Final answer:
To determine the value of Ka for acetic acid from a given pH, calculate the [H+] using the pH, assume [H+] is equal to [CH3COO-], and use the initial concentration of CH3CO2H in the Ka expression. Solve for Ka to find its value.
Step-by-step explanation:
The question asks for the value of Ka for acetic acid, given the pH of a 0.150 M solution of CH3CO2H is 2.78. To find Ka, we can use the definition of pH and the expression for the acid dissociation constant, Ka. The pH is the negative logarithm of the hydrogen ion concentration:
pH = -log[H+]
From the given pH of 2.78, we calculate [H+] as follows:
[H+] = 10^-2.78
Now we set up the expression for the acid dissociation constant, Ka, which for acetic acid is:
Ka = [CH3COO-][H+] / [CH3CO2H]
Given that acetic acid is a weak acid and does not dissociate completely, we assume that the concentration of acetic acid left ([CH3CO2H]) after dissociation is approximately equal to the initial concentration. The concentration of [H+] is equal to the concentration of [CH3COO-] since they are produced in a 1:1 ratio upon the dissociation of acetic acid:
[H+] = [CH3COO-] = 10^-2.78
Therefore:
Ka = (10^-2.78)^2 / 0.150
Upon solving, we find the value of Ka for acetic acid.