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I have an aqueous solution of either $\ce{MgCl2}$ or $\ce{CaCl2}$ in solution with $\ce{K2SO4}$. There is a white precipitate that forms on the bottom that does not dissolve when $\ce{HCl}$ is added (maybe it needs to be in excess?). Is there any way to find out if it's $\ce{Mg^2+}$ or $\ce{Ca^2+}$? I have already tried adding $\ce{NaOH}$, and the result was a not very cloudy, white precipitate, which is not really jelly like, but when compared to stock samples of $\ce{MgCl2}$ and $\ce{CaCl2}$ with $\ce{NaOH}$, they don't match. I tried a flame test but only could see the $\ce{K+}$ (violet flame).

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First, it is no use of putting $\ce{NaOH}$ in the solution as both ion with form white percipitate and insoluble in excess of $\ce{NaOH}$.

Try aqueous $\ce{NH3}$. If the solution contains $\ce{Mg^2+}$ ion , it will white percipitate and insoluble excess of $\ce{NH3}$. However, $\ce{Ca^2+}$ ion will not form any percipitate when $\ce{NH3}$ it added.

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$\ce{MgSO4}$, otherwise known as epsom salt, is soluble. $\ce{CaSO4}$ ($K_\mathrm{sp}=7.1 \times 10^{-5}$), is slightly soluble. It is extremely likely that unless there are some other unknown metal ions in this solution, the white precipitate you describe in the solution is $\ce{CaSO4}$.

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Why not do the following, add an excess of sodium carbonate. Boil the mixture, cool and then centrifudge it down. Pipette off the supernatent. Next repeat the process several times to convert the sulfate into the carbonate.

Next wash the solid with water to remove the sodium carbonate. You now will have pure calcium carbonate or magnesium carbonate.

Next dry the solid on the filter in the following way, transfer into a preweighed crucible. Put it in an oven at 100 oC and dry to a constant mass.

Next when you have the mass of the metal carbonate, put it in a muffle furnace at 700 oC and ash it to a constant mass to get the mass of the oxide. You can then work out by gravimetric method if it was magnesium or calcium in it.

Another method would be to isolate the pure metal carbonate, add a weighed amount to a flask. Add some HCl to dissolve it and then adjust the pH with sodium hydroixde. Next titrate it with EDTA using Eriochrome Black T. This will allow you to determine the number of moles of metal in each gram of the dry carbonate solid.

Years ago an older chemist told me of how he used to measure zinc in mixtures of calcium, magnesium and zinc. He would do the titration with EDTA using Eriochrome Black T to get the total number of moles of Zn / Mg / Ca. He would then do the titration with KCN present to mask the zinc. By difference he would then be able to calculate the number of moles of zinc and the number of moles of calcium / magnesium.

You could always take the easy route and use AAS, ICPOES or even neutron activation, counting the calcium-45 as a method of determining the amount of calcium present in the carbonate solid.

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