Problem: Find out the mole fraction, molality, and normality of a 28% w/w solution of urea, given that the density of the solution is 1.5 g/mL.

Solution:

To find the mole fraction, molality, and normality of the solution, we need to understand the concepts and formulas associated with each term.

Mole Fraction:
The mole fraction (X) of a component in a solution is the ratio of the number of moles of that component to the total moles of all components in the solution.

The formula to calculate mole fraction is:

X = moles of component / total moles of all components

In this case, we have a 28% w/w solution of urea, which means that 28 grams of urea is present in 100 grams of the solution.

First, we need to calculate the moles of urea present in the solution.

Step 1: Calculate the mass of urea present in the solution.
Mass of urea = (28% / 100%) * 100 g = 28 g

Step 2: Calculate the moles of urea using its molar mass.
The molar mass of urea (CH4N2O) is 60.06 g/mol.

Number of moles of urea = mass of urea / molar mass
= 28 g / 60.06 g/mol
= 0.466 mol

Step 3: Calculate the mass of the solvent (water).
Mass of water = 100 g - 28 g = 72 g

Step 4: Calculate the moles of water using its molar mass.
The molar mass of water (H2O) is 18.02 g/mol.

Number of moles of water = mass of water / molar mass
= 72 g / 18.02 g/mol
= 3.998 mol

Step 5: Calculate the mole fraction of urea.
Mole fraction of urea = moles of urea / (moles of urea + moles of water)
= 0.466 mol / (0.466 mol + 3.998 mol)
= 0.104

Therefore, the mole fraction of urea in the solution is 0.104.

Molality:
Molality (m) is a measure of the concentration of a solute in a solution, expressed in moles of solute per kilogram of solvent.

The formula to calculate molality is:

m = moles of solute / mass of solvent (in kg)

In this case, the mass of the solvent (water) is 72 g.

Step 1: Convert the mass of water to kilograms.
Mass of water in kg = 72 g / 1000
= 0.072 kg

Step 2: Calculate the molality of urea.
Molality of urea = moles of urea / mass of water (in kg)
= 0.466 mol / 0.072 kg
= 6.472 mol/kg

Therefore, the molality of urea in the solution is 6.472 mol/kg.

Normality:
Normality (N) is a measure of the concentration of a