Solving the ideal gas law for volume -> length

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SUMMARY

The discussion focuses on solving for the edge length of a cube surrounding molecules of an ideal gas using the ideal gas law, specifically at a temperature of 27.0 degrees Celsius and a pressure of 1.00 atmosphere. The ideal gas law formula V=nRT/p was applied, with R set to 8.2057 x 10^-5 m³ (atm/mol*K). The calculated volume for one mole of gas is 2.46 x 10^-2 m³, leading to a volume per molecule of 4.09 x 10^-26 m³. The correct edge length of the cube is determined to be 3.44 x 10^-9 m, confirming the calculations are accurate.

PREREQUISITES
  • Understanding of the ideal gas law (V=nRT/p)
  • Knowledge of Avogadro's number (6.02 x 10^23)
  • Basic principles of volume calculation and cube root extraction
  • Familiarity with unit conversions (Celsius to Kelvin)
NEXT STEPS
  • Study the implications of the ideal gas law in real-world applications
  • Learn about molecular spacing and its effects on gas behavior
  • Explore advanced topics in thermodynamics related to gas laws
  • Investigate the relationship between pressure, volume, and temperature in different gas scenarios
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Students in physics, chemistry enthusiasts, and anyone interested in the practical applications of the ideal gas law and molecular behavior in gases.

jaded18
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[SOLVED] solving the ideal gas law for volume --> length

Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube.

What is the length L of an edge of each small cube if adjacent cubes touch but don't overlap?
______________

I know that the ideal gas law states V=nRT/p and that in this case R=8.2057(10^-5) m^3 (atm/mol*K), p=1atm, T=27+273K. What is n? Well if I calculate the volume of one mole of the gas, I get V=2.46(10^-2) m^3. And then when I use this result to find the volume of one molecule (the volume of the imaginary cube that is assumed to surround each molecule, I get V=( 1/(6.02*10^23))(8.2057)(27+273)= 4.09*10^-26 m^3

Then don't I just use this volume per molecule that I just calculated to find the length of a side of the cube by taking the cube root of it?! Why isn't the answer 0.000000003m?!

No one at the physics forum could help, so if you know how to do this prob correctly, any feedback will be awesome
 
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I think you've done it properly. You get 3.44 x 10^-9 m. That's the right magnitude anyway. Maybe ask your teacher?
 

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