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 ~80oC, and read a volume/temperature pair at about 5oC intervals to 50oC. At this point, you will cool the bath to below 5oC and read the final temperature (Tfinal) and volume (Vfinal.)
Be sure that you record the barometric pressure Patm!
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 (nair) trapped in the cylinder; to do this, use the final volume and temperature (those measured at a temperature below 5oC.) 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 50oC, 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 50oC, calculate the partial pressure of water Pwater in the following way:
Where Patmis the measured atmospheric pressure and Pair 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 Pwater 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, ΔHvap 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 = -ΔHvap/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 ΔHvap.
Your data now consist of the vapor pressures of water Pwater 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 65oC, and compare your value to that listed in Appendix B of your text.
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 Pair and Pwater, 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 Pwater 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 ΔHvap and the vapor pressure of water at 65oC; 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.)