Understanding Molality
* Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent.
* In this case, we have a 3.71 m solution, meaning there are 3.71 moles of solute for every 1 kilogram of water (the solvent).
Calculating Mole Fraction
The mole fraction of a component (solute or solvent) is the ratio of the number of moles of that component to the total number of moles in the solution.
1. Moles of Solvent:
* Since we have 1 kg of water, and the molar mass of water is 18.015 g/mol, we can calculate the moles of water:
* Moles of water = (1000 g) / (18.015 g/mol) = 55.51 mol
2. Total Moles:
* Total moles in the solution = moles of solute + moles of water
* Total moles = 3.71 mol + 55.51 mol = 59.22 mol
3. Mole Fraction of Solute:
* Mole fraction of solute (X_solute) = (moles of solute) / (total moles)
* X_solute = 3.71 mol / 59.22 mol = 0.0626
Therefore, the mole fraction of the solute in a 3.71 m aqueous solution is 0.0626.
