##### 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:

a_{AB} = k_{A}/ k_{B}

from which also

a_{AB} = P_{A}^{v}/ P_{B}^{v}
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) y_{A} = k_{A} x_{A};

(2) 1-y_{A} = k_{B} (1-x_{A});

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

(3) y_{A} = a_{AB} x_{A} / [1 + (a_{AB} - 1) x_{A}]

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:

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