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Can the solubility of a compound be used in conjunction with stoichiometry?

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Blueberries116:
I'm confused exactly on how to use the concept of solubility to get the amount of separation from a certain solute in the solution.

This arises from attempting to solve a problem regarding this matter. The problem described is as follows:

[itex]400[/itex] grams of anhydrous sodium sulphate ([itex]Na_{2}SO_{4}[/itex]) is dissolved in a liter of hot water. The solution is then let to cool carefully until reaching [itex]20^{\circ}C[/itex] to remain oversaturated with respect to the formed decahydrate [itex]Na_{2}SO_{4}\cdot 10H_{2}O[/itex]. Then a small sack of the latter salt is added to the solution, separating the excess of [itex]Na_{2}SO_{4}[/itex] by [itex]100\,mL[/itex] of water. What amount of the decahydrate would had been separated?

The given alternatives are:

[itex]\begin{array}{ll}
1.&249\,g\,\textrm{to}\,259\,g\\
2.&318\,g\,\textrm{to}\,327\,g\\
3.&689\,g\,\textrm{to}\,698\,g\\
4.&721\,g\,\textrm{to}\,730\,g\\
5.&890\,g\,\textrm{to}\,899\,g\\
\end{array}[/itex]

Although not given as information for this problem. I am assuming that the required information is the solubility of the sodium decahydrate at [itex]20^{\circ}C[/itex]. Wikipedia entry mentions that the solubility of that salt is [itex]44\frac{g}{100\,mL}[/itex] for that temperature.

What I assumed is that

[itex]400\,g\,Na_{2}SO_{4}\times\frac{142+180\,g\,Na_2SO_{4}\cdot 10 H_{2}O}{142,\g.Na_{2}SO_{4}}\,mL-100\,mL\frac{44}{100}=863\,g[/itex]

Therefore that would be the grams of sodium sulphate decahydrate but I'm not sure if that would be the ammount. I'm confused why do the alternatives features a range?. How does it appear that?. Can somebody explain this to me?. I'm not very sure about the value of the solubility of the sodium sulphate decahydrate. I've did some research on CRC's handbook and Lange's as well but there isn't given the solubility of that specific salt. Perhaps do anybody in this forum has the information, so It can match any of the alternatives.

My major concern with this question is why the answer is given in a range?. Shouldn't it be a specific amount?. What could had been intended by the author?. Can somebody help me with this?.

AWK:
Wikipedia says that number 44g/100 ml concerns heptahydrate (but this is probably an error - should be decahydrate)

https://www.saltwiki.net/index.php/Sodium_sulfate_heptahydrate

The ranges of solubility concern eventual rounding errors.

Borek:

--- Quote from: Blueberries116 on December 30, 2019, 11:28:28 PM ---Then a small sack of the latter salt is added to the solution, separating the excess of [itex]Na_{2}SO_{4}[/itex] by [itex]100\,mL[/itex] of water.
--- End quote ---

My English fails me, I have no idea what it is intended to mean :(

Blueberries116:

--- Quote from: Borek on December 31, 2019, 03:01:13 AM ---
--- Quote from: Blueberries116 on December 30, 2019, 11:28:28 PM ---Then a small sack of the latter salt is added to the solution, separating the excess of [itex]Na_{2}SO_{4}[/itex] by [itex]100\,mL[/itex] of water.
--- End quote ---

My English fails me, I have no idea what it is intended to mean :(

--- End quote ---

I'm also confused about that assertion in the question. But how could this ammount be found?. The given information on the wiki about salt is not very clear with the solubility of the sodium sulphate. I'm still stuck with this problem. Does it exist a way to solve it?.

Borek:

--- Quote from: Blueberries116 on January 01, 2020, 04:56:45 PM ---I'm also confused about that assertion in the question. But how could this ammount be found?. The given information on the wiki about salt is not very clear with the solubility of the sodium sulphate. I'm still stuck with this problem. Does it exist a way to solve it?.
--- End quote ---

No way to say if the problem can be solved as long as we don't understand what the question really is.

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