Calculate Percent Dissociation of HBrO

[Gott_ist_tot]

Here is what should be an easy problem that I am somehow messing up

Homework Statement

Calculate the percent dissociation of 0.063 M Hydrobromous acid, HBrO. Do not solve the quadratic equation even if the percent dissociation is high.

Homework Equations

The Attempt at a Solution

I looked up K_a and found it to be 2.3*10^-9. After doing an equilibrium chart I got that x^2 = (2.3*10^9)(0.63). Therefore, x = 1.20 * 10^-5. I then divided this by 0.063 and multiplied by 100. I got 0.02% as a final answer. This does not sound right due to the hint and I was told it was wrong (online homework.

For the equilibrium table I just assumed that
HBrO + H2O <--> H3O + BrO.

Thanks for any help. I don't know why I am having so much trouble with this one.

 

[Gokul43201]

There's a couple typos in there, but the method looks okay, and I get a similar answer. Also, it's strange that they do not give you a value of the Ka to use. Reported values are notoriously different. I've just looked and found several values between 2.0 and 2.5 (times 10^-9M). Also, the software that checks your homework might require some specific number of sig figs (you've only got one).

 

[Gott_ist_tot]

Yeah, it was sig figs. 0.019. Thanks. Sorry for to use you guys for such a problem.