Common Ion Effect

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ieatshrimp24

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Hypothetical scenario (as in none of these values are true).
Barium chromate solid (Ksp = 1 x 10^-5) is at equilibrium with its dissociated ions. If calcium chromate (Ksp = 1 x 10^-10) is added into solution, what will happen?

I'm wondering if the common ion effect still takes place even though the Ksp of the introduced solid is much lower than the the other Ksp value. My reasoning is that not enough chromate ion dissociates from calcium chromate to cause the reverse reaction of barium chromate dissolution. Is this true? Or will even the slightest amount of chromate addition cause precipitation of barium chromate solid?

Thanks.

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