At 80 degrees Celsius, the vapor pressure of pure liquids x, y and z are 385, 190 and 66 mm Hg. what pressure must be exerted on the surface of the solution containing one mole of x, three moles of y, and two moles of z for the boiling point to begin at 80 degrees Celsius?

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To calculate the pressure required for the boiling point to begin at 80 degrees Celsius, we need to find the total vapor pressure of the solution.

The total vapor pressure of the solution can be calculated using Raoult's law, which states that the vapor pressure of a component in the solution is proportional to its mole fraction. The mole fraction (x) of a component can be calculated by dividing the number of moles of that component by the total number of moles of all components.

Given:
Vapor pressure of x (Px) = 385 mm Hg
Vapor pressure of y (Py) = 190 mm Hg
Vapor pressure of z (Pz) = 66 mm Hg
Number of moles of x (nx) = 1 mole
Number of moles of y (ny) = 3 moles
Number of moles of z (nz) = 2 moles

Step 1: Calculate the mole fraction of each component.
Mole fraction of x (Cx) = nx / (nx + ny + nz)
= 1 / (1 + 3 + 2)
= 1 / 6
= 0.1667

Mole fraction of y (Cy) = ny / (nx + ny + nz)
= 3 / 6
= 0.5

Mole fraction of z (Cz) = nz / (nx + ny + nz)
= 2 / 6
= 0.3333

Step 2: Calculate the partial pressure of each component.
Partial pressure of x (Px') = Px * Cx
= 385 mm Hg * 0.1667
= 64.166 mm Hg

Partial pressure of y (Py') = Py * Cy
= 190 mm Hg * 0.5
= 95 mm Hg

Partial pressure of z (Pz') = Pz * Cz
= 66 mm Hg * 0.3333
= 22 mm Hg

Step 3: Calculate the total vapor pressure of the solution.
Total vapor pressure (Ptotal) = Px' + Py' + Pz'

Therefore,
Ptotal = 64.166 mm Hg + 95 mm Hg + 22 mm Hg
= 181.166 mm Hg

So, the pressure that must be exerted on the surface of the solution for the boiling point to begin at 80 degrees Celsius is 181.166 mm Hg.

To determine the pressure required for the boiling point of the solution to begin at 80 degrees Celsius, we need to use Raoult's Law. Raoult's Law states that the vapor pressure of a component in a solution is directly proportional to its mole fraction.

First, we need to calculate the mole fraction of each component in the solution. The mole fraction (denoted by the symbol X) is the ratio of moles of a specific component to the total number of moles.

Given:
- One mole of x
- Three moles of y
- Two moles of z

Total moles in the solution = 1 + 3 + 2 = 6 moles

Now, we can calculate the mole fraction for each component:

Mole fraction of x = (moles of x) / (total moles) = 1 / 6
Mole fraction of y = (moles of y) / (total moles) = 3 / 6 = 1 / 2
Mole fraction of z = (moles of z) / (total moles) = 2 / 6 = 1 / 3

Next, we need to determine the partial pressure of each component using Raoult's Law. The partial pressure (denoted by P) is calculated by multiplying the mole fraction of a component by its vapor pressure at that temperature.

Partial pressure of x = (mole fraction of x) * (vapor pressure of x at 80 degrees Celsius) = (1 / 6) * 385 mm Hg
Partial pressure of y = (mole fraction of y) * (vapor pressure of y at 80 degrees Celsius) = (1 / 2) * 190 mm Hg
Partial pressure of z = (mole fraction of z) * (vapor pressure of z at 80 degrees Celsius) = (1 / 3) * 66 mm Hg

Now, we can calculate the total pressure required for the boiling point to begin at 80 degrees Celsius by summing up the partial pressures of each component:

Total pressure = Partial pressure of x + Partial pressure of y + Partial pressure of z

Total pressure = [(1 / 6) * 385 mm Hg] + [(1 / 2) * 190 mm Hg] + [(1 / 3) * 66 mm Hg]

After performing the calculations, you can determine the pressure required for the boiling point to begin at 80 degrees Celsius.