Calculate the mole fraction of the solute in the following aqueous solutions

3.25% ethanol, by volume (d= 0.993 g/ml ; pure C2H5OH, d= 0.789 g/ml )

its in the textbook solution manual question 13.31, i havent done it yet but if i get a chance to do it before you i will post it up

thnks i got it ...

To calculate the mole fraction of the solute in an aqueous solution, we need to determine the moles of the solute and the moles of the solvent.

First, let's find the moles of ethanol (C2H5OH) in the solution.

Given:
- Volume percent of ethanol in the solution = 3.25%
- Density of the solution = 0.993 g/ml
- Density of pure ethanol = 0.789 g/ml

Step 1: Calculate the mass of the ethanol in the solution.
To do this, we need to determine the volume of ethanol in the solution.

Volume of ethanol = Volume percent of ethanol in the solution x Volume of the solution

The volume of the solution is not provided in the given information, so we cannot calculate the exact volume. However, for calculation purposes, let's assume that we have 100 mL of the solution.

Volume of ethanol = 3.25% x 100 mL = 3.25 mL

Step 2: Calculate the mass of ethanol in the solution.

Mass of ethanol = Volume of ethanol x Density of the solution
Mass of ethanol = 3.25 mL x 0.993 g/mL
Mass of ethanol = 3.22325 g

Step 3: Calculate the moles of ethanol.

Molar mass of ethanol (C2H5OH) = 2(12.01 g/mol) + 6(1.01 g/mol) + 1(16.00 g/mol) = 46.07 g/mol

Moles of ethanol = Mass of ethanol / Molar mass of ethanol
Moles of ethanol = 3.22325 g / 46.07 g/mol
Moles of ethanol ≈ 0.07 mol

Now let's move on to finding the moles of the solvent, which is water (H2O).

Since we assumed the total volume of the solution to be 100 mL, we can assume that the volume of the water in the solution is 100 mL - 3.25 mL (volume of ethanol) = 96.75 mL.

Step 4: Convert the volume of water to grams.

Mass of water = Volume of water x Density of water

The density of water is approximately 1 g/mL.

Mass of water = 96.75 mL x 1 g/mL
Mass of water = 96.75 g

Step 5: Calculate the moles of water.

Molar mass of water (H2O) = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol

Moles of water = Mass of water / Molar mass of water
Moles of water = 96.75 g / 18.02 g/mol
Moles of water ≈ 5.37 mol

Finally, let's calculate the mole fraction of the solute (ethanol).

Mole fraction of ethanol = Moles of ethanol / (Moles of ethanol + Moles of water)
Mole fraction of ethanol = 0.07 mol / (0.07 mol + 5.37 mol)
Mole fraction of ethanol ≈ 0.013

Therefore, the mole fraction of ethanol in the given aqueous solution is approximately 0.013.

I assume you have this now and don't need additional help.