calculation of bubble and dew point
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Calculation of Bubble and Dew point 2013
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Calculating Bubble & Dew Points for Ideal Mixtures
Calculating Bubble
& Dew Points forIdeal Mixtures
Calculation of the bubble and dew points of a mixture is key to the understanding of distillation columns. This article describes how to calculate bubble and
dew points for ideal mixtures.
Introduction
When a liquid mixture begins to boil, the vapour does not normally have the same composition as the liquid. The components with the lowest boiling point
(i.e. the more volatile) will preferentially boil off. Thus, as the liquid continues to boil, the concentration of the least volatile component drops. This results in
a rise in the boiling point. The temperatures over which boiling occurs set the bubble and dew points of the mixture.
The bubble and dew points can be defined as:
1. The bubble point is the point at which the first drop of a liquid mixture begins to vaporize.
2.
The dew point is the point at which the first drop of a gaseous mixture begins to condense.
For a pure component, the bubble and dew point are both at the same temperature - its boiling point. For example, pure water will boil at a single
temperature (at atmospheric pressure, this is 100oC).
For ideal mixtures (i.e. mixtures where there are no significant interactions between the components), vapour-liquid equilibrium is governed by Raoult's Law
and Dalton's Law.
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Raoult's Law
Raoult's Law states that the partial pressure of a component, PA, is proportional to its concentration in the liquid. So for component A,
Where:
PA - Partial pressure of component A
Po
A- Vapour pressure of component A
xA - Liquid mole fraction of component A
Dalton's Law
Dalton's Law states that the total pressure is equal to the sum of the component partial pressures. Thus for component A, its partial pressure, PA, is
proportional to its mole fraction in the gas phase:
Where
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PTotal - Total System Pressure
yA - Vapour mole fraction of component A
Dew Point Calculation
The dew point is the temperature at which a gas mixture will start to condense. For an ideal mixture, we can use Dalton's and Raoult's Laws to calculate the
dew point. By combining the two equations, we can calculate the liquid mole fractions for a given vapour composition, i.e.:
Calculating the dew point is iterative. Firstly we guess a temperature which allows us to calculate the vapour pressure Po
for each component (the vapour
pressures of pure components can be calculated using the Antoine Equation - Antoine Coefficients for many components are presented elsewhere on this
site).
The pure component vapour pressures can then be used to calculate the liquid mole fraction for each component, x, using the above equation. The sum of
all the liquid mole fractions should add up to 1 at the dew point. If the sum is greater than 1, the temperature guess is too low. If the sum is less than 1, the
temperature guess is too high. Adjust the temperature until the liquid mole fractions add up to 1.
Example Calculation: Estimating the Dew Point
A gas has the following composition: 75mol% n-pentane, 20mol% n-hexane, 5mol% n-heptane. What is its Dew Point at atmospheric pressure (760 mmHg)?
The normal boiling points of pentane, hexane and heptane are 36oC, 69
oC and 98
oC respectively, so the dew point at atmospheric pressure will lie within this
temperature range. As a first guess, take a temperature of 40oC.
The vapour pressure of each component can be estimated using their Antoine Equation (see our separate article). So at 40oC, the vapour pressure of each
component is as follows:
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Assuming ideal behaviour, the liquid mole fractions at the dew point can be calculated using:
Thus
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Adding the liquid mole fractions together gives: 0.655 + 0.542 + 0.409 = 1.606. This is greater than 1, meaning that 40oC is below the dew point. Re-guessing
the temperature at 50oC, 58
oC, 53
oC and 54
oC:
Temperature 40oC 50
oC 58
oC 53
oC 54
oC
xPentane 0.655 0.475 0.374 0.434 0.421
xHexane 0.542 0.374 0.283 0.336 0.325
xHeptane 0.409 0.267 0.194 0.237 0.227
Total 1.606 1.116 0.851 1.006 0.972
Table 1: Dew Point Calculation – temperature iteration
As can be seen in the table above, the dew point for this mixture at atmospheric pressure is just over 53oC.
Bubble Point Calculation
The bubble point is the temperature at which a liquid mixture will start to boil. As with a dew point calculation, we can use Dalton's and Raoult's Laws to
calculate the bubble point. By combining the two equations, we can calculate the vapour mole fractions for a given liquid composition, i.e.:
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Again, as with the dew point, calculating the bubble point is iterative. Firstly we guess a temperature which allows us to calculate the vapour pressure Po
for
each component. This is then used to calculate the vapour mole fraction for each component, y, using the above equation. The sum of all the vapour mole
fractions should add up to 1 at the bubble point. If the sum is greater than 1, the temperature guess is too high. If the sum is less than 1, the temperature
guess is too low. Adjust the temperature until the vapour mole fractions add up to 1.
Example Calculation: Estimating the Bubble Point
A liquid has the following composition: 75mol% n-pentane, 20mol% n-hexane, 5mol% n-heptane. What is its Bubble Point at atmospheric pressure (760
mmHg)?
The normal boiling points of pentane, hexane and heptane are 36oC, 69
oC and 98
oC respectively, so the bubble point at atmospheric pressure will lie within
this temperature range. As a first guess, take a temperature of 40oC.
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The vapour pressure of each component can be estimated using their Antoine Equation (see our separate article). So at 40oC, the vapour pressure of each
component is as follows:
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Assuming ideal behaviour, the vapour mole fractions at the bubble point can be calculated using:
Thus
Adding the vapour mole fractions together gives: 0.857 + 0.074 + 0.006 = 0.937. This is less than 1, meaning that 40oC is below the bubble point. Re-guessing
the temperature at 50oC, 45
oC, 42
oC and 41
oC:
Temperature 40oC 50
oC 45
oC 42
oC 41
oC
yPentane 0.857 1.183 1.011 0.918 0.888
yHexane 0.074 0.107 0.089 0.080 0.077
yHeptane 0.006 0.009 0.008 0.007 0.006
Total 0.937 1.299 1.108 1.005 0.971
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Table 2: Bubble Point Calculation – temperature iteration
As can be seen in the table above, the bubble point for this mixture at atmospheric pressure is just under 42oC.