In recrystallization from boiling water of benzoic acid contaminated with acetanilide, you begin with an impure sample of 5 grams. If the % composition of the acetanilide impurity in the sample is 6.3 %, what is the minimum amount in mL of solvent (water) required for the recrystallization

This question is incomplete, the complete question is;

In recrystallization from boiling water of benzoic acid contaminated with acetanilide, you begin with an impure sample of 5 grams. If the % composition of the acetanilide impurity in the sample is 6.3 %, what is the minimum amount in mL of solvent (water) required for the recrystallization

Compound      Solubility in water at 25°C      Solubility in water at 100°C

Benzoic Acid      0.34 g/100mL                           5.6 g/100mL

Acetanilide         0.53 g/100mL                           5.5 g/100mL

The minimum amount in mL of solvent (water) required for the recrystallization is 91 mL

Explanation:

Given the data in the question;

mass of sample = 5 g

percentage composition of the acetanilide impurity = 6.3%

mass of the acetanilide in impure sample will be;

⇒ 6.3% × 5 g = 0.315 g

Mass of benzoic acid in impure sample;

⇒ 5 g - 0.315 g = 4.685 g

now, solubility in water at 100°C for benzoic acid = 5.6 g/100mL

hence 4.685 g of benzoic acid is soluble in x mL

x = [ 100 mL × 4.685 g ] / 5.6 g

x = 83.66 ≈ 84 mL

Also, solubility in water at 100°C for acetanilide = 5.5 g/100mL

hence 0.315 g of benzoic acid is soluble in x mL

x = [ 100 mL × 0.315 g ] / 5.5 g

x = 5.727 ≈ 6 mL

So, the minimum amount in mL of solvent (water) required for the recrystallization will be;

⇒ 85 mL + 6 mL = 91 mL

The minimum amount in mL of solvent (water) required for the recrystallization is 91 mL