Diffusion Coefficient Calculation

[smoez]

Hello everyone i've been stuck on this problem for four days now and its nearing the due date, I don't know what to do I've hit a wall with my solution posting online is my last resort
The problem, all variables and given/known data
Consider a horizontal glass tube with an inner diameter of 5 mm and a length, L, of 500 mm filled with pure nitrogen gas at a temperature of 25C, pressure of 101.3kPA. The tube is capped at both sides. At t=0 one cap is removed exposing one end to oxygen gas at same temperature and pressure.


Calculate the Diffusion Coefficent of oxygen gas in a binary mixture of nitrogen gas with these conditions.


Relevant equations


Diffusion Equation
$\displaystyle D = \frac {3 \pi}{8} (\frac {k T}{2 \pi \mu})^{0.5} \frac {1}{\rho \sigma}$
k is the boltzmann constant
T is temperature
$\displaystyle \mu = \frac {m1 m2}{m1 + m2}$ is reduce mass, m is mass
$\displaystyle \sigma N_2 = 0.43 nm^2$ is the collision cross section of Nitrogen (O₂ = 0.4 nm²)
$\displaystyle \rho$ is the density


Attempt
My attempt at a solution started with calculating the moles of Nitrogen Gas using the cylinder parameters
$\displaystyle n = \frac {PV}{RT}$, where $\displaystyle V = \pi r^2 L$
$\displaystyle n = \frac {101300 \times \pi \times (0.0025^2) 0.5}{8.31\times 298}$
$\displaystyle n = 4.00 \times 10^{-4} mol$


Then solved for mass
$\displaystyle m = n\times Molar Mass Nitrogen/1000$
$\displaystyle m = 4.00\times 10^{-4} \times 28.02/1000$
$\displaystyle m = 1.10\times 10^{-5} kg$


Then solved for density
$\displaystyle \rho = \frac {1.10\times 10^{-5}}{ pi(0.0025^2)0.5}$
$\displaystyle \rho = 1.14 kg/m^3$


Heres where I get stuck: I originally DID NOT notice that $\displaystyle \sigma$ was in nm² and continued using $\displaystyle \sigma = 4.3\times 10^{-10} m$ and solved for a diffusion coefficient of ~5 x 10^-1 m²/s. I know this is wrong but the value makes sense as the two molecules are gasses meaning diffusion is fairly rapid. Using the correct $\displaystyle \sigma = 1.89 \times 10^{-19} m$ I get like 5000000 m² /s which is incorrect obviously. However, I don't know where i went wrong I looked through my calculations several times and I really don't know what to do


Please please help!