Respuesta :
Explanation:
The given data is as follows.
Initial volume of aspirin = 1.00 L
Initial concentration of aspirin = 0.500 M
Initial pH = 1.86
Hence, hydronium ion concentration will be calculated as follows.
pH = [tex]-log[H^{+}][/tex]
or, [tex][H^{+}] = 10^{-pH}[/tex]
= [tex]10^{-1.86}[/tex]
= [tex]13.8 \times 10^{-3} M[/tex]
As, buffer containing aspirin and its conjugate base is formed in 1 L solution.
Hence, moles of aspirin are 0.500 moles and moles of the conjugate base are 0.25 moles.
So, upon dissociation the concentration of acetylsalicylate ion and hydronium ion are the same.
Hence, [tex]pK_{a}[/tex] value will be calculated as follows.
[tex]K_{a}[/tex] = [tex]\frac{[H^{+}]^{2}}{[Aspirin]}[/tex]
= [tex]\frac{[13.8 \times 10^{-3}]^{2}}{0.50}[/tex]
= [tex]3.8 \times 10^{-4}[/tex]
Also, [tex]pK_{a} = -log [K_{a}][/tex]
= [tex]-log [3.8 \times 10^{-4}][/tex]
= 3.41
Now, using Henderson-Hasselbalch equation we determine the pH as follows.
pH = [tex]pK_{a} + log \frac{[CH_{3}COO^{-}]}{[Aspirin]}[/tex]
= 3.41 + [tex]log \frac{[0.25]}{[0.5]}[/tex]
= 3.11
Determine the hydronium ion concentration of buffer as follows.
[tex][H^{+}] = 10^{-pH}[/tex]
= [tex]10^{-3.11}[/tex]
= [tex]7.76 \times 10^{-4}[/tex] M
Therefore, we calculate the recent dissociation as follows.
% dissociation = [tex]\frac{\text{Amount dissociated}}{\text{Initial concentration}} \times 100%[/tex]
= [tex]\frac{0.000776}{0.50 M} \times 100%[/tex]
= [tex]1.5 \times 10^{-3}[/tex] × 100
= 0.15%
Thus, we can conclude that the value of % dissociation of new buffered solution is 0.15%.
