Question

In propanol, cholesterol is 2.7 times more soluble at 43°C than at 20°C. If a saturated propanol solution is prepared at 43°C , what proportion of the cholesterol will crystallize upon cooling to 20°C?

Answer 1

Won't that be 1/2.7? If you want to make that a whole number it would be 37/100
Try it with some numbers. Let's suppose it is 20 times more soluble at 43 than at 20 and we place 20 g, heat the propanol to 43 and all of it will go into solution. Now we cool it to 20 C and how much comes out? Of course 1 g crystallizes so the proportion crystallized is 1 which crystallized over 20, the amount we started with or 1/20.
Now suppose we start with 10 g at 43 and cool to 20. How much will crystallize? That will be 0.5 g. Proportion crystallized is 0.5/10 or 1/20.