Answer:
pH ≈ 7.26 - (-3.12) ≈ 10.38
Step-by-step explanation:
To calculate the pH at which an aqueous solution of the acid is 0.076% dissociated, you can use the formula for percent dissociation:
Percent Dissociation = (Dissociated / Initial concentration) * 100
In this case, the percent dissociation is given as 0.076%. Let's denote the initial concentration of the acid as [A].
0.076% = (Dissociated / [A]) * 100
To simplify the equation, divide both sides by 100:
0.00076 = Dissociated / [A]
Now, let's assume that the initial concentration [A] is equal to the concentration of the undissociated acid [HA] since only a small fraction dissociates.
0.00076 = Dissociated / [HA]
The dissociated portion can be expressed as [H+] since it represents the concentration of hydrogen ions in the solution. Since the acid is monoprotic, the concentration of [A-] (conjugate base) is equal to [H+].
0.00076 = [H+] / [HA]
To solve for [H+], take the negative logarithm (base 10) of both sides:
-log([H+]) = -log([HA]) + log(0.00076)
Since pKa = -log(Ka), where Ka is the acid dissociation constant, we can rewrite the equation as:
-pH = -pKa + log(0.00076)
Rearranging the equation, we get:
pH = pKa - log(0.00076)
Substituting the given pKa value (7.26) into the equation:
pH = 7.26 - log(0.00076)
Now, calculate the value using a calculator:
pH ≈ 7.26 - (-3.12) ≈ 10.38
Therefore, at a pH of approximately 10.38, the aqueous solution of the acid would be 0.076% dissociated.