Raoult’s law , Dalton’s law , Concept of Volatility and Relative Volatility as applied to Distillation,Introduction of Mass Transfer Operation

1. Raoult’s law , Dalton’s law , Concept of Volatility and
Relative Volatility as applied to Distillation

2. Content
 Introduction of Mass Transfer Operation
 Distillation
 Raoult’s law
 Dalton’s law
 Volatility
 Relative volatility

3. Introduction of Mass Transfer Operation
 Mass transfer is a transport of components under a chemical
potential gradient.
 The component moves to the direction of reducing concentration
gradient. The transport occurs from a region of higher concentration
to lower concentration.
 Equilibrium is reached when the gradient is zero. The transport or
migration of one constituent from a region of higher concentration to
that of a lower concentration is known as mass transfer.
 Mass transfer operations depend on molecules diffusing from one
distinct phase to another and are based upon differences in the
physico-chemical properties of the molecules, such as vapour
pressure or solubility. For interphase mass transfer, there is a
concentration gradient between bulk and interface, however under
steady state, at interface equilibrium is assumed.

4.  Mass transfer operation plays an important role in many industrial
processes.
 A group of operations for separating the components of mixtures is
based on the transfer of material from one homogeneous phase to
another.
 These methods is covered by the term mass transfer operations which
include techniques like gas absorption and stripping, liquid-liquid
extraction, leaching, distillation, humidification, drying, crystallization
and number of other separation techniques.

5. Distillation
 Distillation is an operation whereby a liquid mixture of miscible
and volatile substances is separated into individual components or
into group of components by partial vaporization.
 The separation of a mixture of methanol and water into its
components, and separation of petroleum crude into gasoline,
kerosene, fuel oil and lubricating stock are examples of distillation
process.
 The most common methods of distillation are simple distillation
and fractional distillation. Simple distillation can be used when the
liquids to be separated have boiling points that are quite different.
Fractional distillation should be used when the boiling points are
similar

6. Raoult's law
 The observation that the vapour in equilibrium with a mixture
is richer in the more volatile component is expressed
quantitatively as Raoult's Law.
 When two liquids that are completely soluble in one another
are mixed together, the partial pressure of a component
equals the product of its vapour pressure when pure at this
temperature and its mole fraction in liquid state .
PA
* = PA. xA
 Miscible pairs of liquids are said to behave ideally if the
contribution of each component to the total vapour pressure is
directly proportional to its mole fraction.

8. Dalton’s law
 It states that in a mixture of non-reacting gases, the
total pressure exerted is equal to the sum of the partial pressure of
the individual gases.
 This empirical law was observed by John Dalton in 1801 and is
related to the ideal gas laws.
PTOTAL= P1 + P2 + ......... + P3

9. Volatality
 Volatility is the tendency of a substance to vaporize.
 Volatility is directly related to a substance's vapour pressure.
 The volatility of any substance in a liquid solution may be defined as
the equilibrium partial pressure of the substance in the vapour phase
divided by the mole fraction of the substance in the liquid solution.
Va = Pa / Xa
 At a given temperature, a substance with higher vapour pressure
vaporizes more readily than a substance with a lower vapour
pressure.

10.  The volatility of a material in the pure state is equal to the vapour
pressure of the material in the pure state. Similarly, the volatility
of a component in a liquid mixture which follows Raoult’s law
must be equal to the vapour pressure of that component in the
pure state
 It is applied to liquids. it may be used to describe the process
of sublimation which is associated with solid substances, such
as dry ice(solid carbon dioxide) and ammonium chloride, which
can change directly from the solid state to a vapour without
becoming liquid .

11. Relative Volatility
 Relative Volatility is defined as the volatility of one
component of a liquid mixture divided by the volatility of
another component of the liquid mixture.
αab = Va / Vb
= Pa Xb / Xa Pb
 It is a measure comparing the vapour pressure of the
components in a liquid mixture of chemicals.
 It is widely used in designing large industrial
distillation processes.
 it indicates the ease or difficulty of using distillation to
separate the more volatile components from the less volatile
components in a mixture.

12. Example
 The boiling characteristics of a mixture of pentane and hexane.
 Pentane and hexane are miscible (mutually soluble), and their
molecules interact with one another only by weak van der Waals
forces. A solution composed of both pentane and hexane will boil at
temperatures intermediate between the boiling points of pentane (36
ᵒC) and hexane (69 ᵒC). If pentane alone was present, the vapor
pressure above the liquid would be due only to pentane.
 However, with pentane as only a fraction of the solution, the vapor
pressure exerted by pentane (P) will be equal to only a fraction of
the vapor pressure of pure pentane at the same temperature (Po),
where X is the mole fraction of pentane, the fraction of pentane
molecules in solution. The same is true for the hexane component.

13.  Phexane = Po
hexane . x hexane
 Ppentane = Po
pentane. xpentane
 Using Dalton's law of partial pressures, we can now
calculate the total vapor pressure of the solution, which is
the sum of the partial vapor pressures of the individual
components.
 Ptotal = Ppentane + Phexane
 Being able to calculate the total vapor pressure of a
solution can be extremely useful

14.  From ideal gas law we get the equation.
Ypentane =
Ppentane
Ptotal
 With the fact that the total mole fractions of pentane
and hexane must equal one, a single expression for
the total vapor pressure of the solution can be
derived.
xhexane + xpentane = 1

15.  Ptotal = xpentane (Po
pentane – Po
hexane) + Po
hexane
 Finally, the combination of equations ,plus Raoult's law, allows the
calculation of the mole fraction of pentane in the vapor state.
 Ypentane =
Po
pentane. xpentane
Xpentane (Po
pentane – Po
hexane) + Po
hexane
 So if we know the vapor pressures of pure pentane and pure hexane
at various temperatures and the composition of the liquid you can
calculate the fraction of pentane in the vapor above the solution.
This kind of calculation can be used to construct a temperature-
composition diagram, sometimes called a phase diagram.

17. Reference
 “Mass Transfer Operation”, third edition by Robert E.
Treybal

18. Thank you