Calculate the mole fraction of the solute.
3.10% ethanol, by volume (d=0.993 g/mL; pure C2H5OH, d=0.789 g/mL)
To calculate the mole fraction of the solute, we need to determine the number of moles of the solute (ethanol) and the total number of moles of all components in the solution. Here's how you can find the mole fraction:
1. Determine the mass of ethanol in the solution:
Mass of ethanol = Volume of solution × Density of ethanol × % ethanol by volume
= Volume of solution × (0.789 g/mL) × (3.10/100)
2. Convert the mass of ethanol to moles using its molar mass:
Molar mass of C2H5OH = 12.01 g/mol (C) + 2 × 1.01 g/mol (H) + 16.00 g/mol (O)
= 46.07 g/mol
Moles of ethanol = Mass of ethanol / Molar mass of ethanol
3. Calculate the moles of the solvent (water) in the solution:
Since the solution is mostly ethanol, we can assume that the volume of water is negligible, and therefore the moles of water are also negligible.
4. Calculate the total number of moles:
Total moles = Moles of ethanol + Moles of water
5. Calculate the mole fraction of ethanol:
Mole fraction of ethanol = Moles of ethanol / Total moles
By following these steps, you will be able to calculate the mole fraction of the solute (ethanol) in the given solution.