Dalton Law, Daltons law formula and Results Law for Distillation

Dalton's law, It states that the total pressure exerted by a gas/vapour mixture is equal to the sum of the partial pressures of components present in it. Thus, it expresses the addictive nature of the partial pressures.

Mathematically, for a binary system:

P = pa +pb, Where P is the total pressure. 

For an ideal gas or vapour, the partial pressure is related to the mole fraction of the component in the gas or vapour phase by the relation.

 {tocify} $title={Table of Contents}

The formula of partial pressure

Partial pressures = Mole fraction X Total pressure

Thus, for Component A Or (a) 

pa = ya. P, where ya is the mole fraction of A in a vapour phase.

Knowing the vapour pressures of components A and B at various values of temperature, x-y data can be generated for an ideal solution as follows:

pA = pA. xA

pB = pB. (1-xA) 

pA = yA. P

pB = yB. P

Wet get

pA. xA = yA. P

yA = pA/P. xA-------- 01

Similarly  yB = pB/P.xB

We have  yB+yB = 1 and xB = 1-xA

yA + yB = 1

Putting values of yA and yB from equations up, and of xB in terms of xA we get

pA/P.xA + pB/P (1-xA) =1

pA. xA + pB. - pB. xA = P

xA(pA - pB) = P - pB

xA = P - pB/pA - pB

Knowing xA corresponding equilibrium value of vapour phase concentration yA is obtained with the help of equations (--01). 

Raoult's Law

It is commonly used for predicting the vapour-liquid equilibrium for an ideal solution in equilibrium with an ideal gas mixture from the pure component vapour pressure data. It states that the equilibrium partial pressure of a component/constituent in a solution at a given temperature is equal to the product of its vapour pressure in the pure state and its mole fraction in the liquid phase. 

Thus, for a binary (two-component) system, if pA is the equilibrium partial pressure of A pA is the vapour pressure of A in the pure state and xA is the more fraction of A in the liquid phase, then, 

The formula of Raoult's law

pA = pA xA and pB = pB xB

= pB(1 - xA) as xA + xB = 1

Where

pB = equilibrium partial pressure of B

xB = mole fraction of B in liquid phase

pB = vapour pressure of pure B.

Relative volatility

The volatility of A, It is defined as the ratio of the partial pressure of A to the mole fraction of A in a liquid phase. 

Relative volatility formula

The volatility of A = pA/xA

Similarly 

Volatility of B = pB/xB

The relative volatility of component A concerning component B is the ratio of the volatility of A (the more volatile component) to the volatility of B. It is also known as the volatility of A concerning B and is denoted by the symbol aAB. 

Relative volatility is the measure of separability by distillation. When @=1 a separation by distillation is not possible. The separation by distillation is possible for relative volatility values greater than one. The larger the value of the relative volatility, the easier the separation by distillation. 

Take these Notes is, Orginal Sources: Unit Operations-II, KA Gavhane

>Differential or Simple Distillation