Isotonic Solutions and Osmolarity:

Isotonic solutions are solutions that have the same osmolarity as the surrounding fluid or solution. Osmolarity refers to the concentration of solute particles in a solution. In biological systems, osmolarity is an important factor in maintaining cell shape and function.

Determining Osmolarity:

To determine the osmolarity of a solution, we need to consider the number of particles in the solution rather than just the mass of the solute. This is because different solutes can have different molecular weights and thus different numbers of particles per mole.

Urea Solution and Nonvolatile Solute:

In this case, we have a solution containing 10 grams per decimeter cube (10 g/dm³) of Urea. We are also given that this solution is isotonic with a 5% solution of a nonvolatile solute.

To determine the osmolarity of the Urea solution, we need to know the molecular weight of Urea. The molecular weight of Urea is approximately 60 g/mol.

Now, let's calculate the osmolarity of the Urea solution:

1. Calculate the number of moles of Urea:
Number of moles = mass / molecular weight
Number of moles = 10 g / 60 g/mol
Number of moles = 0.1667 mol

2. Calculate the osmolarity:
Osmolarity = number of moles / volume in liters
Osmolarity = 0.1667 mol / 1 dm³
Osmolarity = 0.1667 mol/dm³

Comparing with Nonvolatile Solute:

Now, we are given that the Urea solution is isotonic with a 5% solution of a nonvolatile solute. To determine the molecular weight of this nonvolatile solute, we need to convert the percentage into grams per decimeter cube.

1. Convert 5% into grams per decimeter cube:
5% = 5 g/100 cm³ = 50 g/dm³

2. Calculate the molecular weight of the nonvolatile solute:
Molecular weight = mass / number of moles
Molecular weight = 50 g/dm³ / 0.1667 mol/dm³
Molecular weight ≈ 300 g/mol

Therefore, the molecular weight of the nonvolatile solute in the 5% solution is approximately 300 g/mol.

Answer: c) 300g/mol