If at #"71226 Pa"# of pressure, ethoxyethane boils at #25^@ "C"#, then what vapor pressure is needed to boil at #78^@ "C"# if across the temperature range we can assume that #DeltaH_"vap" = "29.1 kJ/mol"#?

#"418897 Pa"#, or #"4.13 atm"#.

Recall the Clausius-Clapeyron equation (at least the name):

#ln(P_2/P_1) = -(DeltaH_"vap")/(R)[1/T_2 - 1/T_1]#

where:

• #P# is the vapor pressure of the liquid at the particular temperature #T#.
• #DeltaH_"vap"# is the enthalpy for the vaporization process.
• #R = "8.314472 J/mol"cdot"K"# is the universal gas constant.

Basically, this equation describes how to determine vapor pressure at a new temperature. You were given the following info:

• #DeltaH_"vap" = "29.1 kJ/mol"#
• #P_1 = "71226 Pa"# at #T_1 = 25.0^@ "C"#
• #P_2 = ???# at #T_2 = 78.0^@" C"#

The #DeltaH_"vap"# was written as #DeltaH_"vap"^@# because #T_1# happened to be the same temperature as defined for standard thermodynamic temperature and pressure (#25^@ "C"# and #"1 atm"#, or sometimes #"1 bar"# in some newer texts).

Anyways, to calculate the new vapor pressure, we arbitrarily chose #P_1# for the given pressure and are to calculate #P_2#.

#P_2/P_1 = "exp"[-(DeltaH_"vap")/(R)[1/T_2 - 1/T_1]]#

#P_2 = P_1"exp"[-(DeltaH_"vap")/(R)[1/T_2 - 1/T_1]]#

where #"exp"("stuff")# is the function #e^("stuff")# to keep the equation from looking too small.

So, plug stuff in to get:

#color(blue)(P_2) = ("71226 Pa")"exp"[-(29.1 cancel"kJ/mol")/(0.008314472 cancel("kJ/mol")cdotcancel"K")[1/(78.0 + 273.15 cancel"K") - 1/(25.0 + 273.15 cancel"K")]]#

#=# #color(blue)("418897 Pa")#

That means the vapor pressure increased at a higher temperature.

This should make sense because a higher temperature implies a higher average kinetic energy, so the molecules at the surface of the solution can escape the solution more easily, increasing the vapor pressure above the solution.

In #"torr"# this would be #"3141.99 torr"#, which is about #"4.13 atm"#, so this is rather unusual. But it make sense because the boiling point of ethoxyethane is about #34^@ "C"#, and we're well past that.