Question

Calculate the vapor pressure of a solution of 0.99 mol of cholesterol in 5.4 mol of toluene at 32°c. pure toluene has a vapor pressure of 41 torr at 32°c. (assume ideal behavior.)

Answer 1

Step-by-step explanation:

No. of moles of cholesterol solute,
`n_(1)` = 0.99 mol

No. of moles of toulene solvent,
`n_(2)` = 5.4 mol

Hence, total number of moles of solution will be as follows.

n =
`n_(1) + n_(2)`

= 0.99 mol + 5.4 mol

= 6.39 mol

Therefore, mole fraction of cholestrol solute (
`\chi_(1)`) is as follows.

=
`\frac{\text{no. of moles of chloesterol}}{\text{Total number of moles of solution (n)}}`

`\chi_(1)` =
`(0.99 mol)/(6.39 mol)`

= 0.154

Vapor pressure of pure toulene solvent (
`p^(o)`) = 41 torr

Vapor pressure of solution = P

Hence, formula to calculate relative lowering of vapor pressure is as follows.

Relative lowering of vapor pressure =
`(p^(o) - P)/(p^(o))`

As per relative lowering of vapor pressure colligative property, the relative lowering of vapor pressure is equal to the mole fraction of solute.

Hence,
`(p^(o) - P)/(p^(o))` =
`\chi_(1)`

`(41 torr - P)/(41 torr)` = 0.154

41 torr - P = 6.314

P = 34.686 torr

or, = 35 torr

Therefore, we can conclude that vapor pressure of the solution is 35 torr.