Final answer:
The acid dissociation constant (Ka) for phenol, given the pH of 6.09 for a 0.005 M solution, is calculated to be 1.32 x 10⁻¹⁰.
Step-by-step explanation:
To calculate the acid dissociation constant (Ka) for phenol, we can use the given pH of the solution, which is 6.09. First, we convert the pH to the concentration of hydrogen ions ([H+]) using the following formula:
[H+] = 10^-pH
Substituting the given pH value:
[H+] = 10⁶'⁰⁹ = 8.13 x 10⁻⁷ M
Since phenol is a weak acid, it partially dissociates in solution as follows:
C₆H₅OH(aq) → C₆H₅O-(aq) + H+(aq)
At equilibrium, the concentration of H+ ions equals the concentration of C₆HₐO- ions, and is equal to x, while the concentration of undissociated phenol is (0.005 - x). Because phenol is a weak acid and the solution is dilute, we can approximate x to be much smaller than the initial concentration of phenol, allowing us to simplify the equation to:
Ka = [H+][C₆H₅O-]/[C₆H₅OH] ≈ [H+]^2 / [C6H5OH]
Then we substitute the values:
Ka ≈ (8.13 x 10⁻⁷)² / 0.005 = 1.32 x 10⁻¹⁰
The calculated Ka for phenol is 1.32 x 10⁻¹⁰.