What is the percent ionization of 0.25 M iodic acid, HIO3, solution?

Question

Ka=1.7*10^-1

Answer choices:
a) 94.6%
b) 55.2%**correct
c) 27.1%
d) 18.7%

I couldn't get it to work out to that percent. Thanks in advance for any help.

Answer 1

I have only one correction...

(x squared) / (.25 - x) = .17

Now solve...

(x squared) = .0425 - .17x
(x squared) + .17x -.0425 = 0

Now, quadratic formula...

x = 0.1379910312

And lastly, to get percentage...

.1379910312/.25 * 100 = 55.2 %

Answer 2

If x is the conc. of H+ and IO3- ions,
x^2/.25-x = 0.17
With Ka of the order of 10-4 or lower, the subtration of x can be ignored with little error since x<<.25. Here, the subtraction can't be ignored. You can solve this either as a quadratic or by trial and error.