An aqueous solution of ethanol ,CH3CH2OH (M=46.08 g· mol-1), that is 12.00% ethanol by mass , has a density of 0.9808 g·mL-1 at 20℃. What is the molality of ethanol in this solution?
To find the molality of ethanol in the solution, we need to know the amount of ethanol in moles and the mass of the solvent (water) in kilograms.
Given:
Mass percent of ethanol = 12.00%
Density of solution = 0.9808 g/mL
Molar mass of ethanol (CH3CH2OH) = 46.08 g/mol
Step 1: Calculate the mass of the solution.
Given the density of the solution is 0.9808 g/mL, we can use this to find the mass of the solution.
Mass of solution = Volume of solution × Density of solution
Step 2: Calculate the mass of ethanol present in the solution.
Since the solution is 12.00% ethanol by mass, we can calculate the mass of ethanol.
Mass of ethanol = (12.00/100) × Mass of solution
Step 3: Calculate the molality of ethanol.
Molality is defined as the moles of solute (ethanol) per kilogram of solvent (water).
Molality = Moles of ethanol / Mass of solvent (in kg)
Step-by-step calculations:
Step 1:
Mass of solution = Volume of solution × Density of solution
Since we do not have the volume of the solution, we cannot calculate the mass yet. Let's proceed to Step 2.
Step 2:
Mass of ethanol = (12.00/100) × Mass of solution
Since we don't have the mass of the solution either, we can't calculate the mass of ethanol yet. However, we know that the solution consists of ethanol and water, and water is the main component of the solution. So, we can assume that the mass of the solution is mostly due to water.
Step 3:
Molality = Moles of ethanol / Mass of solvent (in kg)
Since we assume the mass of the solution is mostly due to water, we can use the mass of the solution as a close approximation to the mass of the solvent.
Molality = Moles of ethanol / Mass of solution
Now, let's calculate the moles of ethanol based on the given information:
Moles of ethanol = Mass of ethanol / Molar mass of ethanol
We still don't have the mass of the solution, but we can calculate it based on the density and the volume formula:
Density = Mass of substance / Volume of substance
Volume of substance = Mass of substance / Density
If we assume that the density of the solution is approximately the same as the density of water (since water is the main component), we can calculate the volume of the solution using the density given:
Volume of solution = Mass of solution / Density of solution
Now, we can substitute the values and calculate the volume of the solution:
Volume of solution = Mass of solution / Density of solution
Volume of solution = Mass of solution / 0.9808 g/mL
At this point, we don't have the mass of the solution, so unfortunately, we cannot calculate the volume of the solution or the moles of ethanol.