How Many Air Molecules Were Released from the Compressed Tank?

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SUMMARY

The discussion focuses on calculating the number of air molecules released from a compressed tank using the ideal gas law equations PV = NkT and PV = nRT. The user initially calculated the number of molecules at 50 atm and 17 atm, resulting in an incorrect final count of 8.758e21 molecules released. The error stems from the improper use of pressure units in the equations, as atmospheres must be converted to pascals for accurate calculations. The correct approach involves ensuring consistent units throughout the calculations.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of unit conversions, particularly pressure from atmospheres to pascals
  • Familiarity with Avogadro's number and molecular calculations
  • Basic thermodynamics principles related to gases
NEXT STEPS
  • Learn about unit conversions for pressure, specifically converting atmospheres to pascals.
  • Study the ideal gas law in depth, focusing on its applications in different conditions.
  • Explore the concept of Avogadro's number and its significance in molecular calculations.
  • Investigate common pitfalls in thermodynamic calculations involving gases.
USEFUL FOR

Students in physics or chemistry, engineers working with gas systems, and anyone interested in thermodynamics and molecular calculations will benefit from this discussion.

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A tank of compressed air of volume 1.0 m^3 is pressurized to 50 atm at T = 273 K. A valve is opened and air is released until the pressure in the tank is 17 atm. How many air molecules were released?


I tried this problem using PV = NkT and PV = nRT. I realize the difference in these equations and I was wondering if this in fact the right equations to use? I ran 50 atm through and then 17 atm through. I then subtracted the initial N minus the final N. This didn't work.


This is what I did:

(50 atm)(1.0 m^3) = N(1.38e-23)(273)
N = 1.327e22

(17)(1.0 m^3) = N(1.38e-23)(273)
N = 4.512e21

Nfinal = (1.327e22) - (4.512e21)
Nfinal = 8.758e21

This is the wrong answer. What should I do?
 
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Check your units, can you really use atmospheres with that equation?
 

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