chem
posted by nicole on .
show why ka(kb)=kw for this pair of conjugate acidbase: H2C6H6O6 and HC6H66 ^1

It's too long and too confusing using long formulas. Let's cut that to ANY acid and its conjugate base, HA.
The conjugate base is A^ so if we add that to water we have
..........A^ + HOH ==> HA^ + OH^
(HA)(OH^)
 = Kb for the conjugate base.
(A^)
Now let's multiply that by (H^+)/(H^+)
I must use ..... for spacing and it still may not look very good.
(HA)(OH^)......(H^+)
 x  = Kb
(A^)............(H^)
Now look at the equation.
In the numerator, (H^+)(OH^) = Kw.
In the denominator, we have the reciprocal of Ka. Note that is (A^)/(H^+)(A^) which is just 1/Ka. Therefore, Kb = Kw*1/Kb or just Kw/Kb.