A solution of 2.9 m weak acid is 0.52 ionized. what is the ka value of this acid

We can get the Ka value from this formula:

Ka = [H+] [A-} / [HA]

So we need to know [H+] & [A-] & [Ha] to get the Ka value

[H+] = 2.9 * 0.52/100 = 0.01508 M

and when [H+] = [A-]

∴[A-] = 0.01508 M

∴ [HA] = 2.9 - 0.01508 = 2.88 M

So by substitution:

Ka = [0.01508][0.01508] / 2.88

= 7.9 x 10^-5