Topic 1: Vapour-Liquid Equilibrium

Question 1

What is an intensive variable?

Answer 1

Intensive variables are constant throughout a given phase or possibly throughout the whole system ( density, temperature, pressure)

Question 2

What is the phase rule

Answer 2

The rule states that the number of degrees of freedom is equal to the number of chemical components plus 2 minus the number of phases

Nf=Nc +2 - Np

Question 3

How many degrees of freedom does a binary mixture in two- phase vapour- equilibrium have?

Answer 3

It has two degrees of freedom because if we use the phase rule the number of degrees of freedom is equal to the number of components which is two (binary mixture) + 2 minus the number of phases which is 2 (two phase system). 2+2-2 is equal to 2.

Question 4

What is the more volatile component?

Answer 4

If we have a binary mixture (two components where the total number of moles is equal to the number of moles of component 1 and number of moles of component 2)
The notation for the mole fraction of component i (where i is equal to 1 or 2 depending on which component you want to refer to) is :
xi= ni/(n1+n2) Where ni is the number of moles of component i

Since the two mole fractions add up to unity, we specify just the mole fraction of component 1.

Component 1 is then normally chosen to be the more volatile component.

Question 5

What is the notation for the more volatile component?

Answer 5

z: refers to the mole fraction of the more volatile component in the feed of a steady flow process or in the whole system of a batch process
x: refers to the mole fraction in the liquid phase
y: refers to the mole fraction in the vapour phase

Question 6

Describe the five stages of expansion of a mixture in a variable volume

Answer 6

Imagine a syringe containing liquid, closed at one end and plunger free to move regulated at atmospheric pressure. Basically as we move from stage 1 to stage 5 the mixture expanded, increasing the volume and increasing the temperature.

Stage 1: we have a sub-cooled liquid state, we have a single homogenous liquid phase
Stage 2: we have the bubble point as the mixture expands and the volume increases. This is where the first bubble of vapour appears.
Stage 3: the volume increases as the mixture continues to expand. This is an point in the two phases region. Macroscopic amounts of liquid and vapour appear.
Stage 4: we have the dew point. This is the vanishing point of the last drop of liquid.
Stage 5: we have superheated vapour. This is a single homogenous vapour phase.

Question 7

What is the material balance equations for binary VLE (molar basis)?

Answer 7

We’re looking at stage 3 of the expansion of a mixture in a variable volume and we’re concerned with the more volatile component ( x, y, z notation)

nmix =nL +nV

z.nmix = x.nL + y.nV

z= qx+ (1-q)y

Where q is the liquid fraction
q=nL/nmix= (y-z)/(y-x)

Question 8

What is the enthalpy balance for binary VLE?

Answer 8

hmix = qhL + (1-q).hV

Question 9

What is an extensive variable?

Answer 9

An extensive variable scales with the system size such that, in the system is divided into two parts, the value for the whole system is the sum of the values of the two parts

Question 10

How do you use the phase rule for a binary system?

Answer 10

A binary mixture in a two phase vapour liquid equilibrium contains two components and two phases. Therefore it has two degrees of freedom according to the phase rule.

If temperature or pressure is fixed using experimental VLE measurements, then one degree of freedom remains.

The state of the system can then be determined by one composition variable because the equilibrium temperature can be modelled as a function of the mole fraction x.
T=T(x).
y=y(x)

Question 11

What does x generally represent in a mixture

Answer 11

x represents the mole fraction of component 1 in the liquid

Question 12

What does y generally represent in the mixture?

Answer 12

y represents the mole fraction of component 1 in the vapour

Question 13

What’s is the mole fraction of component i?

Answer 13

The mole fraction of component i is the number of moles of component i divided by the total number of moles.

xi= ni/(n1+n2)

Where ni is the number of moles of component i
And n1+n2 is the total number of moles in a binary mixture.
And i can either be component 1 or component 2

Question 14

What does the composition variable z represent in a binary mixture?

Answer 14

z represents the mole fraction of the more volatile component (MVC) in the feed for a steady flow process or in the whole system for a closed batch process.

Question 15

What does the composition variable y represent in a binary mixture.

Answer 15

y represents the mole fraction of the more volatile component in the vapour phase.

Question 16

What does the composition variable x represent in a binary mixture?

Answer 16

x represents the more volatile component (MVC) in the liquid phase.

Question 17

What classifies a component as more volatile?

