Calculation of Molar Mass of Solute

Given:
- Mass of solute (m) = 2.34g
- Mass of solvent (M) = 40g
- Boiling point elevation (ΔTb) = 0.81K
- Boiling point constant (Kb) = 2.53Kkg/mol

Formula:

ΔTb = Kb × m / W2
where W2 = mass of solvent in kg
m = molality of solution

molality (m) = moles of solute / mass of solvent in kg
molar mass of solute = mass of solute / moles of solute

Solution:

First, we need to find the molality of the solution using the given data:

ΔTb = Kb × m / W2
0.81 = 2.53 × m / 0.04
m = 0.0321 mol/kg

Now, we can find the moles of solute:

molality (m) = moles of solute / mass of solvent in kg
0.0321 = moles of solute / 0.04
moles of solute = 0.001284 mol

Finally, we can find the molar mass of the solute:

molar mass of solute = mass of solute / moles of solute
molar mass of solute = 2.34g / 0.001284 mol
molar mass of solute = 1821.05 g/mol

Therefore, the molar mass of the solute is 1821.05 g/mol.

Explanation:

When a solute is dissolved in a solvent, the boiling point of the resulting solution is higher than that of the pure solvent. This is known as boiling point elevation and is directly proportional to the molality of the solution. The proportionality constant is known as the boiling point constant (Kb).

The formula used to calculate the molar mass of the solute is based on the fact that molality is the number of moles of solute per kilogram of solvent. By calculating the molality of the solution, we can find the number of moles of solute. Dividing the mass of solute by the number of moles of solute gives us the molar mass of the solute.

In this case, we are given the mass of solute, mass of solvent, boiling point elevation, and boiling point constant. By using the formula and substituting the given values, we can calculate the molality of the solution. From there, we can find the number of moles of solute and finally the molar mass of the solute.