Finding what fraction of molecules have speeds over a certain value

AI Thread Summary
To determine the fraction of oxygen gas molecules with speeds between 375 m/s and 380 m/s at 500 K, the Maxwell-Boltzmann distribution is utilized. The distribution function provides the probability of molecules having a specific speed, but calculating the number of moles over a speed range requires integration of the function. The user initially sought guidance on applying the distribution to find the number of molecules exceeding 380 m/s and later confirmed they found the solution. Understanding the application of the Maxwell-Boltzmann distribution is crucial for solving such problems in statistical mechanics.
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Homework Statement


A sample of oxygen gas with molar mass 32 g/mol contains 5.0 moles and is at a temperature of 500 K. How many moles of the gas have speeds between 375 m/s and 380 m/s?

Homework Equations


Maxwell Boltzmann Distribution:
f(v) = 4\pi[\frac{M}{2pi RT}]^(3/2) * v^2 * e^[(-Mv^2)/(2RT)]

The Attempt at a Solution


I know that this function gives the probablility of having the molecules at some speed v, but I'm not sure how to translate this over a range or how to calculate the number of moles over this range.
 
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Do you know how to use the M-B distribution to find out how many molecules have a speed greater than 380 m/s?

Do you know how to use the M-B distribution to find out how many molecules have a speed greater than 375 m/s?
 
I figured it out, thanks!
 
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