Problem:
An aqueous solution of 2% non-volatile solute exerts a pressure of 1.004 bar at the normal boiling point of the solvent. What is the molar mass of the solute? (P°H2O = 1.013 bar)

Solution:

1. Understanding the problem:
We are given that the aqueous solution contains a non-volatile solute, and it exerts a pressure of 1.004 bar at the boiling point of the solvent. We need to determine the molar mass of the solute.

2. Applying Raoult's Law:
Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent. In this case, the solvent is water (H2O), and the solute is non-volatile. The mole fraction of the solute can be calculated using the given concentration of the solution.

3. Calculating mole fraction of the solute:
We are given that the solution contains 2% non-volatile solute. This means that for every 100 grams of the solution, 2 grams are the solute. To calculate the mole fraction, we need to convert the mass of the solute to moles.

Assuming we have 100 grams of the solution, the mass of the solute is 2 grams. Since the molar mass of the solute is unknown, we'll represent it as 'M'.

Moles of solute = mass of solute / molar mass of solute
Moles of solute = 2 grams / M grams per mole

4. Applying Raoult's Law equation:
According to Raoult's Law, the vapor pressure of the solution (P) is given by the equation:
P = Xsolvent * P°solvent

Where:
P = vapor pressure of the solution
Xsolvent = mole fraction of the solvent
P°solvent = vapor pressure of the pure solvent

In this case, our solvent is water (H2O) and its vapor pressure at the boiling point is given as P°H2O = 1.013 bar.

5. Rearranging the equation:
Since we know the vapor pressure of the solution (P) and the vapor pressure of the solvent (P°solvent), we can rearrange the equation to solve for the mole fraction of the solvent (Xsolvent).

Xsolvent = P / P°solvent

6. Calculating the mole fraction of the solvent:
Using the given data:
P = 1.004 bar
P°H2O = 1.013 bar

Xsolvent = 1.004 bar / 1.013 bar
Xsolvent = 0.9911

7. Solving for the molar mass of the solute:
Now that we have the mole fraction of the solvent (Xsolvent), we can solve for the molar mass of the solute using the equation:

Xsolvent = moles of solvent / (moles of solvent + moles of solute)

Since the solute is non-volatile, we can assume that it does not contribute significantly to the total moles in the solution. Therefore,