calculation of bubble and dew point

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Calculation of Bubble and Dew point 2013

Syed Muzamil Ahmed Email: [email protected]

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.





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





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:





Assuming ideal behaviour, the liquid mole fractions at the dew point can be calculated using:

Thus





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.:





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.





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:





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





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.

calculation of bubble and dew point

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