achieve homework problem 3

[605815546]

For the third problem on the homework (muscles produce lactic acid), I have a query about a hint that was given when I initially got the problem wrong:
"In general, if the percent ionization is less than 5%, the assumption that the amount of lactic acid dissociated in solution is negligible is valid and the answer will be the percent ionization. In this case, the percentage is greater than 5%. Therefore, the percent ionization must be calculated using the quadratic equation instead."
This makes sense, but since the percent ionization is calculated AFTER having done the quadratic equation, how would you know beforehand that it's less than 5%? Why do we not approximate in this problem when Ka is less than 10^-3?
thanks so much in advance!!

[Vincent Palomo 3L]

So even though the Ka is less than 10^-3, its only slightly less than 10^-3. I would say that since Ka is so close to 10^-3 the approximation is more likely to wrong, so its just safer to use the quadratic formula when the Ka is so close to 10^-3.

I hope this helps