What is the mass of potassium nitrate which crystallizes?

[lioric]

Homework Statement

20g of saturated solution of potassium nitrate is cooled from 68 to 36 degree Celsius
What is the mass of potassium nitrate which crystallizes?
Potassium nitrate solubility per 100g of water
68 degree Celsius = 120g
38 degree Celsius = 60g

Homework Equations

I tried without equations just cross multiplying

The Attempt at a Solution

Please check if my answer is correct

Since the question says 20g of solution which means it's mass of potassium nitrate + water
So since
120g = 100g water = 220g solution (120+100)

120g = 220g
X = 20g
X= 10.9g of potassium nitrate in unknown amount of water

20-10.9= 9.1g of water

Therefore 20g of solution is actually 10.9g of potassium nitrate in 9.1g of water at 68 degree Celsius

In 38 degree Celsius = 60g potassium nitrate per 100 g of water

So
60g = 100g
X = 9.1g

X = 5.46g potassium nitrate in 38 degree Celsius in 9.1g water

Amount of potassium nitrate crystallized
10.9-5.46=5.44

Is this calculation correct?

 

[BvU]

The calculation is. The numbers are not.

 

[lioric]

The calculation is. The numbers are not.

Numbers are not? Please do tell what I did wrong? Or at least tel me which part?

 

[BvU]

X= 10.9g of potassium nitrate

10.1-5.46=4.64g

 

[lioric]

Oh that's right it s a typo
Actually I was wondering why I got 4.5 while in my original working I got 5.4
I thought I made a calculation error
Thanks
And thank you for your time

 

[BvU]

And of course the dissolved nitrate/water ratio drops by a factor of 2, the amount of water stays the same, so the amount of dissolved nitrate halves too...

 

[lioric]

And of course the dissolved nitrate/water ratio drops by a factor of 2, the amount of water stays the same, so the amount of dissolved nitrate halves too...

Could explain that part a bit more

 

[BvU]

120 g/100g water goes to 60 g/100 g water, so y g/x g water goes to $1\over 2$ y g/x g water.

 

[lioric]

120 g/100g water goes to 60 g/100 g water, so y g/x g water goes to $1\over 2$ y g/x g water.

Wow
Thank you very much