The Vapor Pressure of a Pure Liquid

							Chemistry 361                                                                           JMS 9/04
Fall 2009                                                                               DLC 9/2008

                           The Vapor Pressure of a Pure Liquid

SECTION 1: INTRODUCTION

The boiling point of a liquid is defined as the temperature at which the vapor pressure becomes equal
to the external pressure above the surface of the liquid. In a closed system there is an equilibration
between the liquid and the gas phases. The boiling point of a liquid is directly proportional to the
applied pressure above the liquid. In this experiment you will determine the dependence of the
boiling point of a liquid with pressure and will obtain the molar enthalpy of vaporization.

SECTION 2: THEORETICAL BACKGROUND

The boiling point of a liquid is the temperature at which the gas and liquid phase of a substance are at
equilibrium. This temperature is directly dependent of the external pressure above the liquid. For
example, the boiling point of water at sea level (P = 1.0 atm) is 100.0 oC, but it decreases if the
pressure is lowered (for instance, at increased altitude).

For any chemical system, the Gibbs phase rule (Eq. (1)) allows us to establish how many
independent variables are required to describe the system thermodynamically. These variables are
also called the degrees of freedom (F) of the system. These are related to the number of components
in the system (C) and the number of phases present (Φ):

                                      F=C–Φ+2                  (1)

For a pure liquid (one component) that is in equilibrium with its vapor (2 phases), the phase rule tell
us that F = 1 – 2 + 2 = 1. That is, that there is only one independent variable is required to describe
the system. In other words, that at equilibrium the vapor pressure of the liquid is dependent on the
temperature, or vice versa.
Such dependence is stated thermodynamically by the Clapeyron equation:

                                       dP   ∆H vap
                                          =                    (2)
                                       dT T∆Vvap

where ∆H vap is the molar enthalpy of vaporization and ∆Vvap is the difference between the molar
volumes of the vapor and the liquid. Since the molar volume of a gas is much larger than the molar
volume of a liquid, then the difference in molar volumes can be approximated, to good accuracy, as
the molar volume of the gas:

                                   ∆Vvap = Vgas − Vliquid ≈ Vgas     (3)

Such an approximation applied to Eq. (2) leads to the Clausius-Clapeyron equation:
CHE361 – Vapor Pressure of a Liquid                                                                        2


                                    dlnP     ∆H vap
                                          =−                       (4)
                                   d(1/T)     RZ

In this equation, R is the gas constant, and Z is the compressibility factor of the gas. The integrated
form of Eq. (4) is:

                                             ∆H vap 1
                                   lnP = −            +C           (5)
                                              RZ T

where C is an arbitrary constant of integration. It is straightforward to see that a plot of lnP vs. 1/T
                                                    ∆H vap
should yield a straight line with slope equal to −          . Equation (5) assumes that the temperature
                                                      RZ
dependence of the molar heat of vaporization can be ignored.

In this experiment, the vapor pressure and boiling temperature dependence of a pure liquid will be
studied using the boiling point method. A liquid is placed in a flask in a closed system in which the
pressure above the liquid can be adjusted by a combination of the use of a vacuum pump and
addition of air from the surroundings. The liquid is heated until the vapor pressure is equal to the
applied pressure. At this point equilibrium is established and the liquid boils. The temperature and
pressure will be recorded. A reflux condenser keeps the system closed by preventing the vapor from
escaping and returning it to the flask as a liquid.

SECTION 3: EXPERIMENTAL PROCEDURE
You will be using a glass vacuum line. When utilizing a vacuum line, please remember the following
safety recommendations:

A. Wear safety glasses all the time, and make sure that all your neighbors are also wearing their
safety glasses
B. Do not turn off the vacuum pump when you are done with the experiment.
C. Avoid pumping excessive amounts of air through the cold trap. Oxygen may accumulate in the
trap and combust.
D. Make sure to support glass pieces until they are clamped or held by vacuum.

Description of the Apparatus
A glass vacuum line is connected to the boiling flask, which is fitted with a condenser, thermometer,
heater and magnetic stirrer. Stopcock valves in the line allow adjustment of the line pressure either
by evacuation using a vacuum pump, or pressurization with a leak valve. A ballast bulb on the line
facilitates small adjustments of the pressure by providing a large dead volume. A baratron gauge
attached to the line monitors the pressure in the line. Make a detailed sketch of the apparatus when
the experiment is performed to include in your lab report.

