The solubility of cholesterol in 95% ethanol is 32.5 mg/mL at 37°C and 11.5 mg/mL at 7°C. How much 95% ethanol is required to dissolve 1 g of cholesterol at 37°C? If that volume of warm, saturated solution is cooled in a refrigerator to 7°C, how much cholesterol will crystallize?
1000 mg x (1 mL/32.5 mg) = ?? mL at 37 degrees C.
How much will dissolve at 7 degrees C? That will be
??mL from above x (11.5 mg/mL) = ??
To determine how much 95% ethanol is required to dissolve 1 g of cholesterol at 37°C, we need to calculate the volume of ethanol needed.
First, convert the mass of cholesterol to milligrams:
1 g = 1000 mg
Next, calculate the volume of ethanol required using the solubility data:
Given: Solubility of cholesterol in 95% ethanol at 37°C = 32.5 mg/mL
Volume of ethanol required = Mass of cholesterol / Solubility of cholesterol
Volume of ethanol required = 1000 mg / 32.5 mg/mL
Volume of ethanol required = 30.77 mL
Therefore, 30.77 mL of 95% ethanol is required to dissolve 1 g of cholesterol at 37°C.
To calculate the amount of cholesterol that will crystallize when the warm, saturated solution is cooled to 7°C, we first need to determine the volume of the saturated solution at 37°C.
Given: Mass of cholesterol = 1 g
Solubility of cholesterol in 95% ethanol at 37°C = 32.5 mg/mL
Volume of warm saturated solution = Mass of cholesterol / Solubility of cholesterol
Volume of warm saturated solution = 1000 mg / 32.5 mg/mL
Volume of warm saturated solution = 30.77 mL
Now, we calculate the mass of cholesterol that remains dissolved at 7°C using the solubility data at 7°C.
Given: Solubility of cholesterol in 95% ethanol at 7°C = 11.5 mg/mL
Mass of cholesterol remaining dissolved at 7°C = Solubility of cholesterol at 7°C * Volume of warm saturated solution
Mass of cholesterol remaining dissolved at 7°C = 11.5 mg/mL * 30.77 mL
Mass of cholesterol remaining dissolved at 7°C = 354.155 mg
Therefore, 354.155 mg of cholesterol will remain dissolved when the warm, saturated solution is cooled to 7°C, and the rest will crystallize.