1. Understanding the Concepts
* Molality (m): The number of moles of solute per kilogram of solvent.
* Mole Fraction (χ): The ratio of the moles of solute to the total moles of all components in the solution.
2. Assumptions
* We'll assume the solution density is approximately equal to the density of water (1 g/mL). This is a reasonable approximation for dilute aqueous solutions.
3. Calculations
a) Molality (m)
1. Mass of solute (HCOOH) and solvent (water):
* Assume 100 g of solution.
* Mass of HCOOH = 30.1 g
* Mass of water = 100 g - 30.1 g = 69.9 g
2. Moles of solute (HCOOH):
* Molar mass of HCOOH = 46.03 g/mol
* Moles of HCOOH = 30.1 g / 46.03 g/mol = 0.654 mol
3. Molality:
* Molality (m) = (moles of solute) / (kg of solvent)
* Molality (m) = 0.654 mol / 0.0699 kg = 9.35 m
b) Mole Fraction (χ)
1. Moles of solvent (water):
* Molar mass of water = 18.02 g/mol
* Moles of water = 69.9 g / 18.02 g/mol = 3.88 mol
2. Mole fraction of HCOOH:
* Mole fraction (χ) = (moles of HCOOH) / (total moles of solution)
* Mole fraction (χ) = 0.654 mol / (0.654 mol + 3.88 mol) = 0.145
Therefore, the molality of the formic acid solution is 9.35 m, and the mole fraction of formic acid is 0.145.