Procedure
Your instructor will provide you with the liquid to be studied and instruct you on the operation of the
apparatus. Make sure that water is running through the condenser.

    1. With the system completely closed, turn on the magnetic stirrer and apply vacuum to the
       liquid to degas.
CHE361 – Vapor Pressure of a Liquid                                                                   3



   2. Adjust the pressure above the liquid to be between 60 and 90 torr. Then, apply a small
      amount of heat until boiling is established. Record the temperature and pressure when a
      steady boil is reached. A stream of liquid dripping from the thermometer characterizes a
      steady boil. Be careful not to increase the temperature too quickly. The heater is controlled
      by a Variac transformer, which would allow you to control the temperature rather well.

   3. Increase the pressure in the line a little at a time and adjust the temperature of the heater to
      reach boiling. The pressure is increased by allowing a small amount of air to leak into the line
      via a valve. It is recommended to increase the pressure in steps of 20 torr at low pressures
      and in steps of about 150 torr at larger pressures. Proceed until the pressure is about 700 torr.
      Finally, open the system to atmospheric pressure and record the boiling temperature at that
      pressure. You should have several (at least 8 to 10) P vs. T measurements at the end of the
      run.

   4. Make a second run by reducing the pressure from atmospheric pressure to the starting
      pressure of 60-90 torr. Use approximately the same stepping criteria used in step 3. Collect 8
      to 10 pressure vs. boiling temperatures as the pressure is reduced.


SECTION 4: A GUIDE TO THE CALCULATIONS

Simply make a plot of lnP vs. 1/T for all the points from both runs (ascending and descending
pressure). Use a linear regression analysis to obtain the slope and intercept as well as their
uncertainties. ∆H vap is obtained from the slope of the plot according to Eq. (5). Notice that you need
                                                            PV
to determine the value of Z for the vapor. Recall that Z =      . You can estimate Z by finding out the
                                                             RT
molar volume of the compound in the gas phase at the normal boiling temperature (P = 1.0 atm). If
you provide another estimate of Z, this must be justified reasonably.
The normal point of the liquid (i.e. at P = 1.0 atm) is obtained from the equation of the line you
obtained from the linear regression analysis. Make sure you also calculate the uncertainties
associated to these results.

SECTION 5: ITEMS TO INCLUDE IN YOUR LABORATORY REPORT

Data
Include a sketch of the apparatus.
Rather than presenting a table with your data, present them in a graphical way. Plot P (y-axis) vs. T
(x-axis). Distinguish between the measurements made from ascending and descending pressure
readings by using different symbols (or colors) for the point labels. Draw a smooth curve through the
each set of points.

Results
You must include a plot of lnP vs 1/T in which all the points are included to obtain a single line.
Report the slope, intercept, and their uncertainties obtained from the linear regression analysis.
Report the value of Z used in the determination of ∆H vap . Finally, report your experimental ∆H vap
and normal boiling point with their respective uncertainties. Remember to use the 3 and 30 rule.
CHE361 – Vapor Pressure of a Liquid                                                                   4


Because there is a small temperature dependence in ∆H vap , the reported value is considered to
be at the midpoint of the temperature range that you studied experimentally. Report the
temperature corresponding to that midpoint when reporting ∆H vap .

Discussion and Conclusion
Compare the enthalpy of vaporization you obtained with a value obtained from the literature. Discuss
any difference you may find. Remember to report the temperature at which the literature value was
obtained. If the temperature of the experimental value is different than the experimental one, how
large is the temperature dependence of ∆H vap ?
Compare your experimental normal boiling point with the literature value. Discuss about any
differences you find.
As always, discuss potential sources of error and how these may affect you reported results.
These are some questions that may also help you in rationalizing your discussion:

     -   Use the barometric pressure equation, or the national weather service to obtain the
         atmospheric pressure in Denver, CO (1 mile altitude). Estimate the boiling temperature of
         the liquid you studied in Denver (using the trend line equation you obtained). Discuss the
         effect of altitude in boiling point. What would be expected in Mt. Everest?
     -   One may use Z ≈ 1 as an ideal gas approximation when estimating ∆H vap . Is this a
         justifiable assumption?
     -   How would impurities affect your results?

Treatment of Data
You must show a sample for the calculation of both ∆H vap and the normal boiling point of the
liquid. Also show a sample calculation of the boiling point of the liquid in Denver. Make sure ALL
steps are included.
You must also show a sample calculation of the propagation of error analysis on calculating the
uncertainty on all results.