When 25g of a non-volatile solute is dissolved in 100g of water, the vapour pressure is lowered by 0.225 mm. if the vapour pressure of water at 25°C is 17.5 mm, what is the molecular mass of the solute?

a)206 b)302 c)318 d)216

To determine the molecular mass of the non-volatile solute, we can use Raoult's Law, which relates the vapor pressure of a solvent to the concentration of a solute in that solvent. The formula we will use is:

Understanding Raoult's Law

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

P_solution = P°_solvent × X_solvent

Given Data

• Mass of solute (m_solute) = 25 g
• Mass of solvent (water) (m_solvent) = 100 g
• Vapor pressure lowering (ΔP) = 0.225 mm
• Vapor pressure of pure water at 25°C (P°_water) = 17.5 mm

Calculating the Vapor Pressure of the Solution

First, we can find the vapor pressure of the solution:

P_solution = P°_water - ΔP

P_solution = 17.5 mm - 0.225 mm = 17.275 mm

Finding the Mole Fraction of Water

Next, we need to calculate the mole fraction of water in the solution. Rearranging Raoult's Law gives us:

X_solvent = P_solution / P°_solvent

X_solvent = 17.275 mm / 17.5 mm ≈ 0.987

Calculating the Mole Fraction of the Solute

The mole fraction of the solute (X_solute) can be found using the relationship:

X_solute = 1 - X_solvent

X_solute = 1 - 0.987 = 0.013

Relating Mole Fraction to Moles

The mole fraction is defined as the ratio of the number of moles of solute (n_solute) to the total number of moles in the solution (n_solute + n_solvent). We can express this as:

X_solute = n_solute / (n_solute + n_solvent)

We also need to calculate the number of moles of water:

n_solvent = mass of solvent / molar mass of water

Using the molar mass of water (approximately 18 g/mol):

n_solvent = 100 g / 18 g/mol ≈ 5.56 moles

Setting Up the Equation

Now we can set up the equation using the mole fraction of the solute:

0.013 = n_solute / (n_solute + 5.56)

Cross-multiplying gives:

0.013(n_solute + 5.56) = n_solute

0.013n_solute + 0.07218 = n_solute

0.987n_solute = 0.07218

n_solute ≈ 0.07218 / 0.987 ≈ 0.0731 moles

Calculating the Molecular Mass of the Solute

Finally, we can find the molecular mass (M) of the solute using the formula:

M = mass of solute / n_solute

M = 25 g / 0.0731 moles ≈ 342.5 g/mol

Choosing the Closest Answer

Looking at the options provided (206, 302, 318, 216), none of them match exactly, but the closest value is 318 g/mol. Therefore, the molecular mass of the solute is approximately:

318 g/mol