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A chemical equation is a way to predict the way that two or more chemicals will work together. Using what chemists know about the way chemicals act, we add the letter symbols together just like a math problem. In this way we can correctly guess if we will get a new chemical when we mix two or more chemicals together, and what that chemical will be.
For example: An aqueous (liquid) solution of Sodium Chloride (NaCl[aq]) and another aqueous solution of Silver Nitrate (AgNO3(aq)). These mixed together forms Sodium Nitrate (NaNO3(aq)) and Silver Chloride (AgCl(s))
Which in symbols is:
NaCl(aq) + AgNO3(aq) = NaNO3(aq) + AgCl(s)
The solutions formed a solid named AgCl. This formation can be called a precipitate and the reaction between the two solutions a precipitation reaction, because the solid produced is not dissolved, whereas all the other products are dissolved.
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