Question

Determine the vapor pressure of a solution at 25 ⁰C that contains 76.6 g of glucose (C₆H₁₂O₆) in 250.0 mL of water. The vapor pressure of pure water at 25⁰C is 23.8 torr.

Answer 1

Concepts and reason

Colligative property:

It is a property that depends upon the mass of a solute present in a solution. It does not depend on the nature of the solute. Lowering vapor pressure, depression of freezing point and elevation of boiling point are the examples of colligative properties.

Vapor pressure:

Vapor pressure is defined as the pressure exerted by vapors above the liquid surface in equilibrium with liquid at that particular temperature. The vapor pressure of the solution is equal to the vapor pressure of the pure component in the solution multiplied by the mole fraction of that component in the solution.

Fundamentals

The relationship between the vapor pressure of the constituent of a solution and the mole fraction of the constituent (solute) is given by Raoult’s Law.

or

Here,

The vapor pressure of a solution is .

The vapor pressure of pure solvent is .

The mole fraction of solute is .

The mole fraction of solvent is .

The mole fraction of a solute is defined as the number of moles of the component (solute) divided by the total number of moles of all the components (solvent and solute) in the solution.

• Mathematically, it can be expressed as follows.

The density of a substance is the mass of the substance per unit volume. Density is denoted by the symbol .

The given information in the problem is written down.

The given vapor pressure of pure water at is .

The given mass of glucose is .

The given volume of water is .

The density of water is . The mass of water is calculated by the density equation as follows.

Substitute for and for .

The mass of water is obtained to be .

The moles of glucose and water can be calculated as follows.

So, the number of moles of glucose is .

Thus, the number of moles of water is .

Use the below equation to calculate the mole fraction of glucose.

Substitute as follows.

Therefore, the mole fraction of glucose is .

The calculated mole fraction of glucose is .

The given vapor pressure of pure water at is .

Use the below expression to find the vapor pressure of the solution as follows.

Substitute for and for .

Hence, the vapor pressure of the solution is .

Ans:

The vapor pressure of the given solution at is .