How many argon molecules have velocities between 250 m/s and 500 m/s?

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SUMMARY

The discussion focuses on calculating the number of argon molecules with velocities between 250 m/s and 500 m/s in a sealed bottle containing 1 mole of argon and 1 mole of neon at 295K and 1 atm pressure. The key equations utilized include the kinetic energy formula KE = (3/2)kT and the velocity distribution function P(v) dv ∝ 4πv² e^(-(1/2)mv²/kT). The solution involves interpreting the velocity distribution graph, identifying the area under the curve corresponding to argon, and confirming that the argon curve is positioned above the neon curve due to its higher molar mass.

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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 295K. The curves in the Figure (http://phlnx3.pas.rochester.edu/webwork2_files/CAPA_Graphics/Gtype43/prob01a.gif) show the distributions of velocities of the molecules of each gas.
Find the number of molecules of argon which have velocities between 250 m/s and 500 m/s.

Homework Equations


KE = (3/2)kT
P(v) dv \propto 4πv^2 e^((-(1/2)mv^2)/kT) dv
Molar Mass of Argon = 0.03995 kg/mol

The Attempt at a Solution


Totally lost on how to set this one up. I get that I need some sort of bound on the probability of finding Argon between 250 and 500 m/s, and from there I can get an actual number, but for now I'm somewhat lost.
The graph might be giving me the answer right in front of me but I'm also having a hard time reading it (it doesn't help that it's not labeled which curve is which element...).
 
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Argon has a higher molar mass than neon. What does that tell you about which curve is which? As a last resort, you can count area under the curve from 250 to 500.
 
It should be the top curve since vrms would be lower than Neon. I thought it would be harder than that but I just manually calculated the area and got the right answer. Guess I was overthinking it. Thanks!
 

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