Nornographs for Bubble an Dew Points BENZENE-TOLUENE-XYLENE MIXTURES M. H. CHETRICIC University of N o r t h Dakota, Grund Forks, N . D .
repeated until a temperature is obtained which renders the sum unity. Expressed mathematically:
rapid nomographic method for calculating bubble points and dew points of mixtures of benzene, toluene, and rn-xylene is presented. Nomographs for this three-component system have been constructed, and illustrations concerning their uses are given.
where xi = mole fraction of liquid of any component; and IC, = equilibrium constant of 2% a t known pressure and assumed temperature. I n the special case for ideal solutions where Raoult's law applies, Equation 1 may be written:
T
HE calculation of bubble points (less preferably called initial boiling points) of multicomponent liquid mixtures usually requires tedious trial-and-error calculations. This is due t o the fact that assumed temperatures must be used with the various equilibrium constants at known pressures to estimate the vapor composition in equilibrium with a given liquid. If the mole fractions of all the components in the vapor add up to unity, when so calculated, the assumed temperature was correct. If not, a new temperature must be assumed and the calculations
where p = total pressure of system; and pl = vapor pressure of x2 a t assumed temperature. Similarly, for the-calculation of dew points (also referred to &B final boiling points or initial condensation points) of a gaseone
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Figure 1.
Bubble Point Nomograph 430
. I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
February 1949
mixture, trial-and-error solutions are again necessary. Assumed temperatures must be employed with the various equilibrium constants at known pressures to determine the composition of an infinitesimal amount of condensed liquid in equilibrium with a given vapor composition. Temperatures must be assumed until one is reached a t which the sum of the mole fractions of all the components in the liquid equals unity. An expression for dew points, analogous to Equation 1 for bubble points, leads to the relationship:
(3)
Cyl/Kz = 1
where yi = mole fraction of vapor of any component. Further, for the case of ideal solutions and vapors, where K, = p , / p :
PCYZ/P% = 1
(4)
In order to simplify the calculations involved in determining dew points and bubble points of multicomponent mixtures and to eliminate the trial-and-error procedure, nomographs have been constructed for the system benzene-toluene-m-xylene. A nomograph for determining the bubble points of various mixtures of these three components is shown in Figure 1. The bubble poiiit temperature ranges from 75' to 140' C . and the total pressure of the system from 0.5 t o 2.5 atmospheres. Figure 2 gives a nomograph for the determination of the dew points for this same system, with the dew point temperature ranging from 75" to 140" C. and the total pressure from 0.5 to 2.0 atmospheres. Both these charts were constructed on the basis that the liquid solutions are ideal and the vapor is an ideal gas. Accordingly, Raoult's law was assumed to be applicable. To illustrate the simplicity of these nomographic charts, the following examples are given:
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Illustration 1. Given a liquid containing 68.8 mole %benzene, 16.3 mole % toluene, and 14.9 mole % rn-xylene, what is the bubble point of this mixture a t 1.8 atmospheres pressure? Using Figure 1, draw a straight line through the points representing the compositions of the three components. (Actually, only the compositions of two of the components are needed as the line will automatically pass through the composition of the third component.) From the point of intersection of this line with the reference line, draw another straight line through the total pressure of the system, 1.8 atmospheres in this case, and extend this line until it intersects the temperature scale. The intersection on the temperature scale, 110' C., is the bubble point of the mixture. Illustration 2. Given a vapor containing 38.4 mole % benzene, 53.5 mole yo toluene, and 8.1 mole yo m-xylene, what is the dew point of this mixture a t 0.6 atmosphere? Using Figure 2, draw a straight line through the points representing the compositions of any of the two components. From the point of intersection of this line with the reference line, draw another straight line through 0.6 atmosphere OD the pressure scale: extending this line until it intersects the temperature scale. The point of intersection, 90" C., is the dew point of the mixture. The simplicity and speed of estimating dew points and bubble points by these nomographs can be seen readily. The values obtained from these charts are within one degree accuracy, which is sufficientfor calculations of this type. Similar nomographs can be constructed easily for other systems and are especially useful when working with a given system for a considerable period of time. RECDIVED September 8, 1947.
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Figure 2.
Dew Point Nomograph
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