How Many Neon Molecules Have Velocities Between 100 and 200 m/s?

[marmot]

Homework Statement

A sealed bottle at 1 atm of pressure holds 1 mole of neon and 1 mole of argon gas at a temperature of 295 K.

Find the number of molecules of neon which have velocities between 100 and 200 (m/s).

Homework Equations

boltzman distribution

The Attempt at a Solution

"%Maxwell-Boltzmann velocity distribution
syms v
m= 0.0201797;
T=295;
R=8.31
btm=2*pi*R*T;
exponet=((-m*v^2)/(2*R*T))
F=[(4*pi*((m/btm)^1.5))*v^2*exp(exponet)]*1E24
ezplot(F,[0 1500])
integral_all=vpa(int(F, v, 0, inf))
%integral_all = 1 so it checks out
integral_range=vpa(int(F, v, 100, 200))


so I plotted the speed distribution and integrated it from 0
to infinity and it equals 1, so I think I'm on the right
track. However you'll notice the y-axis units don't really
make sense. Even when I fudge it by E24 it's still doesn't
come out right. (I know what you're thinking about a 24
order of magnitude fudge) I get about 4E20 particles which
apparently isn't the right answer. After all this, I'm not
sure if I can bring myself to count up the little hash marks
on the screen to get the area, at least not tonight anyway. "

I copied this from my class's forum btw. i didnt write this but i did exactly the same thing (and no i didnt copy him, its just the obvious choice). can someoene help us tellin us what in gods name we are doing wrong?

 

[marmot]

nvm i solved it

 

[nlightner]

Hello there,

It seems like you are on the right track with your approach to using the Maxwell-Boltzmann distribution to find the number of molecules with velocities between 100 and 200 m/s. However, there are a few things that may be causing your results to be incorrect.

First, it is important to note that the Maxwell-Boltzmann distribution is a probability distribution, meaning it gives the probability of finding a molecule with a particular velocity at a given temperature. So, when you integrate the distribution, you are actually finding the probability of finding a molecule with a velocity within a certain range.

Second, the units of your y-axis do not make sense because you have not taken into account the units of your other variables. In your equation for F, you have multiplied by 1E24, but this does not match the units of the rest of the equation. It may be helpful to check the units of each term in the equation and make sure they all match.

Lastly, when you integrate the distribution, you should only integrate over the range of velocities you are interested in, not from 0 to infinity. This will give you the probability of finding a molecule with a velocity between 100 and 200 m/s.

I hope this helps clarify the issue and points you in the right direction. Keep in mind that the Maxwell-Boltzmann distribution is just one tool in understanding the behavior of gases at a molecular level, and there may be other factors at play in this specific scenario. It may be helpful to discuss your approach with your instructor or classmates to get a better understanding of the problem and how to solve it. Good luck!