TBR CBT 2 PS Question 6

[Eye Cue]

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6. Deuterium enrichment of a species would be enhanced by making which of the following changes in the effusion tube?


A. Increasing the radius
B. Decreasing the radius
C. Increasing the number of segments
C is the best answer. Deuterium enrichment of a species would be enhanced by increasing the length of the effusion tube. This can be accomplished by increasing the number of segments in the tube, making choice C the correct answer and choice D an incorrect answer. Since changing the effusion tube's radius does not affect the length of the tube, we can eliminate choices A and B. The best answer is C.
D. Decreasing the number of segments

Based on the passage, I understood as much as to eliminate A & B. However, I'm having trouble understanding conceptually why more segments would accomplish this. Any takers?

 

[loveoforganic]

I'll do the best I can without the passage. Different mass gases travel at different velocities when they are at the same temperature. For that reason, they effuse at different rates through a closed Vertical cylinder as well. Consider the two extremes. At one extreme, you have a flat cylinder. The gases never seperate from one another. At the other extreme, you have an inifinitely long tube. The gases will have tons of travel distance to separate and will thus become perfectly separated from each other. The same principle is used for uranium isotope purification (through uranium hexafluoride). Look that up if you'd like a more in depth explanation.

 

[Eye Cue]

Ah ha... so really, it didn't matter that the question mentioned Deuterium. I assume it could have been any gas in a sample of different molecular weight...

It's always the wording of certain questions that throws me off. I guess in a case like this it is safe to assume that 'enrichment' is synonymous to 'separation'.

 

[dennis-brodmann]

Based on the passage, I understood as much as to eliminate A & B. However, I'm having trouble understanding conceptually why more segments would accomplish this. Any takers?

I chose B because I thought that if one were to take the variation of the radius to an extreme such as making the radius SO SMALL that only H2(g) seemed to be able to effuse upon collision, that would separate the gases effectively.

I understand why C is right, but I'm trying to see why my rationale was wrong.
Deuterium has an extra neutron, right? Does that have the same radii to a hydrogen atom because we measure atomic/ionic/(and I guess) isotopic radii from the center of mass of the nucleons to the outermost electron?

 

[Sbr2250]

I chose B because I thought that if one were to take the variation of the radius to an extreme such as making the radius SO SMALL that only H2(g) seemed to be able to effuse upon collision, that would separate the gases effectively.

I understand why C is right, but I'm trying to see why my rationale was wrong.
Deuterium has an extra neutron, right? Does that have the same radii to a hydrogen atom because we measure atomic/ionic/(and I guess) isotopic radii from the center of mass of the nucleons to the outermost electron?

There's a few things you need to remember:

1) The size of an atom isn't as much due to its nucleus as it is due to its electron cloud- remember trends for atomic radius, which are based on the relative sizes of these clouds, and adding neutrons is negligible on a basic level.

2) Think about the overall goal of this effusion- to separate D2 from H2. If the radius were reduced so dramatically that only H2 molecules could fit through, the actual time for separation of these isotopes would be highly impractical. Think about trying to move water from one container to the next through a hole the size of a single water molecule. It would take forever. This is why C is also the better answer.

By increasing the segments in the tube, but holding the radius constant, you're effectively making the tube dramatically longer, which will make a big difference when you have two separate molecules traveling at different speeds.