# Diffusion Coefficient of O2 into N2 (Last Resort

• smoez
In summary, when solving this problem, make sure to use the correct collision cross section for nitrogen, and convert it into m2 before plugging it into the equation.
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

## Homework Statement

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.

## Homework 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

## 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:
The issue here is that you have used the wrong collision cross section for nitrogen. While the collision cross section of oxygen is 0.4 nm2, the collision cross section of nitrogen is 0.43 nm2. So, when calculating the diffusion coefficient using the equation mentioned in the homework statement, use the correct cross section value (0.43 nm2). Once you have done that, you need to convert the cross section into m2 by multiplying it with 10^-19. Then, you can plug in the other values in the equation and calculate the diffusion coefficient.

## What is the diffusion coefficient of O2 into N2?

The diffusion coefficient of O2 into N2 refers to the rate at which oxygen molecules diffuse into nitrogen molecules in a given environment. It is a measure of the ability of oxygen to spread or disperse throughout a gas mixture.

## How is the diffusion coefficient of O2 into N2 calculated?

The diffusion coefficient of O2 into N2 is calculated using Fick's Law of Diffusion, which takes into account factors such as the concentration gradient, temperature, and pressure of the gas mixture.

## What factors affect the diffusion coefficient of O2 into N2?

The diffusion coefficient of O2 into N2 can be affected by the temperature, pressure, concentration gradient, and the size and shape of the container in which the gases are contained. It can also be influenced by the type of gas mixture and the presence of other molecules that may interact with oxygen and nitrogen.

## Why is the diffusion coefficient of O2 into N2 important?

The diffusion coefficient of O2 into N2 is important in many scientific and industrial applications. It plays a crucial role in processes such as gas exchange in the lungs, combustion reactions, and the diffusion of gases in the atmosphere. It is also used to understand and optimize gas separation processes in industries such as chemical engineering and environmental science.

## How is the diffusion coefficient of O2 into N2 measured?

The diffusion coefficient of O2 into N2 can be measured using various experimental techniques such as gas chromatography, mass spectrometry, and diffusion cells. These methods involve measuring the change in concentrations of oxygen and nitrogen over time and using mathematical equations to calculate the diffusion coefficient.

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