  In this work, we have estimated self diffusion coefficients along with the
binary diffusion coefficients of mixtures of alkane (methane, ethane, propane
and n-butane) in SPC/E water(H$_2$O). Molecular dynamics study of a binary
mixture of alkane gas and SPC/E water, with alkane as solute and water as
solvent, have been carried out at different temperatures ranging from 283.15 K
to 333.15 K. We have taken a dilute solution of 3 alkane (methane, ethane,
propane and n-butane) molecules and 971 water molecules in a system. The role
of interaction in the structure of the constituents of the system as a function
of temperature is studied with the help of the radial distribution function
(RDF) and the coordination numbers. The self-diffusion coefficient of the
constituents of the mixture was calculated by using mean square displacement
(MSD) and the binary diffusion coefficients of alkane in water have been
calculated by using Darken's relation. The results are then compared with the
available experimental values. The values of self-diffusion coefficients of
water from the present work come in good agreement with the experimental values
within 9% error. The binary diffusion coefficients of ethane, methane, propane
and n-butane agree with the previously reported experimental values. The
dependence of the diffusion coefficients on temperature is approximated by
Arrhenius-type exponential relationship.
