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

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To determine the number of argon molecules with velocities between 250 m/s and 500 m/s, one must analyze the velocity distribution curves provided in the figure. The relevant equations include the kinetic energy formula and the probability distribution function for molecular velocities. The discussion highlights the importance of recognizing that argon, having a higher molar mass than neon, corresponds to a different curve in the graph. By calculating the area under the curve for argon between the specified velocities, the correct number of molecules can be derived. Ultimately, the solution involves interpreting the graph and applying the area calculation method effectively.
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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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