Problem 11: Determine the average value of Kinetic Energy of the particles of an ideal gas at 0^oC and 50^oC. Also find Kinetic Energy per mole of an ideal gas at these temperatures.

Solution:

Step: 1 Overview

From the derivation of Kinetic Energy from Kinetic Molecular Theory, we know that:

K.E=(3/2)kT

Above equation is the equation of Kinetic Energy of particles, to find the Kinetic Energy per mole, we use this formula:

K.E per mole = K.E per particle x N_A
K.E per mole = (3/2)kTN_A

Step: 2 Calculation

Kinetic Energy of particle at 0^oC (273K):

K.E=(3/2)(1.38x10^-23)(273)
K.E=5.65x10^-21J (Ans)

Kinetic Energy of particle at 50^oC (323K):

K.E=(3/2)(1.38x10^-23)(323)
K.E=6.68x10^-21J (Ans)

Kinetic Energy per mole at 0^oC (273K):

K.E per mole =(3/2)(1.38x10^-23)(273)(6.02x10²³)
K.E per mole =3401.3 J/mole (Ans)

Kinetic Energy per mole at 50^oC (323K):

K.E per mole =(3/2)(1.38x10^-23)(323)(6.02x10²³)
K.E per mole =4021.7 J/mole (Ans)