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Physical Laboratory I CHEM 445 Experiment 6 Pressure of a Pure (Revised, 01/10/03)

The vapor pressure of a pure liquid is an intensive property of a compound. That is, the vapor pressure of a liquid is independent of the amounts of the two phases as long as both phases are present. This phenomenon is shown in many physical chemistry textbooks in plots of PV isotherms at temperatures below the critical temperature. The horizontal part of the P vs. V isotherm corresponds to the constant vapor pressure of the liquid. The vapor pressure of every liquid is a strongly increasing function of temperature and a very slightly increasing function of applied pressure.

The equation for the variation of vapor pressure of a liquid with temperature is derived in standard texts and often called the Clausius - Clapeyron equation. (Tinoco, Jr., Sauer, and Wang, Chap. 5; and Noggle, Chap.4). Reasonable approximations have been made to achieve this equation.

1  dP  ∆HVap   = (1) P  dT  RT 2

In Eq. (1), P is the vapor pressure of the liquid, T is the absolute temperature in K, and ∆HVap is the heat of of the liquid. The vapor pressure of a pure liquid is often represented by Eq. (2), the integrated form of Eq. (1) with the additional assumption that the heat of vaporization is independent of temperature. ∆H ln{P} = A − Vap (2) RT

Although the heat of vaporization of a liquid is not independent of temperature, Eq. (2) will give an accurate fit to vapor pressure data over a wide range of temperatures, as long as the temperature is well below the critical temperature. There are compensating errors in the approximations.

If very accurate data are obtained or if vapor pressures are obtained over a very wide range of temperatures, then the variation of heat of vaporization with temperature should be considered. The following equation is often used,

∆HVap = a′ − b′T (3) However, this equation does not fit the experimental temperature variation for the heat of variation near the critical point. Substituting Eq. (3) into equation Eq. (1) and integrating will give a more elaborate equation for vapor pressure as a function of temperature, in which the constants (either positive or negative) are obtained from a fit to the experimental data. This equation (Kirchoff equation) was proposed empirically many years ago to fit accurate vapor pressure data, a ln{p} = c + + bln{T} (4) T 2

For most systems and for analysis of your data, Eq. (2) is sufficient and ∆HVap is an average heat of vaporization over the temperature range.

From standard , ∆HVap/T is the of vaporization. It was observed experimentally and predicted theoretically that this quantity at the normal boiling point would be relatively constant for many non-associated at ~ 21 cal/molo or ~ 88 J/molo, Trouton’s Rule. [1] Consequently, one may estimate the temperature variation of vapor pressure of a liquid reasonably well near its normal boiling point, simply from the boiling point.

Experimental procedure

You will measure the vapor pressure of cyclohexane.

There are many ways of measuring the vapor pressures: in this experiment you will use an isoteniscope in a stirred water bath whose temperature you can change relatively easily. The ‘system’ is made up of a vacuum pump to reduce pressure, an ice/water cold trap to capture sample , a 3-way stopcock, an isoteniscope to contain your sample, a large empty jar (ballast tank) used to reduce the pressure fluctuations, and an open-end mercury manometer to measure system pressure. Additionally, a water bath, controllable heater, and a stirrer are provided to control temperature of the isoteniscope.

A digital thermometer is provided to measure the temperature. Read and record the temperature to ± 0.01 oC. The temperature will be changing slowly as you perform the experiments; so this accuracy is probably not justified, but record it anyway.

The 3-way stopcock controls pressure changes in the system. If open to the pump, pressure is reduced (performed initially to pump down the system, and to reduce pressure during cooling). If opened to atmosphere, pressure is increased in the system (performed during heating) and to shut down the system.

IMPORTANT: As you begin the experiment, check the bath temperature! It should be approximately the same as room temperature. If much warmer, remove some water and use ice to reduce bath to ~ room temperature.

Remove an isoteniscope from the drying oven in the adjacent lab and allow it to cool to room temperature.

Fill the vacuum pump cold trap container with ~ a 50:50 mixture if ice and water. If necessary, add more ice during the course of the experiment. Note that LOTS of ice will be needed later in the experiment, so this is a good time to stock up with several pans-full.

