Re: How do you experimentally measure partial pressures in a mixture of gases?

March 8, 2006
Coker College
Hartsville, SC

Dear Gavin:

There is a very nice experimental setup with which one can determine the vapor pressure of a liquid as a function of temperature. At Coker, we use a 125−mL Erlenmeyer flask fitted with a Vernier™ Corporation one-hole rubber stopper through which a 2-way Vernier™ plastic valve can be fitted and onto which is attached a small-diameter flexible tubing (also provided by Vernier™). The tubing is then connected to a Vernier™ gas pressure sensor which is interfaced with a computer and which uses Vernier’s™ LoggerPro™ software program to log in and analyze the data.

The procedure is to inject a small volume of the liquid whose vapor pressure is to be determined through the open valve into the flask via a Vernier™ plastic syringe. The valve is then closed. This is done after the pressure of the air in the flask is measured. When the liquid enters the flask its vapor pressure adds to the pressure of the air (the separate pressures are called “partial pressures”). The gas sensor measures the total pressure in the flask, so the partial pressure of air must be subtracted from the computer-reading of total pressure to determine the partial pressure of the liquid by itself.

The flask is immersed in a water bath whose temperature can be raised (or lowered), so a set of pressure readings at a set of corresponding temperatures can be logged into the computer as the experiment proceeds. Each time, however, the pressure of the air must be subtracted from the total pressure reading to get the vapor pressure of the liquid at those temperatures. The problem here is, that as the temperature is increased, not only does the vapor pressure of the liquid increase, but the partial pressure of the air also increases. Which means before the air pressure is subtracted from the total pressure, it must be “corrected” for temperature. This correction is carried out by assuming the air obeys the Ideal Gas Law (PairV=nairRT). The correction is carried out using the proportion:

(Pair at T / Pair at T1) = (T / T1)

and solving for Pair at T.

One of the thermodynamic properties of the liquid which can be determined from its vapor-pressure-temperature data is its molar heat of vaporization. This is accomplished by re-casting the data in the form of the Clausius-Clapeyron Equation, whose expression is graphed in the format of a straight line. The molar heat of vaporization is then calculated by multiplying the negative of the slope of the line by the gas constant R (which appears in the ideal gas law equation above).

You can find the specific equipment you need (and which can be ordered from Vernier™) by accessing its website: http://www.vernier.com/

However, you asked about determining the partial pressures of a two- component solution, both of whose components are volatile. As far as I can tell, there is no device that can easily measure the partial pressure of one of the components to the exclusion of the other. There may be an approach using the technique of absorbtion spectroscopy which can translate the absorbance values of the gas phase into concentration values then converting those to partial pressures (by applying the Clapeyron- Clausius Equation to each component). However, there is a standard experiment we have carried out in our Physical Chemistry Lab which uses the procedure known as constant-pressure distillation. In this experiment we essentially boil a set of solutions with differing concentrations of the two components at atmospheric pressure and collect the distillate (the condensed vapor) by cooling the vapor with a water condenser. We then determine the relative concentrations (in mole-fraction units) of the components of the distillate and separately those of the residue (the liquid that hasn’t been distilled off) using an Abbé refractometer. A plot of concentrations versus temperature is then made, whose graph gives us information about the extent of the solution’s deviation from Raoult’s Law.

This experiment may be found in the book Experiments in Physical Chemistry by Garland, Nibler, and Shoemaker, 7th Edition (or earlier editions), McGraw-Hill Publishers (2003). In the 7th edition it can be found as Experiment 14: Binary Liquid-Vapor Phase Diagram (pp 208−215).

Sincerely,

P.M.Fichte