The V.P. of pure water at 0 20 C is 17.5mm of Hg. A solution of sucrose is prepared by dissolving 68.4g of sucrose in 1000g of water. Calculate the V.P. of the solution.

To determine the vapor pressure of a sucrose solution, we can use Raoult's Law, which states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent. Let's break this down step by step.

Step 1: Calculate the Moles of Sucrose and Water

First, we need to find the number of moles of sucrose (C₁₂H₂₂O₁₁) and water (H₂O). The molar mass of sucrose is approximately 342 g/mol, and the molar mass of water is about 18 g/mol.

• Moles of Sucrose:

  Using the formula:

  Number of moles = mass (g) / molar mass (g/mol)

  Number of moles of sucrose = 68.4 g / 342 g/mol ≈ 0.200 moles

• Moles of Water:

  For 1000 g of water:

  Number of moles of water = 1000 g / 18 g/mol ≈ 55.56 moles

Step 2: Calculate the Mole Fraction of Water

The mole fraction (X) of a component in a solution is calculated as follows:

X_water = moles of water / (moles of water + moles of sucrose)

Substituting the values we calculated:

X_water = 55.56 / (55.56 + 0.200) ≈ 0.9996

Step 3: Apply Raoult's Law

Raoult's Law states:

P_solution = X_solvent × P_solvent

Where:

• P_solution is the vapor pressure of the solution.
• X_solvent is the mole fraction of the solvent (water in this case).
• P_solvent is the vapor pressure of the pure solvent (water at 20°C is 17.5 mm Hg).

Now substituting the values:

P_solution = 0.9996 × 17.5 mm Hg ≈ 17.5 mm Hg

Final Result

The vapor pressure of the sucrose solution is approximately 17.5 mm Hg. This indicates that the addition of sucrose has a minimal effect on the vapor pressure, which is typical for non-volatile solutes like sucrose.

In summary, by calculating the moles of solute and solvent, determining the mole fraction, and applying Raoult's Law, we can effectively find the vapor pressure of a solution. This method is widely applicable in various fields of chemistry, particularly in solutions and colligative properties.