Final answer:
The acid dissociation constant (Ka) of aspirin is determined using the provided pH and molarity, as well as the dissociation equation. After calculating the hydronium ion concentration, Ka is found using the assumption of minimal dissociation for the weak acid aspirin, leading to a result of approximately 3.62 x 10^-5.
Step-by-step explanation:
To determine the Ka of aspirin (acetylsalicylic acid, HC₉H₇O₄), we have the dissociation equation:
HC₉H₇O₄(aq) + H₂O(l) ⇌ H₃O+(aq) + C₉H₇O₄⁻(aq)
Given the concentration is 0.20 M and the pH is 2.57, first we need to convert the pH to [H3O+] using the formula [H3O+] = 10-pH which gives us 2.69 x 10-3 M.
Since aspirin is a weak acid, we can assume that the initial concentration of aspirin is approximately equal to the final concentration (0.20 M) due to minimal dissociation. We can then use the formula Ka = [H3O+][C₉H₇O₄⁻] / [HC₉H₇O₄] to find the acid dissociation constant (Ka).
With [C₉H₇O₄⁻] being approximately equal to [H3O+] at equilibrium, Ka can be calculated as (2.69 x 10-3)2 / 0.20 M. The resulting Ka is approximately 3.62 x 10-5.