Question

Calculate the vapor pressure (in torr) at 298 K in a solution prepared by dissolving 38.5 g of the non-volatile non-electrolye urea {CO(NH2)2} in 142 g of methanol. The vapor pressure of methanol at 298 K is 122.7 torr. Give your answer to 2 decimal places.

Answer 1

Answer: The vapor pressure of methanol solution at 298K is 107.12 torr

Step-by-step explanation:

As the relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.

The formula for relative lowering of vapor pressure will be,

`(p^o-p_s)/(p^o)=i* x_2`

where,

`(p^o-p_s)/(p^o)`= relative lowering in vapor pressure

i = Van'T Hoff factor = 1 (for non electrolytes)

`x_2` = mole fraction of solute =
`\frac{\text {moles of solute}}{\text {total moles}}`

Given : 38.5 g of urea is present in 142 g of methanol

moles of solute (urea) =
`\frac{\text{Given mass}}{\text {Molar mass}}=(38.5g)/(60g/mol)=0.64moles`

moles of solvent (methanol) =
`\frac{\text{Given mass}}{\text {Molar mass}}=(142g)/(32g/mol)=4.4moles`

Total moles = moles of solute + moles of solvent = 0.64 + 4.4 = 5.04

`x_2` = mole fraction of solute =
`(0.64)/(5.04)=0.127`

`(122.7-p_s)/(122.7)=1* 0.127`

`p_s=107.12torr`

Thus the vapor pressure of methanol solution at 298K is 107.12 torr