TEMPERATURE DEPENDENCE OF THE VAPOR PRESSURE OF WATER AND by variablepitch333

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									Chem 434                                                                                Experiment 2
TEMPERATURE DEPENDENCE OF THE VAPOR PRESSURE OF WATER AND
    AQUEOUS SALT SOLUTIONS

Introduction:
     Water is unique among the components of the atmosphere in that it exists in all of its three
phases simultaneously on Earth. It is also unique in that it has a comparatively high heat capacity
per mass and a large enthalpy of vaporization (and sublimation). When water evaporates, heat is
consumed from the surroundings, and when it condenses, heat is released to the surroundings.
For this reason, accurate predictions of water phase change are critical to understanding of the
Earth’s atmosphere and heat balance.
     A closed, well-mixed, vessel containing liquid water and air rapidly achieves an equilibrium
state where the rate of evaporation from the liquid surface and condensation on the liquid surface
are equal. We define the equilibrium vapor pressure of water, ps , as the partial pressure of water
in this state. The subscript s refers to the fact that the water vapor is saturated. This saturated
situation is also referred to as 100% relative humidity. The relative humidity, RH, is defined by
the equation
                                         RH = 100 * pv /ps                                         (1)
where pv is the partial pressure of water vapor. A sample of air that has a relative humidity less
than 100% is subsaturated. That air sample carries less water vapor than the parcel would carry if
it were equilibrated with excess liquid water. For this reason, if this parcel comes in contact with
liquid water, the liquid would evaporate and draw heat from the surroundings.
    The saturation vapor pressure of water, ps , increases rapidly with increasing temperature.
This means that the relative humidity is also a function of the temperature of the air parcel. When a
subsaturated air sample cools, ps decreases, but the partial pressure of water vapor, pv , remains the
same (the parcel is assumed to not mix with other air samples). At some point, the partial pressure
of water exceeds the saturation vapor pressure, or equivalently, the RH exceeds 100%, and water
vapor condenses out of the vapor. This condensation releases heat to the surroundings.
     In warm regions with liquid water present (the tropics), solar input provides energy to
evaporates the liquid water and produce humid air. This wet air then transports poleward where
the temperatures decrease, driving condensation and heat release. Therefore, we see that prediction
of the saturation vapor pressure of water is critical for understanding heat transport on Earth.
     In addition to the temperature dependence of the saturation vapor pressure of water, air also
contains aerosol particles. These particles are typically composed of sulfate (SO42-) compounds or
sea salt particles (predominantly NaCl). These particles act as condensation nuclei for water vapor,
which means that water condenses on their surface. This process turns a dry aerosol particle into
an aqueous salt solution. Therefore, we are also interested in the equilibrium vapor pressure of
water above sulfate and sodium chloride salt solutions. Typically, the equilibrium vapor pressure
of water above a salt solution is diminished by the presence of the solute. As the concentration of
solute in the water solvent increases, the vapor pressure lowers more and more. Thus, an initially
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dry aerosol condenses water vapor at a relative humidity lower than the pure water saturation vapor
pressure (or less than 100 % RH, noting that RH is defined with respect to pure water and ignores
aerosol loading). The aerosol then becomes a more dilute solution, and the saturation vapor
pressure above this solution increases. The dilution process continues until equilibrium is
reestablished.
     In this laboratory, we investigate temperature dependence of the equilibrium vapor pressure of
water using Fourier transform infrared (FTIR) spectroscopy. We then use a thermodynamic
analysis to understand this temperature dependence and extract the heat and entropy of vaporization
of water. Then, we investigate the behavior of concentrated aqueous solutions of sulfate
compounds and sodium chloride. This investigation allows us to understand the behavior of
various types of aerosols in the atmosphere.

Experimental method:
    This experiment is based on quantitative FTIR spectroscopy. We use the infrared absorption
of water vapor as a measure of the partial pressure of water in a gaseous sample. The experimental
setup is shown below:

                                                                     Vent to
                                                                     atmos.
                                 Flow
                                 Meter
                                           Humidifier
                                            (in bath) IR cell (in FTIR)




     Dry air is slowly bubbled through a sample of water contained in a carefully thermostated
vessel. The bubbling process equilibrates the water vapor in the flowing air with the liquid water
at the thermostat temperature. Therefore, the air flowing out of the humidification vessel contains
the saturation partial pressure of water, ps . This air then flows into the FTIR absorption cell,
where the partial pressure of water is measured. The spectrum of water contains many lines, each
of which has an intensity which depends on the pressure of water and the temperature of the water
vapor during the measurement. To remove the temperature effect in the spectrum, we flow the
humidified air out of the thermostatted water bath and into the FTIR, where it equilibrates its
temperature with the room. The thermostat is held at temperatures lower than the room
temperature, therefore, the relative humidity of the flowing gas is always below saturation in the
flow cell. This point is important, because, vapor that condenses before reaching the flow cell
would decrease the partial pressure of water vapor and make the measurement invalid.

