Calculation of Molarity

Molarity is defined as the number of moles of solute present in one liter of solution. To calculate the molarity of urea in the given solution, we need to determine the number of moles of urea present.

The molar mass of urea (CH4N2O) is calculated as follows:
C: 12.01 g/mol
H: 1.01 g/mol
N: 14.01 g/mol
O: 16.00 g/mol

Therefore, the molar mass of urea is:
12.01 + 4(1.01) + 14.01 + 16.00 = 60.06 g/mol

Given that the solution contains 40 g of urea, we can calculate the number of moles using the formula:
Number of moles = mass of solute / molar mass

Number of moles of urea = 40 g / 60.06 g/mol = 0.666 mol

Now, we need to calculate the molarity using the formula:
Molarity = number of moles / volume of solution (in liters)

Since the volume of the solution is not provided, we cannot calculate the molarity.

Calculation of Mole Fraction

Mole fraction is defined as the ratio of the number of moles of a component to the total number of moles in the solution. To calculate the mole fraction of urea in the given solution, we need to determine the total number of moles of all components.

Given that the solution contains 100 g of solution, and 40 g of urea, we can calculate the number of moles of water using the formula:
Number of moles of water = (mass of solution - mass of urea) / molar mass of water

The molar mass of water (H2O) is:
H: 1.01 g/mol
O: 16.00 g/mol

Therefore, the molar mass of water is:
2(1.01) + 16.00 = 18.02 g/mol

Number of moles of water = (100 g - 40 g) / 18.02 g/mol = 3.331 mol

The total number of moles in the solution is the sum of the moles of urea and water:
Total moles = moles of urea + moles of water = 0.666 mol + 3.331 mol = 3.997 mol

Now, we can calculate the mole fraction of urea using the formula:
Mole fraction of urea = moles of urea / total moles

Mole fraction of urea = 0.666 mol / 3.997 mol = 0.1665

Therefore, the mole fraction of urea in the solution is 0.1665.

Summary:
- The molarity of the urea solution cannot be determined without knowing the volume of the solution.
- The mole fraction of urea in the solution is found to be 0.1665.