Here is the full question:
A chemistry graduate student was given 500 mL of a 1.60 M hydrocyanic acid (HCN) solution. Hydrocyanic acid is a weak acid with [tex]K_a = 4.9 \times 10^{-10}[/tex]. What mass of KCN should the student dissolve in the HCN solution to turn it into a buffer with pH = 9.16?
Answer:
36.85 g
Explanation:
From the given information above:
Recall that number of moles of HCN = mass of HCN / molar mass of HCN= mass of HCN / molar mass of HCN
Therefore;
the number of moles of HCN = [tex]\dfrac{500 \times 1.60}{1000}[/tex]
the number of moles of HCN = [tex]\dfrac{800}{1000}[/tex]
the number of moles of HCN = 0.8
The acid dissociation constant [tex]K_a[/tex] = [tex]4.9 \times 10^{-10}[/tex]
Thus the pKa = [tex]- log (4.9 \times 10^{-10})[/tex]
pKa = 9.31
However, the pH is given as:
[tex]pH = pKa + log \bigg ( \dfrac{KCN}{HCN} \bigg )[/tex]
[tex]9,16 =9.31 + log \bigg ( \dfrac{KCN}{0.8} \bigg )[/tex]
[tex]9,16 -9.31 =log \bigg ( \dfrac{KCN}{0.8} \bigg )[/tex]
[tex]-0.15 =log \bigg ( \dfrac{KCN}{0.8} \bigg )[/tex]
KCN = 0.566 mol
The standard molar mass of KCN = 65.11 g/mol
Thus, the mass of KCN = number of moles of KCN × molar mass of KCN
the mass of KCN = 0.566 × 65.11
the mass of KCN that the student needs to dissolve in HCN is = 36.85 g
