Calculating the Molecular Mass of Urea

Urea is a compound that is used in many industrial and agricultural applications. In order to determine the molecular mass of urea, we need to use its isotonic properties with sucrose.

Understanding Isotonicity

Isotonicity refers to the concentration of a solution that is equal to that of another solution. In this case, we know that 1.78% urea is isotonic with 10% sucrose. This means that the concentration of urea in the solution is equal to the concentration of sucrose in the solution.

Using the Formula for Isotonicity

The formula for isotonicity is:

M1V1 = M2V2

Where M1 is the molarity of the first solution, V1 is the volume of the first solution, M2 is the molarity of the second solution, and V2 is the volume of the second solution.

In this case, we know that the molarity of sucrose is 0.555 M (10% sucrose) and the molarity of urea is unknown. We also know that the volume of the sucrose solution is equal to the volume of the urea solution.

By using the formula for isotonicity, we can solve for the molarity of urea:

M1V1 = M2V2
0.555 M x V = M x V
0.555 M = M

This means that the molarity of urea is 0.555 M.

Calculating the Molecular Mass of Urea

The formula for molarity is:

Molarity = moles of solute / liters of solution

If we rearrange this formula, we can solve for the moles of solute:

moles of solute = molarity x liters of solution

We know that the molarity of urea is 0.555 M and the concentration of urea is 1.78%. This means that there is 1.78 g of urea in 100 mL of solution.

We can use this information to calculate the moles of urea:

moles of urea = 0.555 M x 0.1 L = 0.0555 moles

The molecular mass of urea can now be calculated using the formula:

molecular mass = mass / moles

We know that the mass of urea is 1.78 g, so we can plug in the values:

molecular mass = 1.78 g / 0.0555 moles = 32 g/mol

Therefore, the molecular mass of urea is 32 g/mol.

Conclusion

In conclusion, the molecular mass of urea can be determined by using its isotonic properties with sucrose. By using the formula for isotonicity and the formula for molarity, we can calculate the moles of urea and use this information to calculate its molecular mass. The molecular mass of urea is 32 g/mol.