In this experiment the vapor pressure of a liquid is measured at several temperatures. The enthalpy of vaporization is calculated using the Clausius-Clapeyron equation.

Vacuum system consisting of pump, ballast tank, open arm mercury manometer, and connections (L); isoteniscope (S); Pressure and temperature sensor with serial box (S); two liter beaker (S); magnetic stirrer-hot plate combination (S), Temperature probe (S), Pressure probe (S), Probe manuals (M).

100 ml toluene (S); 100 ml of an UNKNOWN liquid (S); about 100 ml rinsing acetone.

The isoteniscope method is used[3]. This apparatus measures the vapor pressure of a liquid sample directly (see figure 1). The sample is contained in the glass bulb and in the U-tube portion of the isoteniscope. The sample in the U-tube serves as a differential manometer; when the two levels are equal, the pressures on both sides of the U-tube are the same. As the vapor pressure of the liquid sample rises, air is admitted by means of the auxiliary apparatus to equalize the pressure, and this pressure of air can be read using the a pressure sensor (or manometer) and the pressure inside the isoteniscope is equal to the pressure read by the sensor.

Figure 1. Picture of an isoteniscope.

Figure 2. Apparatus for the determination of the vapor pressure of a liquid.

All joints must be air-tight. The 3-way stopcock leading to the pump serves two purposes. It provides a means of cutting the pump out of the system once the line is evacuated and acts as an air inlet. Figure 3 shows the evacuating and shut off positions of this stopcock. Also shown is the position of the stopcock for letting air into the system. ALWAYS USE TWO HANDS TO TURN STOPCOCKS. HOLD THE BARREL OF STOPCOCK WITH ONE HAND AND ROTATE THE PLUG WITH THE OTHER.

Air Air Air

System System System

Pump Pump Pump

Evacuate system air to system air to pump

Figure 3. Display of three way stop cock, F.

The pressure sensor should be connected to the system as shown in Figure 2, the temperature sensors placed in the water bath, and the serial box set up with the pressure sensor in Port 1 and the temperature sensor in Port 2. The Sensor choice from the "Set up" menu will allow the Port 1 and Port 2 to be activated as a pressure-pressure probe and direct temperate probe respectively.

Check the system for leaks as follows. Connect the empty isoteniscope to the appropriate hose, open the stopcock leading to the manometer and to the pressure sensor, close the stopcock to the air and turn the stopcock near the pump to the evacuating position. Turn on vacuum pump and evacuate the system. Turn the three way stopcock to let air into the pump, then immediately turn off the pump. The line pressure as indicated by the pressure sensor should remain constant. If it does not, consult instructor. Then calibrate the pressure sensor using the calibration procedure in the experiment menu. Calculate the pressure in the system by subtracting the manometer pressure from the baromentric pressure. Since the bore of the manometer tube may not be uniform, the position of the mercury in both arms of the manometer should be read and recorded. The "Keep" command box will appear on the screen and can be used to store one point of the two point calibration. Now open the three way stopcock to let around 40 cm of air pressure into the system and again use the "Keep" command to store the second point of the calibration. Again, the pressure inside the system is the barometric pressure minus the manometer pressure. The temperature sensor can be calibrated in the same manor using ice water and boiling water.

In the "Set up" menu, "Data Collection" command can be used to set "sampling (Rate)" to sample with "event entry". That means when you excite a "collect data" command using the mouse, type in a 1, 2 ,3 ... etc. as the event marker, to collect temperature and pressure data for the same time event. Then the vapor pressure at particular temperatures can be recorded.

Rinse the isoteniscope with a little acetone; shake out the excess and place in the oven to dry. To fill the isoteniscope while it is still warm, place the open end of the isoteniscope under the surface of the liquid, which will be sucked in as the bulb cools. Fill the bulb about two-thirds full and be sure that there is sufficient liquid in the U-tube to serve as a differential manometer.

Adjust the temperature of the H2O bath to a starting temperature in the range of 10 -15oC; use ice if necessary. Assemble the system with sample. Open stopcock H and turn F to the evacuation position. Turn pump on and reduce pressure in the line until the sample begins to bubble out of the isoteniscope to sweep air out of the sample and U-tube. THIS IS THE MOST IMPORTANT STEP.

Care must be taken not to vaporize too much of the liquid from the U-tube portion of the isoteniscope. The evaporation can be minimized by using the three way stopcock to control the rate of evacuation during the degassing process. Partial misalignment of the bore slows down the evacuation process. Once the bubbling of the air through the U-tube begins, the bore can be completely misaligned; this has the effect of cutting the vacuum pump out of the line while at the same time air bubbles continue to sweep through the U-tube. As long as there is a steady stream of bubbles through the sample in the U-tube, degasification is not complete. You must continue to carefully evacuate the system, adjusting the three way stopcock as required, until there is a noticeable intermittent delay in the sweeping of the bubbles through the U-tube. Once degassification is complete, turn stopcock clockwise to the shut off position for the vacuum (CAUTION: Do not shut off pump while it is still under vacuum!). Immediately, but carefully equalize the pressure on both sides of the inverted U-tube by letting air in through stopcock F. The adjustment must be made cautiously to prevent air from bubbling back through the U-tube. If this does happen, the air must be boiled out again. Record the temperature of the bath and the pressure when the differential manometer indicates no difference in pressure. The manometer should be used to check the pressure sensor several times during the experiment. Tap the manometer with a pencil frequently to keep the mercury from sticking. Increase the temperature of the bath by a suitable amount, and repeat the determination of the vapor pressure.

