At this pressure, how many molecules of air would there be in a 50 ?c experimental chamber with a volume of 0.050 m3 ?

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11-04-2017
Physics

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At this pressure, how many molecules of air would there be in a 50 ?c experimental chamber with a volume of 0.050 m3 ?

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Edufirst Edufirst · Answer 1 · 2017-04-14T11:31:24+02:00

The pressure is p = 4.0 * 10 ^ -11 Pa.

Then, use the ideal gas equation: pV = nRT

Call #m the number of molecules. #m is n * Avogadro's number, #m = nA => n = #m/A

=> pV = (#m / A) RT => #m = pV*A / (RT)

p = 4.0 * 10 ^ -11Pa
V = 0.050m^3
A = 6.02 * 10^ 23
R = 8.314 J/(K*mol)
T = 50 + 273.15 K = 323.15 K

Now, plug in the numbers:

#m = 4.0 * 10^ -11Pa * 0.050 m^3 * 6.02 * 10^ 23 (molec/mol) / (8.314 J/(K*mol) * 323.15K)

#m = 448,138,552 molecules