Question

The lowest pressure ever obtained in a laboratory setting is 4.0×10−11 Pa.

Part A

At this pressure, how many molecules of air would there be in a 50 ∘C experimental chamber with a volume of 0.030 m3 ?

Express your answer as a number of molecules.

Answer 1

Universal gas constant = R = 8.314 J/(mol.K)

Pressure of the air = P = 4 x 10^-11 Pa

Volume of the chamber = V = 0.03 m³

Temperature of the air = T = 50 ^oC = 50 + 273 K = 323 K

Number of moles of air in the chamber = n

PV = nRT

(4x10^-11)(0.03) = n(8.314)(323)

n = 4.47 x 10^-16 mol

Avogadro's number = N₀ = 6.022 x 10²³

Number of molecules of air in the chamber = N

N = nN₀

N = (4.47x10^-16)(6.022x10²³)

N = 2.69 x 10⁸

A) Number of molecules of air in the experimental chamber = 2.69 x 10⁸