How Do You Calculate the Percent by Mass of Na2SO4 * 10H2O in a Hydrated Sample?

[Nano]

Homework Statement

A thoroughly dried 1.283 sample of Na2SO4 is exposed to the atmosphere and found to gain 0.395 in mass. What is the percent, by mass, of Na2SO4 * 10H20 in the resulting mixture of anhydrous and the decahydrate?

Homework Equations

1 mol Na2SO4 = 142.0428 g
1 mol H20 = 15.994 g

The Attempt at a Solution

Don't really know where to start. I found the moles of Na2SO4 in 1.283 g sample (.009032) and the moles H20 in sample once it had gained weight (1.678 sample, .118133 mol H20)

 

[Borek]

If you know number of moles of water, can you calculate number of moles of hydrate that was produced? Number of moles of anhydrous sulfate left?

 

[Nano]

I found the moles hydrate in the .11813 mol H2O by dividing it by 10 mol h2o per mol hydrate. Then I divided that by the 1.678 g hydrate mixture (1.283 +.395 g gained) to find the percentage mass. But that was not right either

 

[Borek]

Judging from what you wrote you divided number of moles by mass. You need to divide mass by mass.

 

[Nano]

I saw the mistake after I posted it and converted the moles hydrate to g, but the resulting mass was greater that 1.678 (giving a percentage greater than 100)

Basically what I have to do is find
g hydrate (Na2SO4*10H2O) / 1.678 g mixture
and multiply that by 100 to get ther percentage by mass, right?
From that, I tried again working backwards to find moles H20 like you said. I converted 1.678 g hydrate to moles H20 and got .52105 mol H20. Now I'm not sure where to go from there; I tried converting that to grams hydrate but ended up back to 1.678 g of course.

 

[Borek]

Probably some math error.

Please list:

number of moles of water
number of moles of hydrate
mass of the hydrate

as you have calculated.

 

[Nano]

.052105 mol water
.00521 mol hydrate
1.89059 g hydrate

 

[Borek]

0.052105?

 

[Nano]

Do I convert .395 g to moles water to find the moles water (since all of the mass gained is water)?

 

[Borek]

What else can you use?