In junior Chemical Engineering laboratory, you will study the diffusion and solubility of $C{O}_2$ in an

organic solvent using a diffusion cell like the one sketched here. Let's suppose that the gas space

at the top of the diffusion cell is approximately $2cm$ high and $4cm$ in diameter. Further suppose

that the gas in the head of the cell is pure $C{O}_2$ at $298K$ and $1$ bar pressure. Note that $C{O}_2$ has a

collision diameter $d$ of $0\mathrm{.}40nm.$

What does gas kinetic theory predict for the gas self$-$diffusion constant $D_{11}$

of $C{O}_2$ gas in the cell, in $c{m}^2{s}^{-1}?$

Use the Stokes$-$Einstein relationship to estimate the diffusion constant of $CO$

$2$ in the Stoddard solvent. How does this compare with the diffusion constant in

the gas phase? Why?

We found in class that the probability for a molecule to diffuse a distance $x$

in time $t$ is Gaussian with mean $0$ and standard deviation $=\sqrt[\phantom{2}]{2D_{11}t}.$ About

how long will it take for $\frac{1}{3}$ of the molecules starting at the center of the gas

space to diffuse all the way to the surface of the liquid, i$.$e$.,>1cm?$

How many collisions on average does one of these diffusing $C{O}_2$ molecule

make with other gas molecules on the way from the middle of the vapor space

to the surface of the solvent?