Distillation

Distillation involves the creation of vapor-liquid (equilibrium) mixtures by the addition of heat. Antoine equation which is an empirical way of relating the vapor pressure to the temperature.

Bubble Point: If a mixture of specific composition is heated, the temperature at which the first bubble of vapor appears is known as the bubble point. The total vapor pressure generated by the components together becomes equal to the imposed pressure. Dew Point: When a mixture is cooled, at a fixed pressure, the temperature at which the first drop of liquid appears is known as the dew point.

Calculating Bubble & Dew Points for Ideal Mixtures.

When a liquid mixture begins to boil, the vapor 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,

PA - Partial pressure of component A

PoA - 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:

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, 69oC and 98oC 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 behavior, the liquid mole fractions at the dew point can be calculated using:

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, 58oC,

53oC and 54oC:

Temperature 40oC 50oC 58oC 53oC 54oC

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 vapor 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 vapor pressure Po for each component. This is

then used to calculate the vapor mole fraction for each component, y, using the above

equation. The sum of all the vapor 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, 69oC and 98oC 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:

Adding the vapor 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, 45oC, 42oC and 41oC:

Temperature 40oC 50oC 45oC 42oC 41oC

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.

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Difference between total and Partial Condenser:

In a total condenser the temperature is lowered to a level on which all gasses turn to liquids.

With a partial condenser you can separate gasses on their dew point. It means that the

temperature is set to a level on which one or several gasses leave the partial condenser as a

liquid and the others as a gas.

Relative Volatility

In order to separate a binary mixture using distillation process, there must be differences in volatilities of the components. The greater the difference, the easier it is to do so. A measure for this is termed the relative volatility.

We define volatility of component-i as: partial pressure of component-i divide by mole fraction component-i in liquid

For a binary mixture of A and B, therefore:

Volatility of A = pA / xA

Volatility of B = PB / xB

Where p is the partial pressure of the component and x is the liquid mole fraction.

Relative volatility is the ratio of volatility of A (MVC) over volatility of B (LVC):

Relative volatility is therefore a measure of separability of A and B.

Since xB = 1 - xA, we have:

Replace with pA = yA PT; pB = (1 - yA) PT so as to express everything in MVC:

Dropping subscript 'A' for more volatile component, and simplifying: we obtain the equation for

relative volatility:

When a = 1.0, no separation is possible: both component-A and component-B are equally volatile. They will vaporize together when heated. Solving the above equation for a = 1.0, we obtain: y = x.

The larger the value of a above 1.0, the greater the degree of separability, i.e. the easier the

separation. Recall that when a system has reached equilibrium, no further separation can take

place - the net transfer rate from vapor to liquid is exactly balanced by the transfer rate from

liquid to vapor. Therefore, separation by distillation is only feasible within the region bounded by

the equilibrium curve and the 45o diagonal line. From the equilibrium curve, we see that the

greater the distance between the equilibrium curve and the diagonal line (where y = x), the

greater the difference in liquid and vapor compositions and therefore the easier the separation

by distillation. This is shown in the Figure below:

Composition Changes and Relative Volatility

Relative volatility of a mixture changes with the mixture composition. For example, compare

between the 2 mixtures: the Table below for benzene-toluene (ideal solution).

Note the widely varying values for ethanol-water mixture and the large deviation from avg., and

the relatively small deviation for benzene-toluene mixture. In the case of ethanol-water, we

cannot use the avg. to obtain the mixture VLE data as the results will be in gross error.

[Ref: http://www.separationprocesses.com/Distillation/DT_Chp01-3.htm]