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Assuming a typical nitrogen or oxygen molecule is about 0.3 $\mathrm{nm}$ in diameter, what percent of the room you are sitting in is taken up by the volume of the molecules themselves?

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$0.07 \%$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

Lectures

01:41

Imagine you are sitting in…

02:55

01:23

At room temperature, what …

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For a room $3.0 \mathrm{~m…

01:05

The diameter of nitrogen …

03:26

Estimate the number of air…

02:28

Assuming a nitrogen molecu…

03:42

How many molecules are the…

02:27

If oxygen is $21 \%$ by mo…

02:02

How many $O_{2}$ molecules…

01:44

Estimate the fraction of m…

04:13

Calculate the frequency of…

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(II) Is a gas mostly empty…

02:21

What is the total mass of …

01:22

So we're doing Chapter 18 problems. 65 here. So it says assuming a typical nitrogen or oxygen molecule is about 0.3 nana meters in diameter, what percent of the room you are sitting in is taken up by the volume of these molecules themselves? So we want to find the volume allotted per molecule for a room at one atmosphere 23 degrees Celsius. That's roughly room temperature. And we want to compare this to the volume of an actual molecule modeled by a cubicle ball. You okay? So TV nickels in K B t r I O Gasol, we rearrange for ve call this our allotted boy. So let's be over in the total volume over the total number of molecules and that's given as k b t over now, the actual D molecule. If we model these as to book cubicle volumes between each molecule in Cuba, Gladys, this is gonna be roughly d cubed. Is this d being what they have up there? So if we want to find the percent of the room picking up by the volume of the molecules themselves, then we can take the of the molecule over the allotted for the entire room. Right? So this is given now, as do you Cube over Tbt comes be so we can plug all the sin now. So if we're at one atmosphere, that's 1.13 times 10 to the fifth Pascal's And now our D is 0.3 times 10 to the negative nine meters cube. Take that all over. 1.38 times 10 in the negative, 23 jewels for Kelvin Times to 90 rooms comes 300 copan. Okay, so this comes out to be probably 6.6 times 10 to the negative. For if we put that in percentages, we times it by 100 so 6.6 times 10 to the negative, four times 100 is 0.0 66% or 0.7%. So a very small Harry very, very small amount of the room is actually being taken up by molecules themselves and most of the rooms just space between which, probably what you could imagine

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