How Many Air Molecules Were Released from the Compressed Tank?

[underoathP]

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?

 

[what]

Check your units, can you really use atmospheres with that equation?

 

[m2003]

I would approach this problem by first verifying the units and constants being used in the equations. In this case, the units for pressure should be in Pascals (Pa), not atmospheres (atm). Additionally, the value for the Boltzmann constant (k) should be 1.38e-23 J/K, not 1.38e-23 m^3 atm/K.

Once the correct units and constants are used, the equations PV = NkT and PV = nRT can both be used to solve for the number of molecules released. However, it is important to note that these equations assume an ideal gas behavior, which may not be accurate for all situations.

To use PV = NkT, the temperature must be converted to Kelvin (K = 273 + T). Then, the number of molecules released can be calculated by taking the difference between the initial and final number of molecules, as you did.

To use PV = nRT, the number of moles (n) must be calculated first by dividing the initial pressure (50 atm) by the gas constant (R = 8.314 J/mol K) and the converted temperature (273 K). This will give the initial number of moles in the tank. Then, the final number of moles can be calculated using the final pressure (17 atm) and the same temperature. The difference between these two values will give the number of moles released, which can then be converted to number of molecules by multiplying by Avogadro's constant (6.022e23 molecules/mol).

It is also important to consider other factors that may affect the number of molecules released, such as changes in temperature or the presence of impurities in the compressed air. These can impact the accuracy of the calculations and should be taken into account in any scientific analysis.

In summary, the correct approach to solving this problem would involve using the correct units and constants in the equations and considering any potential factors that may affect the results. It is also helpful to double check the calculations and use multiple methods to verify the answer. If you are still unsure, consulting with a colleague or mentor can also be beneficial in finding the correct solution.