Question

Question #73593

Answer 1

The Clausius-Clapeyron equation relates the vapor pressures of a liquid at two temperatures along with the enthalpy of vaporisation of liquid as follows.

`color(blue)(ln(P_2/P_1)=(DeltaH_"vap")/R(1/T_1-1/T_2))`

where

`DeltaH_"vap"->"Enthalpy of vaporisation"`

`P_1->"Vapor preessure at "T_1K`

`P_2->"Vapor preessure at "T_2K`

`R->"Universal gas constant"`

In our problem for ether we have been given

`T_1=(-22.8+273)K=250.2K`

`T_2=(25+273)K=298K`

`P_1=57.0mm`

`P_2=534mm`

`R=8.314JK^-1mol^-1`

Inserting these in the equation

`color(green)(ln(P_2/P_1)=(DeltaH_"vap")/R(1/T_1-1/T_2))`

`=>color(blue)(ln(534/57)=(DeltaH_"vap")/8.314(1/250.2-1/298))`

`=>DeltaH_"vap"=(298xx250.2xx8.314)/47.8ln(534/57)Jmol^-1`

`~~29.0kJ`