A tube with an inside diameter of $1$ cm and length of $30$ cm is filled with air $($B$)$ and CO$2($A$)$ at a total pressure and temperature of $1$ atm and $3$C$,$ respectively. If the partial pressure of CO$2$ is $0\mathrm{.}75$ atm at one end of the tube and $0\mathrm{.}25$ atm at the other end, find the rate of mass transfer of CO$2$ for the steady$-$state counter diffusion where NB $=-0\mathrm{.}55$ NA $($You can take gas constant $($R$)$ as $8314$ m$3$Pa$/$kgmol$$K$)$

Can you provide a detailed step$-$by$-$step solution using mass transfer formulas?