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Determining which solutions will form a precipitate when mixed together

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What precipitate forms when solutions of the following are mixed: K+, Ca2+, NH4 1+, and Cl-, NO3 1-, CO3 2-?

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The solution provides an explained answer while also mentioning the rules of thumb for this type of problem.

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We mixed 6 ions together. Let us try to figure out all the combinations of salts that could be formed from the following ions by pairing + and - ions together.
We can have:
KCl, KNO3, K2CO3, CaCl2, Ca(NO3)2, Ca(CO3), NH4Cl, NH4NO3 or ...

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