How Long Does It Take for D2 and He-3 Gases to Diffuse Completely in a Pipe?

[gcossio14]

Homework Statement

I don't know how to approach this problem, any help would be appreciated.

i have a pipe 1 meter in length and 4mm in diameter. it containts 2 gases, D2 and He-3.
each half of the pipe contains the 2gases and they are both at 400psi.
how long does it take the gases to diffuse across the pipe completely?

thanks.

Homework Equations

ive looked into grahms law of diffusion but that doesn't seem to be helpful at all in this situation since it give me a proportional rate b/w two different molecules of gas

The Attempt at a Solution

as far as I've gotten is finding the volumes of gas in each half of the pipe... not very far.

 

[anathema]

Thank you for posting your question. I understand your confusion and I am happy to help you approach this problem. To start, let's review some key concepts related to gases and diffusion.

Firstly, gases tend to mix and spread out evenly in a process called diffusion. This happens because gas particles are in constant motion and will naturally move from areas of high concentration to areas of low concentration.

Secondly, Graham's law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its density. This means that lighter gases will diffuse faster than heavier gases.

Now, let's apply these concepts to your problem. You have a pipe that is 1 meter in length and 4mm in diameter, and it contains two gases, D2 and He-3. Each half of the pipe contains the two gases at a pressure of 400psi. To determine how long it will take for the gases to diffuse completely across the pipe, we will need to consider the following factors:

1. The molecular weight of each gas: D2 has a molecular weight of 4 g/mol and He-3 has a molecular weight of 3 g/mol. This means that D2 is heavier than He-3 and will diffuse slower.

2. The pressure of the gases: Both gases are at a pressure of 400psi, which means that they are in equilibrium and there is no net movement of gases between the two halves of the pipe.

3. The volume of each gas: You mentioned that you have already calculated the volumes of gas in each half of the pipe. This is a good start, as it will help us determine the initial concentrations of each gas in the pipe.

To find the final concentrations of each gas in the pipe, we can use the ideal gas law: PV = nRT. Since the pressure and temperature are constant, we can rearrange the equation to find the number of moles (n) of each gas in the pipe. From there, we can calculate the final concentrations of each gas by dividing the number of moles by the total volume of the pipe.

Finally, we can use Graham's law of diffusion to calculate the rate of diffusion for each gas. Since the gases are at the same pressure, we can use the ratio of their molecular weights to determine the ratio of their diffusion rates. This will give us an idea of how much faster one gas will diffuse compared to the other