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I don't understand why there aren't two solutions to the following problem:

You are presented with a white solid and told that due to careless labeling it is not clear if the substance is barium chloride, lead chloride, or zinc chloride. When you transfer the solid to a beaker and add water, the solid dissolves to give a clear solution. Next an $\ce{Na2SO4(aq)}$ solution is added and a white precipitate forms. What is the identity of the unknown white solid?

Now according to the solubility guidelines BOTH $\ce{BaSO4}$ AND $\ce{PbSO4}$ should be able to form as precipitate, and therefore the answer could be both barium chloride and lead chloride.

Where am I wrong here?

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Without quantitative details it could be both. The expected answer depends on to what details the task author expects you to go.

$\ce{PbCl2}$ solubility is about $\pu{1.1 g/100 ml}$. $\ce{BaCl2}$ solubility is about $\pu{36 g/100 mL}$.

It is reasonable to expect the used water/salt ratio was low enough to distinguish Ba and Pb. If you have performed the test, would you use too much water to dissolve both $\ce{PbCl2}$ and $\ce{BaCl2}$ and than was not able to tell, if the precipitate is $\ce{PbSO4}$ or $\ce{BaSO4}$ ?

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  • $\begingroup$ Thank you for answering. There are no further specifications about the problem in the book. If I understand your answer correctly, I should be able to tell whether it's PbCl2 or BaSO4 by gradually adding water and then matching the "dissolution quantity" of water at which the solid starts dissolving with the solubility information that you provided? $\endgroup$ Jan 3 at 13:13
  • $\begingroup$ It should be mentioned in the question that "a small amount" of water is added to the white stuff, before testing the solution with $\ce{Na2SO4}$; or about the same volume of water as the volume of the white salt. $\endgroup$
    – Maurice
    Jan 3 at 15:02
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    $\begingroup$ As mentioned above, the catch in the question might be "the solid dissolves to give a clear solution." Without specifying the amount of solid and water, it's unanswerable, but if the ratio is above a few g/L, then it can't be the lead salt. If that is the whole question transcribed, it is very poorly worded! $\endgroup$ Jan 3 at 15:49

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