Question

In state-of-the-art vacuum systems, pressures as low as 1.00 10-9 Pa are being attained. Calculate the number of molecules in a 1.90-m3 vessel at this pressure and a temperature of 28.0°C. molecules

Answer 1

The number of molecules is 4.574 x 10¹¹ Molecules

Step-by-step explanation:

Given;

pressure in the vacuum system, P = 1 x 10⁻⁹ Pa

volume of the vessel, V = 1.9 m³

temperature of the system, T = 28°C = 301 K

Apply ideal gas law;

`PV= nRT = NK_BT`

Where;

n is the number of gas moles

R is ideal gas constant = 8.314 J / mol.K

`K_B` is Boltzmann's constant, = 1.38 x 10⁻²³ J/K

N is number of gas molecules

N = (PV) / (
`K_B`T)

N = (1 x 10⁻⁹ X 1.9) / ( 1.38 x 10⁻²³ X 301)

N = 4.574 x 10¹¹ Molecules

Therefore, the number of molecules is 4.574 x 10¹¹ Molecules