Tip:
Highlight text to annotate it
X
In this problem we are given the Antoine equation for benzene where is is the log of the saturation
pressure as a function of temperature where temperature is in degrees Celsius and pressure
is in Torr. We want to estimate from this information what is the heat of vaporization
of benzene at 60 degrees C. What we are going to do is take advantage of the Clausius - Clapeyron
equation and we want to know a couple of things. This is a natural log where as the equation
for the Antoine equation is base 10. This is absolute temperature and we will use Kelvin.
Then this is a constant. What we want is the slope of the natural log of the saturation
pressure vs. the inverse of the absolute temperature because that plot should be a straight line
if delta H is not a function of temperature. What we are going to do is assume over a narrow
range that delta H is not a function of temperature. If we assume this what we are going to do
is use the Antoine equation to calculate the values of the saturation pressure. What we
are going to do is calculate the saturation pressure at 55 Centigrade and 65 Centigrade
and assume over that narrow of a temperature range we are going to get a pretty good estimate
if we just take the slope to fit the Clausius Clapeyron equation. We will calculate these
values. We have substituted in 55 Centigrade and 65 Centigrade into the Antoine equation
here. We are going to calculate first the log to base 10 and then calculate the actual
saturation pressure. That is these values. These are from the Antoine equation. We then
take the log of these values to get this and we calculate also the temperature. We take
273.2 add it to 55 and take the inverse. That is where we get this number. Same thing for
65. Now the heat of vaporization divided by R, the negative of that, should be the slope
of this line for these data point. So minus the heat of vaporization divided by the natural
gas constant. That is going to be the slope and delta log of Psat, delta 1 over absolute
temperature. We are just going to take the values from the table and substitute in here.
So I have substituted in the values here using a gas constant value of 8.314 so we end up
with heat of vaporization in J/mol. The Kelvin cancel. We have calculated the heat of vaporization
for benzene at 60 degrees, 32.3 kJ/mol. This is at 60 degree C for the heat of vaporization
of benzene.