Final answer:
The minimum amount of solvent needed to dissolve 10 grams of a compound is 166.67 ml, calculated by using both the boiling and cold solvent solubilities. The maximum yield of crystals expected when cooling the solution is 7 grams.
Step-by-step explanation:
To determine the minimum amount of solvent needed to dissolve 10 grams of the compound, we use the information given that 8 grams of the compound is soluble in 100 ml of boiling solvent and 3 grams is soluble in 100 ml of cold solvent. Therefore, dissolving the entire 10 grams would require more solvent at either temperature. However, to minimize the solvent amount, we dissolve as much as possible at the higher temperature and then the remainder at the lower temperature.
First, we find out how many multiples of 100 ml are needed to dissolve 8 grams of the compound:
8 grams soluble ÷ 10 grams total = 0.8 (80%), which means we need 100 ml of boiling solvent for 8 grams. To dissolve the remaining 2 grams using cold solvent, we calculate the proportion:
2 grams remaining ÷ 3 grams soluble per 100 ml = 0.6667, which corresponds to roughly 66.67 ml of cold solvent.
Adding the two amounts gives us the total solvent required:
100 ml (boiling) + 66.67 ml (cold) = 166.67 ml.
So, the minimum amount of solvent needed to dissolve 10 grams of the compound is 166.67 ml.
For the maximum yield of crystals, we base our calculations on the solubility at the cold temperature. When cooled, 3 grams of the compound can stay dissolved in 100 ml of solvent. Thus, if we dissolve 10 grams in the minimum amount of solvent and then cool the solution, 3 grams will remain in solution and the rest will crystallize out. Consequently, we would expect:
10 grams - 3 grams = 7 grams
7 grams would be the maximum yield of crystals expected from the cooling process.