Question

The solubility of compound A in ethanol is 0.8 g per 100 mL at 0°C and 5.0 g per
100 mL at 78°C. What is the minimum amount of ethanol needed to re-crystallize a
12.0 g sample of compound A? How much would be lost in the re-crystallization,
that is, would remain in the cold solvent?

Answer 1

You can work this by ratio and proportion or by dimensional analysis. Done by ratio and proportion looks like this.
At 78 C, we will need how much of the solvent to dissolve all 12 g?
(5g/100 mL)=(12g/x mL)
Solve for X. I did the math and obtained 240 mL but check me out on my math.

Then how much will we lose when we cool the 240 mL down to zero.
(0.8g/100 mL) = (x/240 mL)
Solve for x grams. This will be the amount that stays in the solvent at the lower temperature; in other words, the amount that would be lost from the initial 12 grams.

Answer 2

1.92 grams

Answer 3

84% maximum percent retrieval