How to Calculate Molar Mass of Solvent in a Solution?

What is the mole fraction of urea in a solvent and how can we determine the molar mass of the solvent in a solution?

Given that the mole fraction of urea in a solvent is 0.1 and the molarity of the solution is 10/9m, how can we calculate the molar mass of the solvent in grams per mole?

Calculation of Molar Mass of Solvent in a Solution

To determine the molar mass of the solvent in a solution where the mole fraction of urea is 0.1 and the molarity is 10/9m, we can follow these steps:

Firstly, it is important to understand the relationships between molarity, molality, and mole fraction in a solution. Molarity (M) is defined as the number of moles of solute divided by the volume of the solvent in liters. Molality, on the other hand, is the number of moles of solute divided by the mass of the solvent in kilograms.

In this case, we are given that the mole fraction of urea is 0.1. This implies that the mole fraction of the solvent is 0.9 since the total mole fraction should sum up to 1. Therefore, for 1 mole of solution, we have 0.1 moles of urea and 0.9 moles of the solvent.

The formula to calculate the molar mass of the solvent is given by: M = m/n, where m is the mass of the solvent and n is the number of moles of the solvent. Since we have 0.9 moles of the solvent for 1 mole of solution, we can express the molar mass of the solvent in terms of the provided molarity:

10/9m = molar mass of the solvent

Therefore, the molar mass of the solvent in grams per mole is 10/9 g/mol.