Exercise 4 | Properties of Gases

A low pressure of 1.0 x 10-5 torr is obtained by means of a vacuum pump.

Calculate the number of molecules in 1.0 L of gas at this pressure and at room temperature (= 25°C).

Ideal-gas equation:

PV = nRT    and    n = N / NA

⇒ PV = NRTNA

⇒ N = PVNART


P = pressure in Pa ⇒ 1.0 x 10-5 torr = 1.3 x 10-3 Pa

V = volume in m3 ⇒ 1.0 L = 1.0 dm3 = 1.0 x 10-3 m3

NA = Avogadro’s number = 6.022 x 1023

R = ideal gas constant = 8.314 m3.Pa.K-1.mol-1

T = temperature ⇒ 25.0°C = 298 K

 

N = 1.3 × 10-3 × 1.0 × 10-3 × 6.022 × 10238.314 × 298 = 3.2 x 1014 molecules