In the absence of experimental data, the coefficient of diffusion in binary gaseous systems can be estimated by the Wilke$-$Lee equation:

D$\_$AB$=(\{3\mathrm{.}03-(0\mathrm{.}98/$M$\_$AB$^0\mathrm{.}5\}(10^(-3))$ T$^1\mathrm{.}5)/($PM$\_$AB$^0\mathrm{.}5\backslash$sigma $\_$AB$^2\backslash$Omega $\_$D $)$

where

DAB $=$ diffusion coefficient, cm$2/$s

MA$,$ MB $=$ molecular weights of A and B

T $=$ temperature, K

P $=$ pressure, bar

$\backslash$sigma AB $=$ collision diameter, a Lennard$-$Jones parameter, $$

$\backslash$Omega D $=$ diffusion collision integral, dimensionless

The collision integral is a function of the temperature and the intermolecular potential field for one molecule of A and one molecule of B$.$ It is tabulated as a function of T$*=\backslash$kappa T$/\backslash$epsi AB$,$ where $\backslash$kappa is the Boltzmann constant and $\backslash$epsi AB is the energy of molecular interaction of the binary system A and B$.$

An approximation of $\backslash$Omega D is obtained from the following equation

where T$*=\backslash$kappa T$/\backslash$epsi AB

a $=1\mathrm{.}06036$ e $=1\mathrm{.}03587$

b $=0\mathrm{.}15610$ f $=1\mathrm{.}52996$

c $=0\mathrm{.}19300$ g $=1\mathrm{.}76474$

d $=0\mathrm{.}47635$ h $=3\mathrm{.}89411$

For a binary system of nonpolar molecular pairs, the Lennard$-$Jones parameters may be obtained as follows

The interaction parameters for the pure components are usually obtained from viscosity data.

In the absence of experimental data, the values of the parameters for pure components may be estimated from the following empirical correlations:

where Vb is the molar volume of the substance as a liquid at its normal boiling point in cm$3/$gmol and Tb is the normal boiling temperature. The molar volume can also be estimated in the absence of data from the relation

where Vc is the critical volume.

Alternatively, the atomic volume of each element present is added together to give the overall molar volume.

Estimate the diffusivities of paracetamol $($C$8$H$9$NO$2)$ in water and ethanol at $298$ K and $1$ bar using the Wilke$-$Lee equation.

Figure $1$: Structure of paracetamol