The solubility of mirabilite (sodium sulfate decahydrate) 1.353 mol/kg is given in Table 1 of my link.
400/142-x means (400/142)-x (see "order of operations")
in your formula is 400/(142-x)
In equation use: x·10·18 +.
There is no confusion concerning the seeding of a solution with crystals of decahydrate.
The confusion comes from: "separating the excess of Na2SO4 by 100 mL of water." but after you correction:19.4 is very close to 1.353·142/10=19.2 g of anhydrous sodium sulfate per 100 g of water
I'm revisiting this question because I'm still stuck on it ??? . Can you explain it in simple terms what's happening because I am still confused at the justification of your mass balance.
I could verify that from your link [itex]19.2\,g[/itex] of anhydrous sodium sulphate per [itex]100\,mL[/itex] or [itex]100\,g[/itex] of water is close to what was given in the problem. But the rest is where I'm still struggling. Can you please explain each term?
x_moles_Na2SO4·10·18 + (400/142-x)·1000/1.353=990
This is the equation which you used:
To which I believe the intended meaning is (after reading what you wrote):
[itex]x\cdot 10 \cdot 18 + \left(\frac{400}{142}-x\right) \cdot \frac{1000}{1.353}=990[/itex]
Solving this produces:
[itex]x=1.95309[/itex]
which corresponds to the moles of sodium decahydrate which translated into grams would become into.
[itex]1.95309 \times 322 =628.498\,g[/itex] which isn't exactly in the third option but is very close.
If I do use [itex]1000[/itex] instead of [itex]990[/itex]
then this becomes into:
[itex]1.9352 \times 322 = 623.1344\,g.[/itex]
But again, what's the justification of this equation?.
[itex]x\cdot 10 \cdot 18 + \left(\frac{400}{142}-x\right) \cdot \frac{1000}{1.353}=990[/itex]
I'm only adding the masses of water contained in the salts?.
moles of anhydrous sodium sulphate-moles of mirabilite=moles of water
Is this what you intended to say?. Why?.
Wouldn't it be the opposite?. Why is the anhydrous first?. Or does this comes from the stoichiometry?. If it is, can you show it in the equation?.
Can you please help clearing out these doubts which I have. ???