Calculating Average Speed of Molecules

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SUMMARY

The average speed of a molecule striking a surface can be calculated using the root mean square speed formula, specifically for hydrogen in this case. The formula used is v(rmss) = (3RT/M)^0.5, resulting in a calculated speed of 1920.12 m/s. This value represents the speed of an individual molecule, while the average speed of all molecules in a gas is typically lower due to the distribution of speeds among different molecules. Understanding this relationship is crucial for accurate molecular speed calculations.

PREREQUISITES
  • Understanding of the ideal gas law
  • Familiarity with the root mean square speed formula
  • Knowledge of molecular mass and its impact on speed calculations
  • Basic principles of kinetic theory of gases
NEXT STEPS
  • Study the ideal gas law and its applications in molecular speed calculations
  • Learn about the Maxwell-Boltzmann distribution of molecular speeds
  • Explore the differences between root mean square speed and average speed
  • Investigate how temperature affects molecular speed in gases
USEFUL FOR

Students and professionals in chemistry, physics, and engineering fields who are interested in molecular dynamics and gas behavior will benefit from this discussion.

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[SOLVED] average speed

Problem:
Calculate the average speed of a molecule that strikes a small surface. How does this compare with the average speed of all molecules?

I started by using the root mean square speed as the average speed of some random molecule, for example hydrogen. So,

v(rmss) = (3RT/M)^.5 = (3*8.314*298/2.016E-3) = 1920.120594 m/s.
What I am confused about is how do I relate this with the average speed of all molecules. I would imagine that it would be a bigger value.

Any help is appreciated.
thanks
 
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