Vapour pressure of pure benzene at a certain temperature is 640 mm Hg. A non-volatile non-electrolyte solid weighing 2.175g is added to 39.0 of benzene. The vapour pressure of solution is 600 mm Hg. What is the molecular mass of solid substance?

To determine the molecular mass of the non-volatile non-electrolyte solid added to benzene, we can use Raoult's Law, which relates the vapor pressure of a solution to the vapor pressure of the pure solvent and the mole fraction of the solvent in the solution. Let's break this down step by step.

Understanding Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution (P_solution) is equal to the vapor pressure of the pure solvent (P_pure) multiplied by the mole fraction of the solvent (X_solvent) in the solution:

P_solution = P_pure × X_solvent

Given Data

• P_pure (vapor pressure of pure benzene) = 640 mm Hg
• P_solution (vapor pressure of the solution) = 600 mm Hg
• Mass of solid = 2.175 g
• Mass of benzene = 39.0 g

Calculating the Mole Fraction of Benzene

First, we need to find the mole fraction of benzene in the solution. We can rearrange Raoult's Law to find X_solvent:

X_solvent = P_solution / P_pure

Substituting the values:

X_solvent = 600 mm Hg / 640 mm Hg = 0.9375

Finding the Mole Fraction of the Solid

The mole fraction of the solid (X_solid) can be calculated as:

X_solid = 1 - X_solvent

So:

X_solid = 1 - 0.9375 = 0.0625

Calculating Moles of Benzene

Next, we need to calculate the number of moles of benzene. The molar mass of benzene (C6H6) is approximately 78.11 g/mol. Using the formula:

moles = mass / molar mass

We find:

moles of benzene = 39.0 g / 78.11 g/mol ≈ 0.499 moles

Relating Moles to Mole Fraction

The mole fraction of the solid can also be expressed in terms of moles:

X_solid = moles of solid / (moles of solid + moles of benzene)

Let the number of moles of the solid be n. Then:

0.0625 = n / (n + 0.499)

Solving for Moles of the Solid

Cross-multiplying gives:

0.0625(n + 0.499) = n

Expanding this, we get:

0.0625n + 0.031125 = n

Rearranging terms leads to:

n - 0.0625n = 0.031125

0.9375n = 0.031125

Thus:

n ≈ 0.0332 moles

Calculating the Molecular Mass of the Solid

Now, we can find the molecular mass (M) of the solid using the formula:

M = mass of solid / moles of solid

Substituting the values:

M = 2.175 g / 0.0332 moles ≈ 65.4 g/mol

Final Result

Therefore, the molecular mass of the non-volatile non-electrolyte solid is approximately 65.4 g/mol.