Put a few boiling chips into the bulb portion of the isoteniscope. {There is doubt whether the boiling chips are actually useful.} In the hood in the adjacent lab, fill the bulb portion ~ ¾- full with cyclohexane using a Pasteur pipette or the plastic squeeze bottle supplied. The exact amount of liquid is not critical. No fluid should be in the U-tube portion at present (a little is OK as long as the tube is not blocked). Slightly tricky manipulation of the isoteniscope is needed to get the liquid into the bulb. 3

Place the isoteniscope in the constant temperature bath at room temperature and attach the connecting hose to the vacuum system. Turn on the vacuum pump with the 3-way stopcock closed (perpendicular to the flow guarantees that the stopcock is closed).

Slowly turn the 3-way stopcock to the vacuum line (color coded) to reduce the pressure in the isoteniscope and the ballast tank. The liquid may boil (bubble) as the pressure is reduced. The liquid will vaporize even though visible boiling does not occur. You can tell from the sound level of the pump and from the changes in the manometer levels whether or not the vacuum pump is evacuating the system.

Continue pumping on the system for a few minutes. Close the stopcock and let the pressure equilibrate, and measure the pressure on the mercury manometer. Record the height of both sides of the manometer. This manometer is a differential manometer, recording the difference between the pressure of the ballast tank and atmosphere. The pressure in the ballast tank and, therefore, in the isoteniscope is equal to (atmospheric pressure) minus (difference in height of the two columns). The left side of the manometer (connected to the ballast bulb) is higher than the right side, which is open to the atmosphere; consequently, the vapor pressure of the liquid is less than atmospheric pressure. Obtain atmospheric pressure from the Hg barometer in the adjacent lab. (See your Lab Instructor if you need instructions about reading the barometer.)

Repeat a few times. Remember that when you evaporate a liquid quickly by reducing the pressure, the temperature of the liquid drops and several minutes are needed for the temperature of the liquid in the isoteniscope to equilibrate with the surrounding water bath.

When the pressure no longer changes on evacuating the chamber, the air has been evacuated from the system. Then tilt the bulb to let enough liquid into the U-tube portion of the isoteniscope to form a “plug”. You will need to remove the isoteniscope from the bath to perform this task. (Careful: don’t disconnect hose.) Record the heights of the two columns (± 1 mm) and bath temperature (± 0.01 oC). You need liquid in the U-tube of the isoteniscope to verify that the pressure in the isoteniscope and the pressure in the ballast tank are equal. The liquid in the U-tube should be at approximately the same level on both sides.

Heating Portion:

Settings on the variable voltage transformer are percentages of the total voltage available to send through the heater. They are not approximate temperature settings. Obtain pressure data at temperature intervals of ~ 5 oC. You do NOT need to achieve any particular temperatures. Don’t choose exact 5.00 oC intervals: such a choice makes others suspicious of the data. You simply need to know the temperature for a given pressure measurement. The temperature of the water bath and the sample will rise slowly while you are taking each pressure measurement and you make pressure measurement “on the fly”. Higher settings on the transformer are needed to obtain higher temperatures.

As the bath warms, you need to adjust pressure in the system by allowing small amounts of air to enter the system (ballast tank) through the 3-way stopcock as vapor pressure of the liquid increases with increasing temperature. As the bath heats, the objective is to allow small amounts of air into the apparatus through the 3-way stopcock to keep liquid levels approximately 4

equal in the isoteniscope U-tube. If levels in the U-tube are equal, the pressure above the liquid sample in the isoteniscope equals system pressure read at the manometer. No error results if bubbles of vapor come OUT of the isoteniscope while heating the sample. However, if air leaks into the isoteniscope because you have raised the pressure in the ballast tank too high, your experiment is invalid and must be repeated (after the air has been evacuated from the isoteniscope).

Vapor pressure measurements should be continued until system pressure roughly equals atmospheric pressure (Hg levels the same on both sides of the manometer). Don’t heat the liquid to cause vapor pressures beyond atmospheric as the system will probably leak.

Cooling Portion:

At the end of heating cycle, continue by obtaining (P, t) data as the temperature is reduced. Turn off the heater and add ice and/or cold water to the water bath. Remove water from the bath using the small beaker provided. LOTS of ice will be needed.

Using the vacuum pump, you must reduce pressure in the ballast tank as you cool the liquid. If you reduce the temperature too rapidly and bubbles go into the isoteniscope, the recorded pressures are not valid. Because of time limitations, you may not be able to reduce the temperature to the initial value, but you should get several points with decreasing temperatures. If you have done the experiment correctly, the pressures obtained with increasing and then with decreasing temperatures should fit well to a single curve.

