Question

A) Calculate how much 95% Ethyl Alcohol will be required to dissolve 0.1 g sulfanilamide at 78 C. (At 80 C, solubility = 210 mg/mL)

B) Using the volume of solvent calculated in Step 1, calculate how much sulfanilamide will remain dissolved in the mother liquid after the mixture is cooled to ) C. (At 0 C, solubility = 14 mg/mL)

Answer 1

As the temperatures that are considered are so close, you can consider the 80ºC conditions as the same for 78ºC. Now change your grams into miligrams of sulfanilamide, which gives you a total of 100mg.
Consider it a linear behavior, and you can calculate the volume of alcohol as:

210mg ---> 1ml
100mg ---> xml

100mg(1ml) / 210mg = 0.48ml

Now, that is considering a 100% ethyl alcohol. To consider a 95% one, divide over that percentage so as to increase the volume as needed:

0.48ml / 0.95 = 0.50ml of ethyl alcohol

In part B, you cool the solvent down to 0ºC ??... if it is so, you must now revert the previous calculation to show how much of the solute will still be dissolved.

14mg ---> 1ml
x mg ---> 0.50ml x = (14mg)(0.50ml)/1ml = 7.02mg will still be dissolved out of 100mg.