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!
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!