Most mixtures in vaporliquid equilibrium have a liquid phase composition that is different from the vapor phase composition. This difference forms the basis for separating mixtures using distillation.
However, for some mixtures in equilibrium, under certain conditions, the composition of the liquid phase equals the composition of the vapor phase. The temperature, pressure, and compositions at which this equality occurs is called the azeotropic point and we say that the mixture forms an azeotrope.
For example, the black curve in Figure 1 shows equilibrium compositions for mixtures of acrylonitrile (a) and cyclohexane (b) at temperatures ranging from the boiling point of pure acrylonitrile to the boiling point of pure cyclohexane. The x axis shows the mole fraction of acrylonitrile in the liquid phase. The y axis shows the mole fraction of acrylonitrile in the vapor phase. The red dot in Figure 1 indicates that if we have an equilibrium mixture with a liquid phase containing 0.20 mol fraction of acrylonitrile, then the vapor phase will contain approximately 0.45 mol fraction of acrylonitrile. (Note that this point corresponds to a temperature of approximately 32 °C.)
Figure 1 also shows that when the liquid phase has an acrylonitrile mol fraction of 0.49, the equilibrium vapor phase will also have an acrylonitrile mol fraction of 0.49. This is thus the mixture's azeotropic point. (At 30.03 kPa.)
One method for determining if a mixture forms an azeotrope, is to compare the slopes at the beginning and end of the mixture's yx compositions curve. If both slopes are either greater than one or less than one, then the curve will "start" and "end" on opposite sides of the 45° line, i.e., the gray line. Since the composition curve is continuous, the curve must pass through the gray diagonal line where the x and y compositions are equal, i.e., an azeotropic point. (See below for further discussion.)
The equations for the slopes are also given in the figure. These equations require values for the vapor pressure and activity coefficients of both components in the mixture. Note that these properties are evaluated at the infinite dilution endpoints. At the endpoints the temperatures correspond to the boiling points of components 'A' and 'B'.
To estimate if a chemical (component 'A') forms an azeotrope with another selected chemical (component 'B'):
The webpage will retrieve physical property data and estimates from Cranium's WebServer Edition, use these values to calculate the limiting slopes, and then display the results in the tables below.
See the following video for instructions on using the structure editor: Video Link. See the following video for an example azeotrope determination: Video Link.
The entered structure was sent to a WebServer Edition of Cranium running in the cloud. Cranium estimated the component A's boiling point. Cranium also retrieved component B's boiling point. These two boiling points were then used to estimate each component's vapor pressure and infinite dilution activity coefficient.
Finally, these physical properties were used to calculate the limiting slopes and determine whether or not an azeotrope is present in the entered mixture at the entered pressure. (Note: because of estimation inaccuracies, mixtures having one or both slopes near 1.0 should be investigated further.)
Component (A) Physical Properties  

Boiling Point  K  
Vapor Pressure  kPa  
Activity Coefficient     
Component (B) Physical Properties  

Boiling Point  K  
Vapor Pressure  kPa  
Activity Coefficient     
Azeotrope Determination  

