How many molecules of monotonic and diatomic gas are in a container?

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SUMMARY

The discussion focuses on calculating the number of molecules of diatomic oxygen and monotonic helium in a 3300 cm³ container at a pressure of 17 atm and a temperature of 25 degrees Celsius. Using the formula N = 1.5 PV/K, the calculated total number of molecules is approximately 6.91 x 1023. The breakdown shows that diatomic oxygen accounts for roughly 3/5 of this total, resulting in approximately 4.15 x 1023 molecules. An important correction noted is that the gauge pressure was underestimated, which should be 18 atm instead of 17 atm.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = nRT)
  • Familiarity with kinetic theory of gases
  • Knowledge of molecular physics, specifically for diatomic and monotonic gases
  • Basic proficiency in unit conversions (e.g., atm to Pa)
NEXT STEPS
  • Study the Ideal Gas Law and its applications in real-world scenarios
  • Learn about the kinetic theory of gases and its implications for molecular behavior
  • Explore the differences between diatomic and monotonic gases in terms of molecular structure and behavior
  • Investigate the impact of gauge pressure versus absolute pressure in gas calculations
USEFUL FOR

This discussion is beneficial for physics students, educators, and professionals in fields such as chemistry and engineering who are involved in gas behavior analysis and molecular calculations.

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1. You have a container of 3300 cm^3. Half of it is diatomic oxygen and half is monotonic helium. Pressure is 17 atm and temperature is 25 degrees C. How many molecules of each substance are in it?



2. PV = 2/3 N(1/2 mv^2) -> PV = 2/3 N (K) -> N = 1.5 PV/K

K_monotonic = 3/2kT = 3/2 (1.38*10^-23)(298k)

k_diatonic = 5/2kT = 5/2 (1.38*10^-23)(298k)




3. N=1.5(17atm*(1Pa/9.869*10^-6 atm)*1650 cm^3 * 1m^3/10^6 cm^3))/((3/2) 1.38*10^-23)(298k))

3/2 factors cancel out. after all the math I get 6.91*10^23.

diatomic is basically 3/5 of that number, 4.15*10^23
 
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masteringphysics is truly an awful piece of software. It turns out that the reason I was getting the wrong answer was because the gauge pressure undermeasures the pressure. It's supposed to be 18, not 17.
 

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