In the previous problem, we determined the Ka of lactic acid (HC3H5O3) to be 1.2 X 10-4.
The degree of ionization of lactic acid in terms of percentage is simply the concentration of lactic acid that reacted divided by the initial concentration of lactic acid.
If you remember, the initial concentration of lactic acid was given as 0.025 M, when we determined the Ka of lactic acid, we found that its molarity at equilibrium was 0.023 M. Therefore the degree of ionization of this acid is equal to how much lactic acid reacted (0.025 - 0.023) = 0.002 divided by 0.025 and this ratio multiplied by a 100.
Thus, in that particular solution, the percentage ionization of lactic acid is 8%.
If we know the Ka value of a weak acid and its initial concentration, we can easily determine the pH of that solution and to what extent is the acid ionized. The following problem is an example of this type:
What are the concentrations of H+ and C2H3O2- in a solution of 0.10 M HC2H3O2? What is the pH of the solution? What is the percentage ionization?
The value of Ka for HC2H3O2 is 1.7 X 10-5
Set up the chemical equilibrium and list all the relevant information:
Substitute the equilibrium concentrations and the value of Ka into the equilibrium constant equation for acid ionization:
A good assumption at this point is that 0.10 - x ~ 0.10. In other words, the value of x is small when compared to 0.10. This simplifies our equation to:
Solving for x we obtain:
x2 = 1. 7 X 10-6
Since x stands for the concentration of H+ and C2H3O2-, 1.3 X 10-3 M is the concentration of both species in that solution. To check if our assumption that the value of x was too small to really affect the initial concentration of 0.10, take the difference of 0.10 - 1.3 X 10-3, to two significant figures, you obtain 0.10. Alternatively, place the numbers back into the Ka expression and check if you get the initial value back.
Which is indeed the case once you round off your answer to two significant figures.
The pH of the solution is simply:
The degree of ionization in terms of percentage is given by:
The concentration of H+ or C2H3O2- gives you the amount of HC2H3O2 that reacted, since at the start of the reaction, there was no products present and therefore their concentrations are directly related to the amount of HC2H3O2 that reacted. Since the stoichiometry of the reaction is 1:1, the number of moles per liter of either ion produced equals to the number of moles per liter of acetic acid that reacted.