The temperature of the bath should be kept practically constant for several minutes before each reading; for if it is changing rapidly, the temperature of the liquid in the isoteniscope will lag behind, and introduce an appreciable error.

Heat the liquid sample slowly up to about 60oC. Take readings at close enough intervals to give a good graph, allowing time for temperature equilibrium. A reading about every 5^o is sufficient. Heat exchange is rapid and a complete run can be made in about 90 minutes. Keep the pressure at equilibrium by slowly letting air in through stopcock F, using the controlled pressurization position as illustrated in Figure 3, as the temperature increases. This avoids boiling away your sample. Again, care must be taken when equalizing the pressure, not to bubble air back through the U-tube portion of the isoteniscope. If this should occur, stop the run and start anew. Read and record the barometric pressure at the beginning and end of each series of measurements.

Adjust the H2O bath to a starting temperature of 10 -15oC and make a second run with toluene. During the second lab period make duplicate runs on an unknown liquid. Required minimum is two runs for toluene, and two runs of the unknown. Time permitting, a third run of toluene and/or the unknown is desirable

Since an open end manometer is used, the pressure in the line is equal to the difference between the observed pressure and the corrected barometric pressure.

P_o,P = corrected and observed pressure

t = temperature of manometer

t_s = temperature at which scale was calibrated, normally 0 ^oC.

(181.8 x 10^-6)

THEORY. When the temperature is raised, the vapor pressure of a liquid increases, because more molecules gain sufficient kinetic energy to break away from the surface of the liquid. When the vapor pressure becomes equal to the pressure of the gas space, the liquid boils. The temperature at which the vapor pressure reaches 760 mm Hg is the standard boiling point.

According to the Clapeyron equation, the temperature coefficient of the vapor pressure of a liquid is given by

V_v, V_l = molar volumes of vapor and liquid

The volume factor in the Clapeyron equation may be written

where Z is the compressibility factor for the vapor. The expression on the right is introduced in the Clapeyron equation, which can then be rearranged to yield

or, approximately,

CALCULATIONS. Two types of graphs are plotted. In one the vapor pressures are plotted against the temperatures, and in the second the logarithms of the vapor pressures are plotted against the reciprocals of the absolute temperatures. Values taken from the literature are plotted also.

The values of the constants A and B in the equation

ln P = A/T +B (6)

are determined by two methods.

First, the best straight line is drawn through the points by eye, and the constants A and B are calculated for this straight line. This may be done by using two points on the line which are far apart and solving the two simultaneous equations for A and B. Alternatively, the slope A may be calculated, and then B calculated, using ln P at some particular temperature. Second, more objective values of A and B can be calculated by the method of least squares using a spread sheet such as Lotus or Excel.

The assumptions made in the derivation of the Clausius-Clapeyron equation limit the accuracy of the heats of vaporization calculated in this way.

Better values may be calculated using Eq. (4). The compressibility factor may be obtained directly from PVT data for the compound under study if they are available. When PVT data are not available, the compressibility factor may be estimated using the Berthelot equation, which may be written

where T_c = critical temperature

P_c = critical pressure

The compressibility factor is calculated for a particular point on the vapor-pressure curve, and the slope of the plot of ln P versus 1/ T at that point is used. The ideal gas law is used to calculate V_v in the factor 1 - V_l/V_v.

It should also be noted that an excellent correlation of vapor-pressure-

temperature data may be obtained by use of the Antoine equation:[5]

log P = -A/(t+C) + B

where A, B, C = constants empirically determined from experimental data

t = temperature, °C

Practical applications. Vapor-pressure measurements are important in all distillation problems and in the calculation of certain other physical properties. They are used in the correction of boiling points and in the recovery of solvents. The concentration of vapor in a gas space may be regulated nicely by controlling the temperature of the evaporating liquid. Humidity conditions, which are so important in many manufacturing processes, depend largely on the vapor pressure of water.

Suggestion for further work. The vapor pressures of other liquids may be determined, using, if possible, liquids whose vapor pressures have not yet been recorded in tables. The sublimation temperature of a solid may be obtained by covering the thermometer bulb with a thin layer of the solid.

The vapor pressure may be determined by an entirely different method, evaluating the amount of liquid evaporated by a measured volume of air.

References

1. G. W. Thomson in A. Weissberger (ed.), "Technique of Organic Chemistry," vol. 1, "Physical Methods of Organic Chemistry," 3d ed., pt. 1, chap. 9, Interscience Publishers, Ine., New York, 1959.

2. C. B. Willingham, W. J. Taylor, J. M. Pignocco, and F. D. Rossini, J. Res. Natl. Bur. Std. U.S., 35:219 (1945).