Finding what fraction of molecules have speeds over a certain value

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SUMMARY

The discussion focuses on calculating the fraction of oxygen gas molecules with speeds between 375 m/s and 380 m/s using the Maxwell-Boltzmann distribution. The sample consists of 5.0 moles of oxygen gas at a temperature of 500 K, with a molar mass of 32 g/mol. The probability density function provided is f(v) = 4π[(M/(2πRT))^(3/2)] * v^2 * e^[-(Mv^2)/(2RT)]. The user successfully determined how to apply this distribution to find the number of molecules exceeding specific speed thresholds.

PREREQUISITES
  • Understanding of the Maxwell-Boltzmann distribution
  • Knowledge of thermodynamic principles, particularly gas laws
  • Familiarity with statistical mechanics concepts
  • Basic proficiency in calculus for integration
NEXT STEPS
  • Learn how to integrate the Maxwell-Boltzmann distribution to find probabilities over specific speed ranges
  • Study the implications of temperature and molar mass on molecular speed distributions
  • Explore applications of the Maxwell-Boltzmann distribution in real-world gas behavior
  • Investigate how to calculate average speeds and root mean square speeds of gas molecules
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Students studying thermodynamics, physicists analyzing gas behaviors, and educators teaching statistical mechanics concepts.

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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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