Question$-3$:

A narrow tube contains Acetone $((C{H}_3{)}_{2}CO)$ at a constant temperature of $313K.$ The total pressure of air $($assumed dry$)$ is $1\mathrm{.}01{10}^{5}Pa.$ Acetone evaporates and diffuses through the air in the tube. The initial height of the acetone was $11mm$ when measured from the top. After sometime during the experiment, the liquid level decreased due to evaporation. The final height recorded was $12mm$ from the top. There is no acetone vapor in the air. However, the air is humid with a percentage relative humidity $\%RH=30\%.$

Assume that the system is isothermal. $($Given Data: Acetone vapor pressure at $313K=55,864$ Pa; Diffusion coefficient $=1\mathrm{.}38{10}^{-5}\frac{m^2}{s}$; Density ~$=785k\frac{g}{m^3}$;$MW=58\mathrm{.}08kg$ per kgmol;$R=($:$8314\frac{m^3.Pa}{\text{k}\text{g}\text{m}\text{o}\text{l}\text{.}K}\}.$

Determine the time taken in the experiment.

Compute the diffusion coefficient of acetone$-$air system for the above case using Fuller et al$.$ correlation and compare its value with the reported value above.