What are `[H^(o+)], [A^(Theta)`, and `[B^(Theta)]` in a solution that is `0.3M HA` and `0.1M HB? K_(a)` for `HA` and `HB` are `1.38 xx 10^(-4)` and `1.05 xx 10^(-10)`, respectively.

Explanation

`{:(HA hArrH^(o+)+A^(Theta),,,K_(a)=1.38xx10^(-4),,),(HB hArrH^(o+)+B^(Theta),,,K_(a)=1.05xx10^(-10),,):}`
It is thus evident on account of low `K_(a)` values for `HB., [H^(o+)]` from `HB` is appreciably small in comparism to `[H^(o+)]` from `HA` and thus may be negleted.
For `HA: K_(a) = ([H^(o+)][A^(Theta)])/([HA])`
`1.38 xx 10^(-4) = ([H^(o+)]^(2))/([HA])`
`[H^(o+)]^(2) = 1.38 xx 10^(-4) xx [HA]`
`1.38 xx 10^(-4) xx 0.03`
Therefore, `[H^(o+)] = [A^(Theta)] = 2.04 xx 10^(-3)M`
Now for `HB: K_(a) = ([H^(o+)][B^(Theta)])/([HB])`
`1.05 xx 10^(-10) = (2.04 xx 10^(-3)xx[B^(Theta)])/(0.1)`
(Since `[H^(o+)]` is provided by acid `HA` and `HB` is almost undissociated)
`[B^(Theta)] = 5.15 xx 10^(-9)M`