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Why is this incorrect?

Ultrashnotebel
in Inorganic Chemistry

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The question is simply to predict the reaction product of S2- and NH4+, and find its equilibrium constant. We have access to the Ka of H2S (which is the Ka of HS-) and the Kb of NH3.
second
HS- + H2O -> S2- + H3O+        ka = 1.1x10-12   => kb = kw/ka = 9.1.10^sup]-3[/sup]    which is the equilibrium constant for the reaction: S2- + H2O -> HS- + OH-

NH3 + H2O -> NH4+ + OH-        kb = 1.774x10-5   => ka = kw/kb = 5.637x10-10    which is the equilibrium constant for the reaction: NH4+ + H2O -> NH3 + H3O+ 

Adding those two reactions together, we find: S2- + NH4+ + 2H2O -> HS- + NH3 + OH- + H3O+

And so by multiplying the constants, we get 51.3x10-13... Which is not at all the answer I'm given. Somehow, the answer is 510.

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