Identifying a Weak Acid: Solving for pH in a 0.50 mol/L Solution - Homework Help

[Euler2718]

Homework Statement

What is the likely identity of a weak acid if a 0.50 mol/L solution of the acid has a pH of 3.18?

Homework Equations

HA + H2O <=> H3O + A

$$K_{a} = \frac{[P]}{[R]}$$

$$[H3O] = 10^{-pH}$$

The Attempt at a Solution

[/B]
I set up an ICE table with the concentration given, then solved for x using the inverse log formula for [H3O], finally I did the following Ka expression:

$$K_{a} = \frac{(6.6 \times 10^{-4})^{2}}{0.5-6.6 \times 10^{-4}} = 8.75 \times 10^{-7}$$

The closets acid to that appears to be carbonic acid (ka = 4.4x10^-7). Any suggestions?

 

[Bystander]

You've doubly ionized a diprotic weak acid at a pH of 3.2? Try it again.

 

[Borek]

You've doubly ionized a diprotic weak acid at a pH of 3.2? Try it again.

I am not sure what you mean, Ka is calculated assuming the acid behaves as a monoprotic. That's not a bad assumption for a carbonic acid (no idea if the OP was aware of the problem, but that's another story).

Sadly, pKa of 6.05 doesn't fit any acid commonly used in introductory chemistry courses. Of those used carbonic acid looks best (but still is way off with the pKa1=6.37).