Raoult’s law , Dalton’s law , Concept of Volatility and

Relative Volatility as applied to Distillation

Content

Introduction of Mass Transfer OperationDistillationRaoult’s lawDalton’s lawVolatilityRelative volatility

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.

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.

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

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.

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

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.

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 .

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. 

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.

Phexane = Pohexane . x hexane

Ppentane = Popentane. 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

From ideal gas law we get the equation. Ypentane =

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

Ptotal = xpentane (Popentane – Po

hexane) + Pohexane

Finally, the combination of equations ,plus Raoult's law, allows the calculation of the mole fraction of pentane in the vapor state.

Ypentane =

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.

Reference

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

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