To what volume should 100ml of any weak acid (HA) with a concentration of 0.2M be diluted to double the percentage ionization?

Answer 1

I think you are looking at this scenario.
Say HA = 0.2 and (H^+) = 0.001M, then
%ion = (0.001/0.2)*100 = 0.5%.
Now if you dilute HA from 100 to 200 mL, (HA) is now 0.1M and %ion, if (H^+) = 0.001, is (0.001/0.1)*100 = 1.0% which is double the initial.
HOWEVER, I'm not convinced that will happen for any and all weak acids.
For example, look at acetic acid with Ka = 1.8E-5. If we use 0.2M HAc, then
1.8E-5 = (x)(x)/0.2 and x = (H^+) = 0.00190 and % ion = 0.949%
Now we dilutethe acid from 0.2 to 0.1 but (H^+) changes. Instead, it is
1.8E-5 = (x)(x)/(0.1) = 0.00134 which is 1.34% and that isn't double 0.949%.
I may have misinterpreted the question; if so let me know.