Some suggested reading: Brown, LeMay p 456 (especially the stuff about the Clausius-Clapeyron equation)

Your raw data will consist of temperatures and their corresponding volumes; you will heat the water
bath to ~80^{o}C, and read a volume/temperature pair at about 5^{o}C intervals to 50^{o}C. At this
point, you will cool the bath to below 5^{o}C and read the final temperature (T_{final}) and volume (V_{final}.)

Be sure that you record the barometric pressure P_{atm}!

To compensate for the volume occupied by the inverted meniscus in the graduated cylinder, subtract 0.2 ml from all volume readings.

Now you are ready to make your calculations. First, you must calculate the number of moles of air (n_{air}) trapped in the cylinder; to do this,
use the **final** volume and temperature (those measured at a temperature below 5^{o}C.) We assume that the air
behaves as an ideal gas, so

Watch your units here - recall that R = 0.0821 liter atm / mol K, so make sure that your pressure is in atm, your volume is in liters, and
your temperature is in K. You should get something on the order of 10^{-4} moles of air.

Now you can calcuate the partial pressure of air in the gas mixture trapped in the graduated cylinder. For each volume-temperature pair
between 80 and 50^{o}C, calculate the following:

Again, watch your units!!

Now, we are studying the dependence of the vapor pressure of water as a function of temperature in this experiment. We therefore need to subtract out the
pressure of the other gases (those besides water) that were trapped in the bubble in the cylinder. For each volume-temperature pair between 80 and 50^{o}C,
calculate the partial pressure of water P_{water} in the following way:

Where P_{atm}is the measured atmospheric pressure and P_{air} is the partial pressure of air
calculated above at each of your measured volumes and temperatures.

You are now ready to rumble. Plot the raw data as P_{water} vs T:

**Fig. 1. Vapor pressure of water as a function of temperature.**

Plot only data points here - do not try to fit a line or draw a curve.

Clearly, the dependence of the vapor pressure of water on the temperature is nonlinear, in agreement with the predictions of the Clausius-Clapeyron equation:

**Notice here that A is a constant, ΔH _{vap} is the enthalpy of
vaporization, and R = 8.314 J /mol K** (it's stil the gas constant, just with different units.)

We linearize this equation by taking the natural log (ln) of both sides; after some minor calisthentics, we get

What this equation tells us is the following: *If the Clausius-Clapeyron equation is obeyed by the substance under investigation,
then a plot of lnP vs 1/T should be linear with a slope = -ΔH _{vap}/R and y-intercept = lnA. *Thus, if we plot lnP vs 1/T, we should get a linear plot,
and if we multiply the negative of the slope of the line by R (again, R=8.314 J /mol K), then we can obtain an experimental value for the enthalpy of vaporization ΔH

Your data now consist of the vapor pressures of water P_{water} and the corresponding temperatures; take the natural log (ln) of each of your vapor pressures, and plot them versus
1/T; here is a sample plot:

**Fig. 2. Vapor pressure of water, linearized and plotted according to the Clausius-Clapeyron equation.**

Have excel calculate and fit the best line to these data; multiply the negative of the slope of this line by R = 8.314 J/mol K, and compare your result to the accepted value of 44.02 kJ/mol (watch the units!!!!)

Also, from your plot, calculate the vapor pressure of water at 65^{o}C, and compare your value to that listed in Appendix B of your text.

**The Report**

You should have the usual introduction and methods sections. The atmospheric pressure must be given in the results section. You should have two tables in the Results
section. Table 1 must show the raw volumes/temperatures and Table two must show the calculated P_{air} and P_{water}, and you must give a brief description of how these quantities were calculated.
**Your tables must be properly labeled and cited in the text**.

Show your plot of the raw P_{water} vs T data, and comment on it (i.e., it is nonlinear, as predicted by the.....). Mention how the data were linearized, and show the plot of the linearized
data (be sure to label your plots as Fig 1 and Fig 2; give them titles and refer to them in the text!!!)

Give your calculated values for ΔH_{vap} and the vapor pressure of water at 65^{o}C; compare your calculated values to the accepted values mentioned above.

Your discussion section should include a the RPE for both the enthalpy of vaporiaztion and your calculated vapor pressure. Include a discussion of sources of error (human error is not an acceptable source of error here.)

This page was last updated on 29-March 2013

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