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Altius COVID Exam #2- Question 7
Justine_5420
#1 Posted : Saturday, July 04, 2020 4:41:29 PM
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Hello,

I have a question pertaining to the Physical Sciences section on the Altius #2 COVID Exam. It is attached to a passage but doesn't require any information from the passage as it is given in the question stem.

This question asks how decreasing the length by 50% and increasing the radius by 100% will affect the number of moles in a new concentration vs. an original concentration. At first glance this is a chem question regarding the idea gas law, but as you look through the Altius solution, it looks like they are applying some physics principles. For example: as you increase the radius by a certain factor, you increase the pressure by that factor, and as you decrease length by a certain factor, you increase volume flow rate by that factor.

Can I approach this question like this? Using this method, I am having difficulty mathematically coming to the ration that they did to find the answer. Should I stick to the ideal gas law? In addition could you please explain how they found increases of a factor of 5 and 2?

Thank you in advance.
INSTR_Radhika_42
#2 Posted : Tuesday, July 07, 2020 5:03:23 PM
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Hello,

Thank you for your question!

In order for me to answer this best, would you be able to post or PM me the passage and solution?

I suspect this has to do with the shape of the container and potentially fluid dynamics which is why the solution may not have used Ideal Gas Law but I'd need more information to be able to shed light.

Thanks!
INSTR_Radhika_42
#3 Posted : Tuesday, July 07, 2020 6:02:13 PM
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Hi, I was able to get access to this question, here's a response to your inquiry:

The Altius solution makes use of Ideal Gas Law but takes a bit of a shortcut so that you don't have to recalculate the volume with the length and radius change.

The law states: PV = nRT and you're asked for a ratio of n2 to n1. Since you know that R and T are not changing you can simplify to PV = n. The ratio reads: n2/n1 = P2V2/P1V1

So ask yourself, do P and V change?

The passage indicates that at max contraction the P = 500 000 Pa and the initial P = 100 000 Pa, this ia 5-fold increase. If P2 increases by 5, then n2 increases by 5 as well for the equation to balance.

Now let's look at V.

Since length and radius change, the V changes. V = (pi)(radius squared)(L) You don't have to fill in all of the details - think about this in terms of proportions. L decreases by a FACTOR of 1/2 and R increases by a FACTOR of 2. So V2 = (pi)(2 radius squared)(1/2L) = (pi)(2R)(1/2L) = 2(pi)RL. The overall effect is that V increases by a factor of 2.

Let's consider both P and V changes together: if P increases by 5 and V increases by 2, then P2V2 increases by 5 x 2 = 10. Therefore, the ratio is 10:1.

Hope this makes sense!
Justine_5420
#4 Posted : Thursday, July 16, 2020 9:48:48 PM
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That's very helpful thank you so much! One follow up: why did you use the equation pi(r^2)x L for the volume?
INSTR_Radhika_42
#5 Posted : Monday, July 20, 2020 11:31:23 AM
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Good question - I saw this as a cylinder! You can use 'h' instead of 'L' if that's more intuitive :)
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