Question

If the fugacity coefficient of the components of a binary mixture are = 0.784, and =0.638 and mole fraction of component 1 is 0.4, write down and expression for the fugacity coefficient Inp, for the mixture.

Answer 1

Answer : The expression for the fugacity coefficient $\ln \phi$, for the mixture is, -0.3669.

Explanation : Given,

Fugacity coefficient of component 1 = 0.784

Fugacity coefficient of component 2 = 0.638

Mole fraction of component 1 = 0.4

First we have to calculate the mole fraction of component 2.

As we know that,

$\text{Mole fraction of component 1}+\text{Mole fraction of component 2}=1$

$\text{Mole fraction of component 2}=1-0.4=0.6$

Now we have to calculate the expression for the fugacity coefficient $\ln \phi$.

Expression used :

$\ln \phi=X_1\ln \phi_1+X_2\ln \phi_2$

where,

$\phi$ = fugacity coefficient

$\phi_1$ = fugacity coefficient of component 1

$\phi_2$ = fugacity coefficient of component 2

$X_1$ = mole fraction of of component 1

$X_2$ = mole fraction of of component 2

Now put all the give values in the above expression, we get:

$\ln \phi=0.4\times \ln(0.784)+0.6\times \ln(0.638)$

$\ln \phi=-0.3669$

Therefore, the expression for the fugacity coefficient $\ln \phi$, for the mixture is, -0.3669.