A container of volume V 30 I contains m 100 g of oxygen at

A container of volume V = 30 I contains m = 100 g of oxygen at a pressure of p = 3 atm. Find the most likely kinetic energy of the oxygen molecules.

Solution

Volume V = 30 lit

               = 30 x10 -3 m 3

Mass m = 100 g

Molar mass of oxygen M = 16 g

Number of moles n = m/M

                            = 100 / 16

                            = 6.25 mol

We know 1 mole = 6.023 x10 ²³ molecules

So, number of molecules in 100 g of oxygen is N = n x 6.023 x10 ²³

                                                                       =6.25 x6.023 x10 ²³

                                                                       = 37.64 x10 ²³

Pressure P = 3 atm = 3 x1.01 x10 ⁵ Pa

We know pressure P =(2/3)(N/V) K.E

From this kinetic energy of the oxygen molecules K.E = (3/2)(V/N)P

K.E = 1.5 x[(30x10 ^-3)/(37.64 x10 ²³) ](3x1.01x10 ⁵)

      = 3.622 x10 ^-21 J