Recrystallization: crystal composition, yield, and mother liquor composition

[mirandasatterley]

Homework Statement

You are given a mixture containing two compounds, A and B. Both compounds have a solubility of 1g/100mL of solvent at 20 degree celsius and 12g/100mL of solvent at 100 degree celsius. The sample is composed of 1.5g of A and 10g of B. At 100 degree celsius all of the sample just dissolves in a minimum amount of solvent. The solution is cooled to 20 degree celsius and crystals are collected. Calculate the composition of the crystals and the yeild of the process. What is the composition of the mother liquor?

Homework Equations

No equations.

The Attempt at a Solution

Compound A: 1.5g x 100mL/12g = 12.5mL
Compound B: 10g x 100mL/12g = 83.3mL
So from this, of the solution (solvent that just dissolves A and B), 12.5mL dissolves A and 83.8mL dissolves B.

When cooled, the solubility is only 1g/100mL, so
Compound A: 12.5mL x 1g/100mL = 0.125g
Compound B: 83.3mL x 1g/100mL = 0.833g
Therefore the crystals collected have composition:
Compound A = 0.125g/(0.125 +0.833)g x 100% = 13.05%
Compound B = 0.833g/(0.125 +0.833)g x 100% = 86.95%

Does any of this make sense? If not, where did I go wrong? I'm also unsure of how to calculate the yeild of the process and the composition of the mother liquor.

Any help is greatly appreciated. Thanks.

 

[Decan]

You already calculated the yield when you figured out the %'s of compound A and B...as for the composition of mother liquor, I have no clue what its asking for.