Achieve Wk 2 #2 Percent Ionization

[Ashley Hiti 1K]

I am little confused by the feedback I got on my first attempt.

Question: The Ka of a monoprotic weak acid is 0.00831. What is the percent ionization of a 0.184 M solution of this acid?

To solve I set 0.00831 = [H+]^2/0.184 and got [H+] = 0.0391.

When I divided this by the molarity of the acid at multiplied by 100 I got 21.3% ionization.

Achieve marked this incorrect and this is the feedback. "The assumption you made is not valid. You should use the quadratic equation instead."

I am not sure what assumption it made/where I should be using the quadratic equation.

[Kiku Shirakata 2A]

Hello,

For #2, I think the invalid assumption you made is in the Ka equation you set up. You wrote 0.00831 = [H+]^2/0.184, but instead, it should be 0.00831 = x^2/(0.184 - x). Sometimes, we are allowed to ignore the 'x' in the denominator when the Ka value is less than 10^-3. However, in this case, we need to include the 'x' because the Ka value is not small enough. By adding that variable, you will need to solve a quadratic equation to find the value of x, which will be equivalent to [H+] at equilibrium.

Hope this helps!

[KatieWu 1E]

Additionally, make sure that after you find x, to find the percent ionization you use the x value and divide it by the initial concentration of the solution, not the equilibrium value.

[RossLechner3E]

It is true that when Ka or Kb is smaller than 10^-3 we can assume the line .184 - x to be just .184, but in this case when you solve the percent protonation and it is more than 5% it is not longer viable to assume 0.184 - x is 0.184. You must use the quadratic formula otherwise the margin of error is just too big to assume.

[Allison Li 2F]

Hi! When k is smaller than 10^-3 we can approximate and ignore the x in the denominator. However, this is not a foolproof method because there can still be errors. In fact, the percentage is greater than 5%, which means this margin of error is too great and we cannot approximate the value of x. In this case, you would need to use the quadratic formula.

[Matthew Li 1B]

you would have to use the quadratic equation to solve for this problem because Ka is big enough where there is greater than 5% percent ionization