Calculate the mass of non-volatile solute having molar mass of 40g/mol,which should be dissolved in 114g octane to reduce its vapour pressure to 80%.

To tackle the problem of calculating the mass of a non-volatile solute needed to reduce the vapor pressure of octane to 80%, we can utilize Raoult's Law. This law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in that solution. Let’s break down the calculation step by step.

Understanding the Components

In this scenario, we know the following:

• Molar mass of the solute: 40 g/mol
• Mass of octane: 114 g
• Vapor pressure reduction: From 100% to 80%

First, let's figure out the initial vapor pressure of pure octane. For simplification, we can assume that the vapor pressure of pure octane (P₀) is 100 mmHg. Therefore, reducing the vapor pressure to 80% means the new vapor pressure (P_solution) is 80 mmHg.

Applying Raoult's Law

According to Raoult's Law:

P_solution = X_octane * P₀

Where:

• X_octane is the mole fraction of octane in the solution.
• P₀ is the vapor pressure of pure octane.

Rearranging the equation to find the mole fraction of octane gives us:

X_octane = P_solution / P₀

Substituting the values:

X_octane = 80 mmHg / 100 mmHg = 0.8

Calculating the Mole Fraction of Solute

Since the mole fractions must add up to 1, we can find the mole fraction of the solute (X_solute):

X_solute = 1 - X_octane = 1 - 0.8 = 0.2

Finding Moles of Octane

Now, we need to calculate how many moles of octane we have. The molar mass of octane (C₈H₁₈) is approximately 114 g/mol.

Calculating moles of octane:

moles of octane = mass of octane / molar mass of octane

moles of octane = 114 g / 114 g/mol = 1 mol

Determining Moles of Solute

Using the mole fraction of the solute, we can find the moles of solute required:

X_solute = moles of solute / (moles of solute + moles of octane)

Let n be the moles of solute:

0.2 = n / (n + 1)

Cross-multiplying gives:

0.2(n + 1) = n

0.2n + 0.2 = n

0.8n = 0.2

n = 0.25 moles of solute.

Calculating the Mass of Solute

Finally, to find the mass of the solute, we can use the formula:

mass = moles × molar mass

mass of solute = 0.25 moles × 40 g/mol = 10 g.

Final Thoughts

In summary, to reduce the vapor pressure of 114 g of octane to 80%, you would need to dissolve 10 g of the non-volatile solute with a molar mass of 40 g/mol. This process showcases the practical application of Raoult's Law and the relationship between vapor pressure and mole fractions in solution chemistry.