Dew Point calculations with an example

The dew point of the temperature at which a liquid begins to condense from a vapor. The calculation is

very simple for a pure component it is the boiling point of the pure component. A simple equation like

Antoine’s equation can be used to calculate this.

For multicomponent mixtures, the vapor-phase composition Yi is given. If along with the vapor

composition, the temperature is given, then we must increase the pressure till the first drop of liquid is

formed. This is called Dew point pressure calculation. If the pressure is given, then we must decrease

the temperature till the formation of liquid. This is called Dew point temperature calculation. In both the

cases the temperature or Pressure is adjusted till the liquid composition of the liquid is equal to 1.

∑Xi = 1.0

We shall calculate Dew point temperature calculations here. For an ideal mixture that follows Raoult’s

law this becomes

∑

Antoine’s equation can be used to calculate the vapor pressure of each component.

( )

Where,

P is the vapor pressure A, B and C are component specific constants T is the temperature

Let us calculate the Dew point temperature of a mixture of Benzene (0.3),

Toluene (0.4) and m-Xylene (0.3) at a pressure of 1 bar.

The Antoine’s coefficient are given in the table below

A B C

Benzene 9.2806 2788.51 -52.36

Toluene 9.3935 3096.52 -53.67

m-Xylene 9.5188 3366.99 -58.04

Note: It is very important to pay attention to the UNITS of the temperature and Pressure as the

parameters have been obtained by regression and the units are very important. Our coefficients are

with temperature in K and pressure in Bars.

To get a first estimate we can get the boiling point of each component by inverting the Antoine’s

equation:

( )

BP (K)

Benzene 352.8266

Toluene 383.315

m-Xylene 411.76

Mole fraction averaged the first estimate is

yi yiT

Benzene 0.3 105.848

Toluene 0.4 153.326

m-Xylene 0.3 123.528

SUM 382.702

Calculate the vapor pressures at this temperature and sum the Liquid mole fractions:

yi PVap yi/PVap xi=yiP/PVap

Benzene 0.3 2.314785 0.129602 0.129602

Toluene 0.4 0.982652 0.407062 0.407062

m-Xylene 0.3 0.42658 0.703268 0.703268

P 0.806496 1.239932

Now take Benzene as or “key” component and get a new estimate of the temperature. We use the

following equation:

∑

Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as

Tnew = 391.33 (K)

PVap yi/PVap xi=yiP/PVap

Benzene 2.870176 0.139364 0.139364

Toluene 1.25006 0.239989 0.239989

m-Xylene 0.558087 0.537551 0.537551

P 1.090628 0.916903

New vapor pressure of “key” (Benzene) component is recalculated

Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as

Tnew = 387.8 (K)

yi Pvap yi/Pvap xi=yiP/Pvap

Benzene 0.3 2.631674 0.151995 0.151995

Toluene 0.4 1.134399 0.264457 0.264457

m-Xylene 0.3 0.500769 0.599079 0.599079

P 0.984707 1.015531

We are getting close:

New vapor pressure of “key” (Benzene) component is recalculated

Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as

Tnew = 388.42 (K)

yi Pvap yi/Pvap xi=yiP/Pvap

Benzene 0.3 2.672546 0.14967 0.14967

Toluene 0.4 1.154134 0.259935 0.259935

m-Xylene 0.3 0.510504 0.587654 0.587654

P 1.002748 0.997259

New vapor pressure of “key” (Benzene) component is recalculated

Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as

Tnew = 388.312 (K)

Since the temperature does not change by more than 0.2 (K) we have reached our solution: For grins we

can calculate the sum of liquid mole fractions.

yi Pvap yi/Pvap xi=yiP/Pvap

Benzene 0.3 2.672546 0.14967 0.14967

Toluene 0.4 1.154134 0.259935 0.259935

m-Xylene 0.3 0.510504 0.587654 0.587654

P 1.002748 0.997259

Thus our Dew Point Temperature for a mixture of Benzene (0.3), Toluene

(0.4) and m-Xylene (0.3) at 1 Bar is 388.12K.