A 0.39 M solution of a weak acid is 3.0% dissociated. Calculate Ka.
A weak acid, HA. 0.03 x 0.39 = 0.0117
................HA ==> H^+ + A^-
initial........0.39.....0....0
change.......0.0117...0.0117..0.0117
equil......0.39-0.0117.0.117..0.0117
Substitute from the ICE chart into Ka expression and solve for Ka.
Watch the significant figures.
To calculate the Ka (acid dissociation constant) of a weak acid, we need to use the given information about the concentration and percent dissociation.
First, let's define the equation for dissociation of the weak acid:
HA ⇄ H+ + A-
The percent dissociation can be calculated using the formula:
% dissociation = (concentration of dissociated acid / initial concentration of acid) * 100
Given that the percent dissociation is 3.0%, we can substitute the values into the formula:
3.0% = (concentration of dissociated acid / 0.39 M) * 100
Rearranging the formula, we can calculate the concentration of dissociated acid:
(concentration of dissociated acid) = (3.0% / 100) * 0.39 M
(concentration of dissociated acid) = 0.03 * 0.39 M
Now, we need to realize that the concentration of A- is equal to the concentration of dissociated acid because the weak acid is monoprotic (it has only one H+ ion in the dissociation equation).
So, the concentration of A- is 0.03 * 0.39 M = 0.0117 M.
Knowing that the concentration of H+ is the same as the concentration of A-, we can write:
[H+] = [A-] = 0.0117 M.
To calculate Ka, we can use the formula for Ka:
Ka = [H+] * [A-] / [HA]
Since [H+] = [A-] = 0.0117 M and the initial concentration of HA is 0.39 M, we can substitute the values into the formula:
Ka = (0.0117 M) * (0.0117 M) / (0.39 M)
Calculating this expression:
Ka ≈ 0.000345 M
Therefore, the Ka value for the weak acid is approximately 0.000345 M.