Question #f7a41

1 Answer
Apr 28, 2016

Answer:

The temperature dependence of vapor pressure, or any other equilibrium constant, depends on the #Delta H# for that process, but we also need a reference point, which is the normal boiling point of water.

Explanation:

The ratio of vapor pressures at two different temperatures, #T_1# and #T_2# can be calculated approximately from the relation

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

Using #T_1 = 373.15 K# (100 C), #P_1 = 1# atm,
and #T_2 = 310.15 K# (37 C)

#ln((P_2)/1) = (40700 J/(mol))/(8.314 J/(mol-K)) (1/(373.15 K)-1/(310.15 K)) = -2.66#

#P_2 = e^(-2.66)# atm = 0.0696 atm = 53.2 torr

The first equation ignores the (slight) temperature dependence of #DeltaH_(vap)#, but the true vapor pressure is only slightly less: 47.1 torr.