Final answer:
The minimum amount of water in which 1.5g of benzoic acid can dissolve at 95°C is 22.06 mL. When the 95°C solution is cooled to 25°C, 0.075g of benzoic acid will remain in solution, while 1.425g will precipitate/crystallize out of the solution.
Step-by-step explanation:
To find the minimum amount of water in which 1.5g of benzoic acid can dissolve at 95°C, we need to use the solubility value given at that temperature. The solubility of benzoic acid in water at 95°C is 68g/L. To convert this to grams per milliliter (g/mL), we divide by 1000. So, the solubility at 95°C is 0.068g/mL. To find the minimum amount of water, divide 1.5g by 0.068g/mL:
Minimum amount of water = mass of solute / solubility = 1.5g / 0.068g/mL = 22.06 mL
For the second part of the question, to determine how much benzoic acid will remain in solution and how much will precipitate/crystallize out when the 95°C solution is cooled to 25°C, we need to compare the solubility at 95°C and 25°C. The solubility of benzoic acid in water at 25°C is 3.4g/L. To convert this to grams per milliliter (g/mL), we divide by 1000. So, the solubility at 25°C is 0.0034g/mL.
To find how much benzoic acid will remain in solution when cooled to 25°C, we multiply the solubility at 25°C by the volume of water used to dissolve the 1.5g of benzoic acid at 95°C:
Amount of benzoic acid remaining in solution = solubility at 25°C * volume of water = 0.0034g/mL * 22.06 mL = 0.075 g
To find how much benzoic acid will precipitate/crystallize out of the solution, we subtract the remaining amount from the initial amount:
Amount of benzoic acid precipitated = initial amount - remaining amount = 1.5g - 0.075g = 1.425 g