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##### 1.7 Constant of Relative Volatility (CRV)

The constant of relative volatility is defined as the ratio between the distribution coefficients of the two components:

aAB = kA/ kB

from which also

aAB = PAv/ PBv

The here above correlations are valid only for binary, ideal systems, following Raoult's law. In this case it is possible to write the following system of equations:

(1)     yA = kA xA;
(2)     1-yA = kB (1-xA);

dividing (1) by (2) and rearranging leads to:

(3) yA = aAB xA / [1 + (aAB - 1) xA]

The relative volatility is often a weak function of temperature and therefore can be considered as constant in a reasonable small range of temperature.
Correlation (3) is also the equation of a curve and can be represented in a x-y diagram as shown below: top

##### Constant of relative volatility for multicomponent system

In the most general case the distribution coefficient for component i is:

ki = [gi f Li,pure] / [fi P ]

but for most practical cases [see assumption in the previous section] we can write:

ki = [gi Pvi] / P

or in the case of ideal mixture when Raoult's law is valid:

ki = Pvi / P

For multicomponent systems it is useful to define the constant of relative volatility with respect to a reference component r:

ai = ki/ kr

with

kr = yr / xr;

Under this assumption one gets:

S yi = kr S ai xi

kr = 1 / S ai xi;

yi = ai xi / S ai xi

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