What is the Number Density of Gas Molecules at Sea Level?

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SUMMARY

The number density of gas molecules in the Earth's atmosphere at sea level is approximately 2.7 x 1025 molecules/m3 when calculated using the ideal gas law (PV = NkT) at standard temperature and pressure (STP). The density of air at STP is 1.3 kg/m3, which serves as a basis for this calculation. The pressure used in the calculation is 101300 Pa, and the temperature is assumed to be 273 K. This method provides a reliable estimate of molecular density in atmospheric conditions.

PREREQUISITES
  • Understanding of the ideal gas law (PV = NkT)
  • Knowledge of standard temperature and pressure (STP) conditions
  • Familiarity with basic thermodynamic concepts
  • Ability to perform unit conversions and calculations involving density
NEXT STEPS
  • Explore the implications of temperature variations on gas density calculations
  • Learn about the molecular composition of air and its impact on density
  • Investigate the effects of altitude on atmospheric pressure and density
  • Study advanced gas laws and their applications in different environmental conditions
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Students in physics or chemistry, educators teaching gas laws, and researchers studying atmospheric science will benefit from this discussion.

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Homework Statement


Estimate the number density of gas molecules in the Earth's atmosphere at sea level.

Homework Equations





The Attempt at a Solution



The question doesn't give me any further information and I am wondering about temperature---should I just say it's at STP? I found in my book that the density of air at STP is 1.3 kg/m^3.

Here's what I did:
PV=NkT

P/kT =N/V
(101300Pa)/(1.38E-23)(273 K)=2.7 * 10^25 molecules/m^3
 
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If they do not specify a temperature, assume standard temperature.

Looks good to me.
 
As a check / alternative - work out how much an 'air' molecule weighs and use the density to work how many molecules.
 

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