Procedure:
   Install the absorption cell in the FTIR. Slide the black mounting plate down into the slot in the
sample holder within the spectrometer. Because room air contains water vapor, it is necessary to

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seal the cell into the sample region. Tape the plastic that is wrapped around the inlet and outlet
tubes of the flow cell down to the top of the spectrometer so that the cell is sealed. A flow of dry
purge air is constantly flowed through the spectrometer and around the flow cell to eliminate water
absorption outside the spectroscopic cell. Now, the cell is in position to measure the water vapor
content in samples that are flowed through it.
     The FTIR requires a blank spectrum that contains no water as a reference for determination of
water content. This blank spectrum is recorded by flowing dry air through the cell. To record this
spectrum, connect the air bottle directly to the inlet of the spectroscopic cell. Make sure that the
metering valve downstream of the regulator is closed and open the stem valve on the top of the air
bottle. The regulator should be set at 2-3 psi on the gauge (it should be there already). This
pressure is kept low so that the cell will not explode in case of blockage of the line further
downstream. Connect the flow meter to the outlet regulator valve and open the metering valve
slowly. Set the flow at around 0.5 lpm on the flow meter. Now you are flowing dry air through
the cell. You should wait at least 5 minutes for any water adsorbed on surfaces to evaporate before
taking the background.
     Start the OMNIC spectroscopic program on the computer. Do this by clicking on the OMNIC
icon under the OMNIC group in windoze. Record a background by going to the menu
collect>collect setup. A window will pop up and you should select 24 scans at 0.25 resolution (in
the first two boxes on the left). The number of scans sets the number of times that the
spectrometer repeats the experiment before reporting an average of the data. Setting it at 24 scans
will achieve a very low noise spectrum. The resolution is the resolution of the spectrum in
wavenumbers (cm-1). We use relatively high resolution because the gas-phase sample has narrow
lines (actually, they are narrower than even this setting). On the right side, change the background
handling so that it says record a background after 6000 minutes (the second check box from the
bottom). Select the OK button at the bottom of the page to record these new settings. Now under
the menu collect select the subheading collect background. A dialog will appear asking you to
prepare the background sample. You have already done this by setting the gas flows correctly. Be
sure you have waited at least 5 minutes after getting the gas flowing and click OK. The spectrum
will take around 4 minutes.
    After the spectrum is done, you get a dialog asking if you want to add the data to window 1.
Reply OK, and the data will appear on the screen. You are looking at the cell’s transmission
spectrum. It should look like a broad bump starting at a low level on the left side (high frequency)
and rising up then cutting off at around 1000 cm-1 on the right side. There are also small water
absorption features (around 3550 - 3950 cm-1 and 1350 - 1950 cm-1) and prominent carbon dioxide
(near 2350 cm-1). These residual absorption features are removed from all successive spectra by
using this spectrum as your background.
     Now you have a background spectrum for all your experiments. Save this background by
going to file and then save as. Move down a directory into the “434F00” directory and select a
filename for your background. A logical system is to use a 3 or 4 letter code for your group then a
serial number like 001 for the first file.


