Question

The vapour pressure of a solution of a non-volatile solute B in a solvent A is 95% of the vapor pressure of the solvent at the same temperature. If the molecular weight of the solvent is 0.3 times the molecular weight of the solute, what is the ratio of the weight of solvent to solute?

A. 0.15
B. 5.7
C. 0.2
D. None of these

Answer 1

The ratio of the weight of solvent to solute is 0.2. The correct answer is option: C. 0.2

Step-by-step explanation:

To find the ratio of the weight of solvent to solute, we can first use Raoult's law to relate the vapor pressure of the solution to the mole fraction of the solvent:

PA = (1-XB)PA, where PA is the vapor pressure of the solvent and XB is the mole fraction of the solute.

Since the vapor pressure of the solution is 95% of the vapor pressure of the solvent, we can write:

0.95PA = (1-XB)PA

Cancelling out PA, we get:

0.95 = 1 - XB

Solving for XB, the mole fraction of the solute, we find XB = 0.05.

Since the molecular weight of the solvent is 0.3 times the molecular weight of the solute, we can write:

MA/MB = 0.3

Using the mole fraction XB, we can write:

XB = nB/(nA + nB)

where nA and nB are the moles of solvent and solute, respectively.

Substituting the molecular weight relationship into the equation, we get:

0.05 = nB/(nA + nB) * 0.3

Simplifying the equation, we find:

0.05/(0.3 - 0.05) = nB/nA

0.05/0.25 = nB/nA

0.2 = nB/nA

So, the ratio of the weight of solvent to solute is 0.2.