A 20 g mixture containing 95% (by weight) of A and 5% of B is recrystallized in toluene (b.p. 110 C). Solubility for compound A is 1.5 g @20 degrees and 10 g @ 110 degrees. For compound B solubility is 0.5 g @20 degrees and 8 g @ 110 degrees. What amount of solvent is needed to obtain pure A and how much pure A will be recovered?

5 answers

Nowhere in your problem do you say what the volume is for the solubility. In most cases it is quoted as 100 mL; therefore, I ASSUME that 1.5 g @ 20 C MEANS 1.5 grams A will dissolve in 100 mL toluene at 20 C, etc.
20 g sample is
95%A or 20 x 0.95 = 19 grams A.
5% B or 20 x 0.05 = 1 grams B.

How much toluene do we need to dissolve the 19 g A? It is 100 mL x (19/10) = 190 mL toluene needed to dissolve 19 grams A @ 110 C. Will that dissolve all of the B? Yes, because you have only 1 g B and the solubility of B at 110 C is 8 grams.

Now we cool the 190 mL toluene to 20 C. How much A comes out?
1.5 g x (190/100) = 2.85 grams A dissolve; thus, 19-2.85 = ?? grams recrystallize so your percent recovery (although the problem doesn't ask for that) is (16.15/20)*100 = ??
You may want to check to see if it will be contaminated with B. We had the 1 g B dissolved in 190 mL toluene at 110 C. At 20 C, B dissolves to the extent of
0.5 x (190/100) = 0.95. Since we had 1.0 g B, all of it will stay in solution at the lower temperature. Check my thinking.
Your answer is correct.
yes
now
we need 200 mL, because we want to dissolve all B. To revover pure A