2.6 g KCN need to be added