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     Once you have saved a spectrum, you can remove it from the display window by clicking on it
(the red spectrum is the selected one) and going to edit and selecting clear. Because it is saved,
you can recover it by going to file and opening it again.
     You now want to make the spectrometer recognize this spectrum as its background. Go into
the collect>collect setup dialog box and click on the lowest button for background handling. This
button selects “use specified background file.” Then click the browse button and select your
background file. Also reset the number of scans to 8 scans and make sure that the final format is
set to “absorbance”. Selection of fewer scans makes the data acquisition faster. We used 24 scans
for the background because every successive measurement relies on a good background. This
makes it worth the extra recording time. Now you are ready to take a spectrum. Collect a blank
spectrum to be sure that your background is good. This blank spectrum consists of a measurement
of the same dry air sample and should show only instrumental noise. To record the spectrum,
under the menu collect, select collect sample. A dialog pops up asking you to prepare for the
spectrum. Select OK.
     When the spectrum is done, add it to window one and examine it. There should be noise all
the way across the spectrum. From 4000 cm-1 to around 1000 cm-1, the noise should be small and
then it should blow up on the right end. It blows up because the cell doesn’t transmit light at this
region and there is only noise. Zoom in on the spectrum by dragging a box in the spectral window
between 4000 and 1000 cm-1 with an vertical scale of around 0.1 to -0.1. Once you drew the box,
click in the box and it will zoom in. You should see only noise (should be around +/- 0.005
absorbance units). Zoom in further to make sure you have no background absorption. If you see
negative peaks in the water regions (listed above), you didn’t wait long enough on recording your
blank and need to record a new background. Repeat the procedure from above until you have a
good background.
     Now you are ready to take the equilibrium vapor pressure data. You are now ready to insert
the humidifier into the line before the spectroscopic cell. Be sure to read this whole paragraph
before attempting to do this procedure. Disconnect the line from the air bottle from the inlet of the
spectroscopic cell. Connect this tube into the inlet of the humidifier. Note that the humidifier IS
directional. If you connect to the outlet, water will jet out the inlet. Be sure you have the inlet by
noting that the flow is into the bubbler tube, then out at the top. Carefully insert the line from the
air bottle into the humidifier inlet. Bubbles should start, but no water should be coming out the
outlet tube. If all is OK, connect the humidifier outlet into the inlet of the spectroscopic cell. Set
the flow back to 0.5 lpm.
      Cool the humidifier slightly (by adding a small amount of ice to the bath). Now allow the
system to equilibrate. You will determine the equilibration time by your experiment, but it does
take a while, so be sure to leave enough time. The primary experimental difficulty in this
experiment is getting the temperature equilibrated. Take a spectrum relatively early (a few minutes
after starting humidified flow) and then take another a few minutes later. Compare the spectra.
Are the peaks growing or shrinking, or the same? Repeat until the peak intensities are stable. Be
sure that the temperature is fairly stable also (<1°C). Save this last spectrum as representative of
this temperature.

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     Now cool the humidifier more and get a point near 10°C. Then remove most of the water
from the bath and get the bath down to near 0°C by making an ice bath. Then again get a medium
temperature point (about 10°C) and then another at near room temperature. Last, take a second
point at iced conditions. You now have 6 spectra, two warm, two medium, and two iced. To
complete the data set, remove the humidifier from the setup and record another blank. It should
also be just noise.

Analysis of the spectra:
     You now need to convert your spectra into water partial pressure measurements. This
procedure involves integration of selected peaks in the water spectra. As this procedure requires a
fair bit of manipulation of the OMNIC program, there is a section later in this handout on using the
integration routines. With the method on this handout, you will convert your six spectra into
measurements partial pressures of water as a function of the thermostat temperature. The resulting
data set is six pressures and six temperatures and is analyzed for thermodyanmic parameters by the
method described in the next section.

The temperature variation of the water partial pressure:
    The equilibrium partial pressure of water is really an equilibrium constant for the reaction:

                                         H2O(l) ↔ H2O(g)                                            (2)
Consider the chemical potential for water in the liquid and gas phases.

                                                         pv 
                                       µ g = µ θ + RT ln θ 
                                                        p 
                                               g
                                                                                                    (3)
                                                     θ
                                               µl = µl
In these equations, θ is the standard state, which we take to be 105 Pa for the gas. Note that liquid
water is a pure state, so the chemical potential has no dependence on the amount of water. At
equilibrium, the chemical potentials of the liquid water and gas phase water are equal, thus we
have:

                                          pv 
                                    RT ln θ  = µ lθ − µ θ = −∆G                                   (4)
                                         p 
                                                          g



Where ∆G is the molar Gibbs energy for the reaction (2).
    The temperature dependence of the equilibrium vapor pressure arises from the temperature
dependence of the Gibbs energy. We can separate the Gibbs energy into enthalpic and entropic
terms.
                                          ∆G = ∆H − T∆S                                             (5)
If we assume that ∆H and ∆S are temperature independent, then we can insert equation (5) into
equation (4) to get:

                                           pv 
                                     RT ln θ  = − ∆H + T∆S                                        (6)
                                          p 
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dividing through by RT,

                                          pv  − ∆H  1  ∆S
                                       ln θ  =          +                                           (7)
                                         p      R T R
Equation (7) shows the relationship between the natural logarithm of pv (divided by standard states)
versus 1/T should be linear with a slope of -∆H/R and an intercept of ∆S/R. You recognize this
analysis as similar to that of the temperature dependence of the Henry’s law constant.

