The vapor pressure of solids & liquids compounds can be useful to determine the thermodynamic stability and shelf life of a variety of products, especially those from the pharmaceutical industry. The accurate quantification of vapor pressure can be very important for the safe use and handling of solid compounds.
This article describes how the Vapor pressure analyser (VPA) from Surface Measurement Systems Ltd can be used to determine the vapor pressure of pesticides using the Knudsen method.
Theory
In this experiment, the Knudsen method was used to determine the vapor pressure of two pesticides, quinclorac and bifenthrin. Both the heat of vaporization (enthalpy of vaporization) and vapor pressure were determined from experimental data using the standard Knudsen Equation (Equation 1) and ClausinsClapeyron Equation (Equation 2):

(1) 

(2) 

(3) 
where P is vapor pressure, R is universal gas constant (8.314m^{3} .Pa.K^{1} .mol^{1)}, T is temperature in Kelvin, M is molecular weight, and A is area of the aperture of the Knudsen cell. The gradient of the linear portion of mass against time data is used to measure dm/dt (Figure 1). The ΔH is the heat of vaporization, and a and b are constants.
Figure 1. A schematic form of Knudsen mass vs time data
Experimental Method
Approximately 0.5mg sample was placed in a Knudsen effusion cell, with an aperture size of 191.8µm. The experiment was carried out in a vacuum VPA system over a constant temperature range.
The pressure of the sample cell was reduced and sustained at around 10^{3} Torr using a rotary pump during the experiment. Using the combination of a turbo pump and a rotary pump, it is possible to obtain a lower ultimate vacuum in the range of 10^{5} ~10^{6} Torr. The graphs below show the liner portion of the raw experimental data:
Figure 2. Raw data of the Knudsen vapour measurement at various temperatures
The vapor pressure of bifenthrin, which has a molecular weight of 422.9g/mol^{1}, was determined using a dedicated Knudsen effusion cell software.
Quinclorac, which has a molecular weight of 242.1g/mol^{1}, had its vapor pressure determined using the gradient of the linear section of the graphs. Tables 1 and 2 summarise the calculation results for bifenthrin and quinclorac, respectively.
Table 1. A summary of the calculation of vapour pressure of bifenthrion
Temp (°C) 
Temp (K) 
Vapour pressure (Pa) 
Log P 
1/T (K^{1}) 
65 
338 
2.149 x 10^{2} 
1.668 
2.959 x 10^{3} 
75 
348 
9.796 x 10^{2} 
1.009 
2.874 x 10^{3} 
85 
358 
2.221 x 10^{1} 
 0.653 
2.793 x 10^{3} 
Table 2. A summary of the calculation of vapour pressure of quinclorac
Temp (°C) 
Temp (K) 
Vapour pressure (Pa) 
Log P 
1/T 
75 
348 
7.9 x 10^{4} 
3.102 
2.874 x 10^{3} 
85 
358 
1.6 x 10^{3} 
2.796 
2.793 x 10^{3} 
In order to determine the heat of vaporization, it is necessary to plot the relationship between temperature and vapor pressure graphically. The logarithm of vapor pressure plotted against the reciprocal of temperature in Kelvin, was predicted to be a linear relationship. The resulting data was then fitted with a straight line, as shown in the graphs below:
Figure 3. Vapour pressuretemperature relationship for bifenthrin
Figure 4. Vapour pressuretemperature relationship for quinclorac
The fitted straight lines shown above can be expressed mathematically using the Equation 4 for bifenthrin and Equation 5 for quinclorac:

(4) 

(5) 
Compared to Equations 2 and 3, it can be seen that the value of the constant b for quinclorac is 3777.8 and that for bifenthrin it is 6127.9. As a result, the heat of vaporization for both chemicals can be calculated as follows:
ΔH = bR = (6127.9) x 8.314 = 50947.36 (J.mol^{1}) for bifenthrin
ΔH = bR = (3777.8) x 8.314 = 31408.63 (J.mol^{1}) for quinclorac
Verification of Measurement Data
In order to verify the experimental data, the vapour pressure calculated using Equations 4 and 5 can be evaluated against published results. Thevapour pressure of bifenthrin at 25°C can be calculated in the following way:

(6) 
Similarly, for quiclorac at 20°C:

(7) 
Compared to published documents and safety data information, the vapor pressure of quinclorac at 20°C is 7.50 x 10^{8}mmHg and that of bifenthrin at 25°C is 1.81 x 10^{7}mmHg, which are in good agreement with the calculation shown above.
Conclusion
The Vapor pressure analyser (VPA) from surface measurement represents an easy way to determine vapor pressures of pesticides using the Knudsen effusion cell method.
The vapor pressure determined using the experimental data for quinclorac at 20°C is 5.42 x 10^{8}mmHg, and that for bifenthrin at 25°C is 6.49 x 10^{7}mmHg. These are in good agreement to the published results of 7.50 x 10^{8} mmHg and 1.81 x 10^{7}mmHg for quinclorac and bifenthrin, respectively.
This information has been sourced, reviewed and adapted from materials provided by Surface Measurement Systems Ltd.
For more information on this source, please visit Surface Measurement Systems Ltd.