Answer 17

the more volatile component will have a lower boiling point than that of the other component

Question 18

What is the bubble point?

Answer 18

The bubble point is the appearance point of the first bubble of vapour.

Question 19

What is the dew point?

Answer 19

The dew point is the vanishing point of the last droplet of liquid.

Question 20

What is the material balance for binary VLE?

Answer 20

N(mixture)= N(liquid)+ N(vapour). OVERALL
total number of moles is equal to the number of moles of liquid + the number of moles of vapour

zN(mixture)= xN(liquid)+ yN(vapour). MVC
total number of moles of the more volatile component….

z= qx +(1-q)y.
Where q is the liquid fraction

Question 21

What is the liquid fraction?

Answer 21

q= N(liquid) / N(liquid) + N(vapour) = N(liquid) / N(mixture)
= (y-z)/(y-x)

Question 22

What is the enthalpy balance for binary VLE?

Answer 22

H(mixture) = H(liquid) + H(vapour). OVERALL ENTHALPY
total enthalpy of the mixture is equal to the total enthalpy of the liquid plus the total enthalpy of the vapour.

zh(mixture)= xh(liquid) + yh(vapour). SPECIFIC ENTHALPY X MOLE FRACTION GIVES TOTAL ENTHALPY

h(mixture) = qh(liquid) + (1-q)h(vapour)

Where q is the liquid fraction

Question 23

Why is the isobaric T,x,y diagram fixed at a pressure below the critical pressures of the two components?

Answer 23

The pressure is fixed below the critical pressures of both components so that their is coexistence over the full composition range.

Question 24

What does the blue curve on the isobaric T,x,y diagram represent?

Answer 24

The blue curve shows the bubble temperatures. These are the temperatures at which the first bubble of vapour appears in the MVC. It is the function T(x) where x is the liquid mole fraction of the MVC

Question 25

What does the red curve on the isobaric T,x,y diagram represent?

Answer 25

The red curve shows the dew temperatures. These are the temperatures at which the last drop of liquid of the MVC vanishes. It is a function T(y) where y is the vapour mole fraction of the MVC

Question 26

What do the end points of the isobaric T,x,y diagram represent?

Answer 26

The end points are the boiling points of the pure components.

x=0 is the boiling point of the LVC because in this case it is at a higher temperature
x=1 is the boiling point of the MVC because in this case it is at a lower temperature.

Question 27

If the mole fraction of the MVC in the feed is z=0.4 the when the mixture starts to boil, what is the mole fraction of the liquid in the MVC and at what temperature if the mixture.
(Slide 10)

Answer 27

When the mixture starts to boil there is only macroscopic amounts of liquid so therefore the mole fraction of the MVC is completely liquid. Therefore z=x. @ z=x=0.4 , T= 96 degrees Celsius

Question 28

If the mole fraction of the MVC in the feed is z=0.4 the when the mixtureis fully vaporised , what is the mole fraction of the vapour in the MVC and at what temperature if the mixture.

Answer 28

When the mixture is fully vaporised there is only macroscopic amounts of vapour. Therefore the MVC is fully vapour and z is equal to y. @ z=y =0.4 , T=102 degrees Celsius

Question 29

What is a tie line?

Answer 29

A horizontal tie line is a construction connecting the compositions of the coexisting phases because they’ll be at the same temperature and pressure

Question 30

Explain why the tie line is useful on the isobaric T,x,y diagram

Answer 30

There are two degrees of freedom for a binary VLE mixture according to the phase rule.

On the isobaric T,x,y diagram for a binary VLE mixture, the pressure is fixed to a value below the critical pressures of the two components (1 DOF)

The tie lines fixes the temperature. So with temperature and pressure fixed, there are no other degrees of freedom. (2 DOF)

With no other degrees of freedom, x and y can be fixed.

X is read from the bubble curve T(x)
Y is read from the dew curve T(y)

Therefore using the material balance: z=qx + (1-q)y
The liquid fraction can be found using : q=( y-z) / (y-x)

Question 31

How are vapour liquid equilibrium temperatures measured experimentally?

Answer 31

There are numerous methods but for low pressures (less than 5 bar) the recirculating method is the most common.

Question 32

Explain the recirculating method.

Answer 32

Glass apparatus is used.
Operated at constant pressure, usually atmospheric.
Liquid boils, condenses and the returns to the reboiler.
Liquid and condensed vapour phases are sampled at steady state and analysed to determine x and y values at measured temperature and constant pressure.
These values are then inputted to form the isobaric T,x,y diagram.