Integration of spectra:
     The spectra you recorded during last week need to be integrated to convert them to partial
pressures of water vapor. To do this, load up the six well-equilibrated spectra you recorded last
time. Blow up the baseline region between 3780 - 4000 cm-1 with a magnified vertical scale so that
the baseline noise is clearly visible. Click on the integral tool (the tool just to the left of the T on
the bottom of the window). Select the region between 3789 and 3955 cm-1 to be integrated. If you
miss the correct region, you can click in and drag the left and right facing triangles to move the
wavenumber limits. Now you need to adjust the baseline to get a good integral. Move the baseline
sliders (the upward facing triangles on the baseline) left and right until they happen to be on a data
point that is near the center of the baseline noise. Get both sliders so the baseline looks good, then
record the corrected integral. This number has units of cm-1, as discussed later. Now to see how
much noise is introduced by the baseline selection, have another member of your group move the
sliders and get what they think is a good baseline. Now record the corrected integral. You can tell
about the error in integration by the difference between your results. Average the results to get an
integral for this spectrum. Now repeat the procedure on each of your group’s spectra. In the end,
you have 6 temperatures and 6 integrals.
    You have now determined the band-integrated absorbance, which we define as I in the
equation

                                              I = ∫ A(ν )dν                                           (8)

where A(ν) is the absorbance as a function of wavenumber, ν. Because absorbance is unitless and
wavenumber has units cm-1, this integral has units of cm-1. The integrated absorption is related to
the partial pressure of water vapor through the relationship

                                          p = B∫ A(ν )dν = BI                                         (9)

where p is the partial pressure, B is the bandstrength for the absorption feature. The bandstrength
of the H2O stretching bands (3789-3955 cm-1) is 2.37 Torr /cm-1. Using equation (9) and your
integrals, you can calculate the partial pressure of water as a function of temperature.

Extraction of the heat of vaporization:
     Analyze the data from the experiment by the thermodynamic method described in the previous
section. Then extract the thermodynamic parameters. In the second lecture, we will discuss
weighted fitting. To take a quick look at the data, use Excel to fit it, but in the final report, you will

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use the weighted fit spreadsheet. You will assume that the experiment has a 5% error in
determination of the partial pressure of water. You will have to propagate this error into ln(pv/pθ )
to do the analysis.

Continuation (Week 2 of the experiment):
    In part one of this laboratory experiment, we investigated the temperature dependence of the
equilibrium vapor pressure of water using Fourier transform infrared spectroscopy. During this
week, we integrate the spectra to get partial pressures of water as a function of the thermostat
temperature. We can then use the thermodynamic analysis described in part one to understand this
temperature dependence and extract the heat and entropy of vaporization of water. During this
week, we also investigate the behavior of concentrated aqueous solutions of sulfate compounds
and sodium chloride. This investigation allows us to understand the behavior of various types of
aerosols in the atmosphere. We also compare our results to the prediction of Raoult’s law.

Preparation of saturated salt solutions:
     Prepare saturated salt solutions of NaCl, the model for sea-salt aerosol, and (NH4)2SO4, the
model for sulfate aerosol. You will need around 40-50 ml of solution in the end. Periodically
check your solution to be sure that it is indeed saturated and its temperature is close to room
temperature (dissolution of the solute can be endo- or exothermic). Also prepare a sample of 40-
50ml of pure deionized water out to equilibrate to room temperature. While you wait for these
solutions to equilibrate, integrate the spectra.

The vapor pressure of water over saturated salt solutions:
      Now the salt solutions have saturated and you are ready to measure water vapor pressure
above these solutions. You will use the same procedure as in part one. Be sure to record a blank
first to make sure you are set up correctly, then record the vapor pressure of pure water, the
sodium chloride salt solution, and the bis ammonium sulfate solution, then a blank again. All these
spectra should be recorded at the same temperature (slightly below room temperature).

Analysis of the spectra:
    Integrate the spectra of the salt solution water partial pressures over the same spectral region
and convert the integrals to partial pressures. Then compare the solution partial pressures to that of
pure water (at the same temperature). Calculate the relative humidity (see part 1) of the vapor
above the salt solutions.

Questions for write-up:
a) For the temperature dependence:
     Analyze the data as described in part 1 (a Van’t Hoff plot). Use 105 Pa as the gaseous
standard state. Extract the standard state entropy and enthalpy of vaporization along with errors
from the weighted fit spreadsheet.
b) For the salt solutions:

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      Imagine a situation where you have aerosol particles made up of a saturated solution of each
salt in water. What would the partial pressure of water above this solution be at equilibrium?
What is the relative humidity under this circumstance? Now imagine a situation where this aerosol
particle contacts air of lower RH. What happens to the particle? Assume the air’s RH is held
constant during this process, which is equivalent to saying that the mass of water in the particle is
negligibly small compared to the mass of water in the air sample. What happens to the particle
when it contacts air of higher RH? Again assume the particle’s water mass is negligible. Re-read
the section of your physical chemistry text on Raoult’s law. How can Raoult’s law be applied to
the current situation? Find the composition of saturated NaCl and (NH4)2SO4 solutions and apply
Raoult’s law to calculate an ideal solution result. Does Raoult’s law work? How well?




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