Phthalic acid, H2C8H404, is a diprotic acid used in the synthesis of phenolphthalein indicator. Ka1= 1.2x 10^-3, and Ka2 = 3.9 x 10^-6. a) Calculate the hydrongen-ion concentration of a .015 M solution. b) What is the concentration of the C8H4O4^2- ion in the solution?
To solve this problem, we need to consider the dissociation of phthalic acid and the formation of its ions in water. Phthalic acid, H2C8H404, is a diprotic acid, meaning it can donate two protons or hydrogen ions (H+). It has two dissociation steps:
H2C8H404 ⇌ H+ + HC8H404-, (Ka1)
HC8H404- ⇌ H+ + C8H4O4^2-, (Ka2)
a) To calculate the hydrogen-ion concentration of a 0.015 M solution, we need to determine how much phthalic acid dissociates in each step.
The first dissociation, represented by Ka1, can be expressed as an equilibrium expression:
Ka1 = [H+][HC8H404-] / [H2C8H404]
We can assume that x is the concentration of H+ and HC8H404- formed. Since H2C8H404 dissociates in a 1:1 ratio to form H+ and HC8H404-, the concentration of H2C8H404 that dissociates is also equal to x.
By using the given Ka1 value, we can write the equilibrium expression:
1.2x10^-3 = x * x / 0.015
From this equation, we can solve for x, which represents the hydrogen-ion concentration.
b) To find the concentration of the C8H4O4^2- ion in the solution, we need to determine how much HC8H404- dissociates in the second step (represented by Ka2).
The equilibrium expression for Ka2 is:
Ka2 = [H+][C8H4O4^2-] / [HC8H404-]
Since the concentration of H+ formed in the second dissociation step is equal to the concentration of H+ from the first dissociation step, which we have solved for in part a), we can calculate [C8H4O4^2-] using the given Ka2 value and the already calculated [H+].
Now let's solve these equations to find the answers:
a) Calculate the hydrogen-ion concentration:
Substituting the given value of Ka1 and the concentration of H2C8H404, we have:
1.2x10^-3 = x * x / 0.015
Rearranging the equation and solving for x:
x^2 = (1.2x10^-3) * 0.015
x^2 = 1.8x10^-5
x ≈ 0.0042
Therefore, the hydrogen-ion concentration in a 0.015 M solution of phthalic acid is approximately 0.0042 M.
b) Calculate the concentration of the C8H4O4^2- ion:
Since the concentration of H+ is the same as the concentration of H+ from the first dissociation step, we can substitute the value of x into the equation for Ka2:
Ka2 = [H+][C8H4O4^2-] / [HC8H404-]
3.9x10^-6 = 0.0042 * [C8H4O4^2-] / (0.015 - 0.0042)
Rearranging the equation and solving for [C8H4O4^2-]:
[C8H4O4^2-] ≈ (3.9x10^-6) * (0.015 - 0.0042) / 0.0042
[C8H4O4^2-] ≈ 0.0107 M
Therefore, the concentration of the C8H4O4^2- ion in the solution is approximately 0.0107 M.