Limiting Slope, Component A  
Limiting Slope, Component B  
Azeotrope Present 
Figure 2 below shows the vaporliquid equilibrium curve for acetone + ethyl acetate at a pressure of 101.3 kPa. From the slopes of the curve at low and high ethyl acetate concentrations, and the observation that most (but not all) vaporliquid equilibrium curves have simple shapes, we conclude that curve is on "one side" of the gray diagonal line. This means that the curve will not cross the gray curve and thus the liquid composition will never equal the vapor composition (except at the pure component end points). (Note that experimental data were used to draw these curves and perform these calculations. Thus, the values may differ from those calculated in this application.)
Figure 3 below shows the vaporliquid equilibrium curve for acrylonitrile + cyclohexane at a pressure of 30.03 kPa. The slopes of the curve at low and high acrylonitrile concentrations are both greater than 1. This means that curve will be on "both sides" of the gray diagonal line. The curve will cross the gray curve at some point and thus the liquid composition will equal the vapor composition at some point. We thus conclude that the acrylonitrile + cyclohexane mixture forms an azeotrope at 30.03 kPa. (Note that experimental data were used to draw these curves and perform these calculations. Thus, the values may differ from those calculated in this application.)
The limiting slopes can be determined in terms of easily obtainable physical properties by using the analysis shown here.
The vaporliquid equilibrium relation, at low pressure, for component A is given by Equation 1.
We can differentiate this equation by x_{a}to obtain the slope of the curve shown in the figure above:
As the concentration of x_{a} approaches 0, the slope approaches:
Using the relationships for the total of mole fractions and the phase equilibrium equation for component B,
we obtain another relationship for y_{a}:
Differentiating this equation by x_{a} we obtain another expression for the slope of the curve shown in the figure above:
Using the total of the liquid phase mole fractions,
Equation 7 now becomes:
As the concentration of x_{a} approaches 1, the slope, as given by Equation 9, approaches:
Figure 1 shows that when an azeotrope is present the slopes at each concentration limit must both be either greater than 1 or less than 1. (Assuming the mixture does not exhibit double azeotropy.) We can thus use this observation with the slopes calculated by Equations 4 and 10 to identify binary azeotropic systems.
The infinite dilution activity coefficients and vapor pressures in Equations 4 and 10 are both temperature dependent properties. Equation 4 represents the slope of the equilibrium curve for a mixture containing almost pure B. Thus the properties used in Equation 4 should be evaluated at the boiling point of pure B. Similarly, Equation 10 represents the slope of the equilibrium curve for a mixture containing almost pure A. Thus the properties used in Equation 10 should be evaluated at the boiling point of pure A.
Thus, we need to have Cranium's WebServer Edition determine the normal boiling points and vapor pressures for the pure components A and B, and activity coefficients at x_{a} = 0 and x_{a} = 1.
As an example, we calculate the slopes for a binary mixture of acrylonitrile (A) and cyclohexane (B). This is the mixture shown in Figure 1 above. The calculations will be done at a pressure of 30.03 kPa.
The first physical properties that must be determined are each component's normal boiling point.
We then use these boiling points to calculate the vapor pressure of each component. Each component's vapor pressure is calculated at a temperature equal to the other component's boiling point.
We next need to calculate the infinite dilution activity coefficients of each component.
We can then insert these physical property values into Equations 4 and 10 to calculate the slopes.
Because both of these slope are greater than one, we can conclude that a mixture of acrylonitrile and cyclohexane at 30.03 kPa will form an azeotrope.
We compared the results of this web application against several experimentally determined azeotropes and nonazeotropic mixtures. The results are shown in the table to the right. All evaluations were done without entering a value for the component A's boiling point, i.e., the normal boiling point of each component A was estimated.
The column labeled "Exp Azeotrope" indicates the presence of an azeotrope as determined from experimental data. The column labeled "Est Azeotrope" indicates the presence of an azeotrope as determined by this web application. If the value in the Est Azeotrope column has an asterisk, the the correct determination was obtained only after a boiling point was entered for component A.
The table shows that 17 of 24 mixtures were correctly classified. 3 of those mixtures that we not classified correctly, were classified correctly once an accurate value was entered for the component A's boiling point.
Mixture (A + B)  Pressure [kPa]  Exp Azeotrope  Est Azeotrope 

1,3Dioxolane + Water  101.3  Yes  Yes 
1Propanethiol + Methylcyclopentane  101.3  Yes  Yes* 
1Propanol + Water  77.1  Yes  Yes 
2Butanone + Ethyl acetate  101.0  Yes 
No

2Butanone + Methylcyclohexane  40.1  Yes  Yes 
2Methyl2propanol + Ethyl acetate  39.8  Yes  Yes 
2Methyl2propanol + Ethyl acetate  101.3  Yes 
No

2Propanol + Water  81.9  Yes  Yes 
Acetic acid + Water  101.3  No 
Yes

Acetone + Ethanol  101.3  No  No 
Acetone + Ethyl acetate  101.3  No  No 
Acetone + Tetrahydrofuran  101.3  Yes  Yes* 
Diethanolamine + Water  6.7  No  No 
Ethanethiol + nPentane  101.3  Yes  Yes* 
Ethanol + Acetone  101.3  No  No 
Ethanol + Water  101.3  Yes  Yes 
Ethyl acetate + Methylcyclohexane  53.1  Yes  Yes 
Ethylene glycol + Water  101.3  No  No 
Fluorobenzene + Ethanol  101.5  Yes  Yes 
Methanol + Acetone  98.3  Yes  Yes 
Methanol + Chloroform  103.5  Yes  Yes 
nHeptane + Benzene  19.8  Yes  Yes 
Propanoic acid + Water  101.3  Yes  Yes 
Styrene + Ethylbenzene  13.3  No 
Yes

The table above shows that the methodology used by this web application is quite good at identify whether or not a mixture will form an azeotrope at a given pressure. However, the table also shows there are some systems for which the application gives incorrect results. In some cases, the slopes calculated by the application are very close to a value of 1. Thus, any errors in the estimation of boiling points, vapor pressures, and activity coefficients, could significantly affect the result.
However, for some systems, e.g., Styrene + Ethylbenzene, the slopes are significantly different than 1. For this system, the estimates for the boiling points and vapor pressures are quite accurate. We thus believe that the estimation of the infinite dilution activity coefficients are in error. We are thus investigating the accuracies of Cranium's infinite dilution activity coefficient techniques for this and the other systems that were incorrectly identified. As always, any suggestions or recommendations are welcome.
The Get Estimates buttons above retrieve your input molecular structure, temperatures, and pressures, package these into a request string and then send it to an instance of our Cranium, Web Server Edition software product running on a Microsoft Azure virtual machine. Cranium processes the request  dissecting molecular structure and estimating physical properties. The resulting estimates are then sent back to this webpage for display.
Click here to learn more about how you can use our Cranium Web Server to distribute your company's physical property data, estimates, and knowledge throughout your organization or contact us for further details.