Answer:
[tex]pH = 5.05[/tex]
Explanation:
pH is derived from the concentration of hydronium ions in a solution. Hydrocyanic acid is HCN.
First, we shall figure out the moles of HCN:
[tex]\frac{3.4g}{27.03g/mol} = 0.125786[/tex]
If HCN was a strong acid:
HCN has a 1:1 ratio of H+ ions, the moles of H+ is also the same.
To find the molarity, we now divide by Liters. This gets us:
[tex]\frac{0.125786 moles}{0.9L} = 0.139762 M[/tex]
Finally, we plug it into the definition of pH:
[tex]pH = -log[H^{+} ][/tex]
[tex]pH = -log(0.139762)[/tex]
[tex]pH = 0.855[/tex]
However, since HCN is a weak acid, it only partially dissociates. The [tex]K_a[/tex] of HCN is [tex]6.2 * 10^{-10}[/tex].
[tex]K_a = \frac{[H^+][A^-]}{[HA]}[/tex]
We can use an ice table to determine that when x = H+,
[tex]K_a = \frac{x^2}{0.125786-x}[/tex]
[tex][H^+] = 8.83*10^{-6}[/tex]
[tex]pH = -log[H^{+} ][/tex]
[tex]pH = -log(8.83 * 10^{-6} )[/tex]
[tex]pH = 5.05[/tex]
