Question

A closed vessel of volume 1 litre contains oxygen at 27°C. Translational kineticenergy of all molecules of oxygen is 3735 joule. Pressure of the gas is nearly​

Answer 1

Given info : A closed vessel of volume 1 lite contains oxygen at 27°C. Translational kinetic energy of all molecules of oxygen is 3735 J.

To find : Pressure of the gas is nearly ..

solution : volume of gas ( = volume of closed vessel) , V = 1 litre

temperature, T = 27°C = 27 + 273 = 300 K

translational kinetic energy, K.E = 3735 J

we know,

for ideal gas, translational kinetic energy is given by, K.E = 3/2 nRT

so, 3735 J = 3/2 × n × 25/3 J/K/mol × 300K

⇒3735 × 2 × 3 = 3 × n × 25 × 300

⇒n = (3735 × 2 × 3)/(3 × 25 × 300) ≈ 3

now using gas equation, PV = nRT

so, P = nRT/V

= (3mol × 0.082 litre.atm/mol/K × 300K)/1 litre

= 73.8 atm ≈ 74 atm

Therefore the pressure of the gas is nearly 74 atm