Calculate the value of Boltzmann constant k . Given: R = 8 . 3 × 10 3 J ( k m o l ) - 1 K - 1 and Avogadro number N = 6 . 023 × 10 26 ( k m o l ) - 1 .

We know that, Boltzmann's constant, k = R N , Thus, k = 8 . 31 × 10 3 6 . 023 × 10 26 = 1 . 37 × 10 - 23 J K - 1

The volume of a gas at the pressure 1 . 2 × 10 7 N m - 2 and the temperature 127 ° C is 2 . 0 l i t r e s . Find the number of molecules in the gas.

In the terms of Boltzmann's constant, the gas equation can be written as, P V = n K T or n = P V k T or n = ( 1 . 2 × 10 7 ) × ( 2 × 10 - 3 ) ( 1 . 37 × 10 - 23 ) × ( 400 ) = 4 . 35 × 10 24

Kinetic energy of oxygen molecule at 0 ° C is 5 . 64 × 10 - 21 J . Calculate Avogadro’s number.

Given that, Temperature, T = 0 ° C = 273 K Kinetic energy, E = 5 . 64 × 10 - 21 J and Universal gas constant, R = 8 . 31 J m o l - 1 K - 1 Now, average kinetic energy, E = 3 2 k T = 3 2 R N T or N = 3 2 R E T = 3 2 8 . 31 5 . 64 × 10 - 21 × 273 or N = 6 . 035 × 10 23

The temperature of a gas filled in a vessel is 273 K and the pressure is 1 . 60 × 10 - 3 N m - 2 . Determine number of molecules in unit volume of the vessel.

Given that, Temperature, T = 273 K Pressure, P = 1 . 60 × 10 - 3 a t m and Volume, V = 1 . 0 L According to ideal gas equation, P V = n R T or 1 . 6 × 10 - 3 × 1 = n × 0 . 0821 × 273 or n = 0 . 071 × 10 - 3 Now, number of molecules, N = 0 . 071 × 10 - 3 × 6 . 023 × 10 23 = 4 . 25 × 10 17

The temperature of a gas-filled in a vessel of the volume 1 . 0 L is 273 K and the pressure is 1 . 60 × 10 - 3 N m - 2 . Determine the average distance between the molecules.

Given that, Temperature, T = 273 K Pressure, P = 1 . 60 × 10 - 3 a t m and Volume, V = 1 . 0 L According to ideal gas equation, P V = n R T or 1 . 6 × 10 - 3 × 1 = n × 0 . 0821 × 273 or n = 0 . 071 × 10 - 3 Now, number of molecules, N = 0 . 071 × 10 - 3 × 6 . 023 × 10 23 = 4 . 25 × 10 17 Average distance between molecules = 1 4 . 25 × 10 17 1 3 = 1 . 33 × 10 - 6 m