Question 33

What are k factors?

Answer 33

The k factor is the vaporisation equilibrium ratio which can be defined for component i as:

Ki= Yi/Xi

where for a binary mixture i is equal to 1 or 2

Question 34

How many k factors does a binary mixture have?

Answer 34

A binary mixture has two components so therefore it has two k factors.

K1= y/x.  MVC (component 1)
K2= (1-y)/(1-x).   COMPONENT 2

Question 35

Why are k factors useful?

Answer 35

The components of a mixture generally differ in volatility. Hence, coexisitng vapour and liquid phases generally have different compositions. K factors generally depend on temperature, pressure and composition in a very complex way.

Question 36

What is relative volatility?

Answer 36

Relative volatility for a binary mixture is defined as

a= k1/k2 = (y/x) / ( 1-y. / 1-x). = y(1-x) / x (1-y)

Therefore y= (a.x) / (1+x(a-1))

Question 37

What trend is observed with relative volatility when temperature increases at constant pressure?

Answer 37

Relative volatility decreases

Question 38

Why do separation processes normally happen below critical pressures according to relative volatilities?

Answer 38

Relative volatility tends towards 1at the critical point because at the critical point, the two phases become indistinguishable.
So x=y and therefore, k is equal to 1. (K=y/x=1/1=1).
Hence, separation processes normally operate below critical pressures so that there volatilities differ.

Question 39

What is the partial pressure in an ideal liquid mixture/

Answer 39

In an ideal liquid mixture, the partial pressure exerted by each component is the product of the liquid mole fraction and saturated vapour pressure Pi*

Partial pressure = xiPi*

Question 40

What is Raoult’s Law for ideal liquids?

Answer 40

Raoults law describes VLE in ideal mixtures.
Total pressure is given by the liquid mole fraction by saturated vapour pressure of both components of the binary mixture.

P= x1P1* + x2P2*

Question 41

How can Raoult’s Law be applied to non-liquids?

Answer 41

Vapour is treated as an ideal gas mixture, so the partial pressure of each component is; yiP

Therefore, yi.P xiPi*

And so, the vapour phase mole fraction are given by: yi = xi. Pi* / P

Question 42

What is an ideal k factor?

Answer 42

According to Raoult’s law, yi.P = xi. Pi* for ideal liquids and ideal vapours.

So if the k factor is k= yi / xi

Then the ideal k factor is k = Pi* / P

Question 43

What is ideal volatility?

Answer 43

If relative volatility is defined for a= k1/k2

Then for ideal gases and ideal liquids a= P1/P2

Therefore, for an ideal mixture, relative volatility is a function of temperature only (over a modest temperature range, so relative volatility is often taken to be constant)

Question 44

What do we need to be able to apply Raoult’s Law?

Answer 44

We need to know the vapour pressures of each component as a function of temperature.

NIST
Empirical correlations like Antoine’s equation

Question 45

What is Antoine’s equation?

Answer 45

log10(P*) = (A-B) / (T+C)
Where A,B,C are substance dependent parameters

Or expressed in dimensionless quantities:

log10(P/kPa) = (A-B) / (T/C+C)
These values have been tabulated for many substances but be careful with the units

Question 46

Does Raoult’s law apply to non-ideal mixtures?

Answer 46

No. Non ideal mixtures deviate from ‘Raoult’s law

Question 47

What is an azeotrope?

Answer 47

An azeotrope is the point of which liquid and vapour have the same composition. They prevent separation of binary mixtures by distillation only.

Question 48

What causes a minimum boiling temperature azeotrope?

Answer 48

Unfavourable’ interactions between the unlike molecules give positive deviations from Raoult’s law (total pressure greater than ideal) and can lead to a minimum-boiling-temperature azeotrope.

Question 49

What causes a maximum boiling temperature azeotrope?

Answer 49

Strong attractions between the unlike molecules give negative deviations from Raoult’s law (total pressure less than ideal) and can lead to a maximum-boiling-temperature azeotrope.

Question 50

What does a large k factor imply?

Answer 50

Large k factors implies high volatility of that component in the mixture

Question 51

What does a large k factor imply?

Answer 51

Large K factor implies high volatility of that component in the mixture

Question 52

What does large relative volatility imply?

Answer 52

Large α implies a vapour phase highly enriched in the MVC