1. Mar 23, 2015

### smoez

Hello everyone, I've been stuck on this problem for three days now I just can't seem to make it work out to a reasonable value

1. The problem statement, 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.

2. Relevant equations

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

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

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

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

Heres where I get stuck: I originally DID NOT notice that $\sigma$ was in nm2 and continued using $\sigma = 4.3\times 10^{-10} m$ 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 $\sigma = 1.89 \times 10^{-19} m$ 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

Edit: did my best to correct the formatting, Borek.

Last edited by a moderator: Mar 24, 2015
2. Mar 29, 2015