Calculation of Mass of Non-Volatile Solute

To calculate the mass of a non-volatile solute that should be dissolved in octane to reduce its vapor pressure to 80%, we need to use Raoult's law. Raoult's law states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution.

Given Data:
- Mass of solute (non-volatile) = 40 g
- Mass of octane = 114 g
- Vapor pressure reduction required = 80%

Step 1: Calculate the mole fraction of octane
The mole fraction of a component in a solution is given by the ratio of moles of that component to the total moles of all components in the solution.

First, we need to calculate the number of moles of octane:
Number of moles of octane = Mass of octane / Molar mass of octane

The molar mass of octane (C8H18) can be calculated as follows:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.008 g/mol
Molar mass of octane = (8 * Molar mass of C) + (18 * Molar mass of H)

Now, we can calculate the mole fraction of octane:
Mole fraction of octane = Moles of octane / (Moles of octane + Moles of solute)

Step 2: Apply Raoult's law to calculate the vapor pressure of octane
According to Raoult's law, the vapor pressure of octane above the solution can be calculated using the mole fraction of octane:

Vapor pressure of octane = Mole fraction of octane * Vapor pressure of pure octane

Step 3: Calculate the reduced vapor pressure
The reduced vapor pressure is given as 80% of the vapor pressure of pure octane. Therefore, we can calculate the reduced vapor pressure as follows:

Reduced vapor pressure = 80% * Vapor pressure of pure octane

Step 4: Calculate the mole fraction of solute
The mole fraction of solute can be calculated as follows:

Mole fraction of solute = 1 - Mole fraction of octane

Step 5: Calculate the moles of solute
Moles of solute = Mole fraction of solute * Total moles of solution

Step 6: Calculate the mass of solute
Mass of solute = Moles of solute * Molar mass of solute

Therefore, by following these steps, we can calculate the mass of the non-volatile solute that should be dissolved in octane to reduce its vapor pressure to 80%.