If your data for decreasing temperatures do not match your data for increasing temperatures, you should obtain an additional set of data for P vs. T with increasing temperatures. Duplicate sets of measurements of P vs. T curves must be obtained and reported to ensure the reliability of your data.

Clean Up:

To end the experiment:

Turn the stopcock to atmosphere to bring the system to atmospheric pressure.

Switch off the vacuum pump. Switch off the stirrer. Switch off the transformer (heater) and reset to 0 (zero).

Remove the isoteniscope and empty its contents, including boiling chips, into the waste solvent container in the hood in the adjacent lab. Place the isoteniscope in the drying oven in the adjacent lab.

Open and inspect the vacuum pump cold trap: empty any condensate into the waste solvent container in the hood in the adjacent lab. Empty the ice/water container and reassemble the trap. If you cannot disassemble the trap, consult your Laboratory Instructor. Do NOT force disassembly!

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Pressure Correction:

For precise results, a correction should be applied to the pressure because the Hg in the manometer is not at 0 oC, as used in defining a standard atmosphere. Data for the corrections −4 from an early CRC Handbook can be represented by the equation, PCorr = PObs(1 – 1.72*10 *t), where t = room temperature in oC.

Calculations and Discussion:

Present your results in a table of vapor pressures, PObs; PCorr; ln{PCorr} or log{PCorr}; and temperature, both oC and K; and 1/T, K-1.

Use a spreadsheet or other data analysis program to analyze and plot your data.

o 1. Construct a plot of PCorr vs. T, either C or K. This is a non-linear plot from which interpolation and extrapolation are difficult. However, this plot will show irregularities in your data easily. After you have obtained an equation to fit your data (from below), plot PCorr vs. T from the equation to see how well your equation fits your primary data. Before the second week allowed for the experiment, plot your P vs. T data obtained from increasing the temperature and from decreasing the temperature on the same graph. If the two sets of data are inconsistent, repeat the experiment by increasing the temperature on another sample of cyclohexane. As noted above duplicate sets of data are required to ensure the reliability of the data. The vapor pressures of all liquids increase significantly with increasing temperature. If your data do not show a significant increase with increasing temperature, then you have either done the experiment incorrectly or have interpreted the data incorrectly.

2. Plot your data in the more common form as ln{PCorr} or log{PCorr} vs. 1/T, according to Eq. (2). Identify the points obtained with increasing temperature and decreasing temperature on your plot. (Use different shapes or colors for the points for the different experiments.) Obtain values for the two constants in this equation. Your program should give you uncertainties in the values for the two constants. If the experiment is done correctly and the data analyzed correctly, this plot should be a reasonably good straight line.

3. Use this equation to plot and compare calculated vapor pressures with experimental vapor pressures as requested in (1) above. In analyzing your data, you should look at the differences between the observed and calculated values for systematic variations. Plot the fractional difference between the observed and “fitted” data, {PCorr(Exp) – P(Calc)}/PCorr(Exp) } vs. T. Note any systematic variation.

4. As you do for all of the experiments, compare your results with literature values: for vapor pressures and for the heat of vaporization of cyclohexane. Give reference(s). Compare your values of ∆HVap/Tnbp with Trouton’s Rule values (given earlier in this experiment). Use your equation for ln{P} or log{P} vs 1/T to calculate the normal boiling point of cyclohexane. Compare your value with literature value(s). 6

Analyze the following set of data (Timmermans, Physico-Chemical Constants of Pure Organic Compounds, Elsevier, 1950), as you analyzed your data: plots of P vs. T, ln{P} or log{P} vs 1/T, {P(Exp) – P(Calc)}/P(Exp) } vs. T, nbp, ∆HVap. t, oC 20.59 23.27 26.89 31.00 35.19 39.08 44.28 P, mm Hg 77.3 87.7 103.6 124.7 149.4 175.9 217.2 t, oC 49.07 54.83 60.78 67.14 74.03 78.89 79.89 P, mm Hg 261.8 324.9 402.4 500.7 627.9 732.1 755.2

References 1. S. Glasstone, Textbook of Physical Chemistry, 2nd Ed., D. van Nostrand Co., New York, 1946.