The diffusivity of the gas pair $O_2-CC{l}_4$ is being determined by observing the steady$-$state evaporation of carbon tetrachloride into a tube containing oxygen, as shown in Figure $($A here denotes $CC{l}_4$ and $B$ denotes $O_2).$ The distance between the $CC{l}_4$ liquid level and the top of the tube is $y_2-y_1=17\mathrm{.}1cm.$ The total pressure on the system is $755mmHg,$ and the temperature is $0C.$ The vapor pressure of $CC{l}_4$ at that temperature is $33\mathrm{.}0mmHg$ and its liquid density is $1\mathrm{.}59\frac{g}{c}{m}^3.$ The cross$-$sectional area of the diffusion tube is $0\mathrm{.}82c{m}^2.$ It is found that $0\mathrm{.}0208c{m}^3$ of liquid $CC{l}_4$ evaporates in a $10-$hour period after steady state has been attained. It may be assumed that the partial pressure of $CC{l}_4$ at $y=y_2$ is zero. Also, assume that $O_2$ is completely insoluble in $CC{l}_4.$ What is the diffusivity of the gas pair $O_2-CC{l}_4(D_{O_2-C{l}_4})$ at $0C?$

Gas Stream of A and B

$($a$)$ Rework the problem of mass$-$transfer through a stagnant gas film $($Stefan$\text{'}$s Problem$)$ discussed in class by neglecting the convective flux of A$.$ Show that this leads to:

$N_{Ay}=\frac{c{D}_{AB}{x}_{A1}}{L}$

In the above expression, symbols have their usual meanings as discussed in class and it is also assumed that the flowing gas$-$stream at the top the tube is pure B$.$

$($b$)$ The above expression in $($a$)$ is a useful approximation if A is present only in very low concentrations. What is the error made in determination of $D_{O_2-CC{l}_4}$ in Problem $2,$ if the result in Problem $3($a$)$ is used?