Question

Determine the probability that an N2 molecule has speed between the most probable speed and twice the most probable speed. Take the temperature to be 300 K and pressure of 1 bar.

please type the answer in pirnting form

Answer 1

An expression for the most probable speed of a gas at given temperature is given as :

v_mp = 2 k_B T / m₀

where, k_B = boltzmann constant = 1.38 x 10^-23 J/K

T = temperature = 300 K

m₀ = mass of a gas molecule = [(28 x 10^-3) / (6.022 x 10²³)] kg

then, we get

v_mp = [2 (1.38 x 10^-23 J/K) (300 K)] / (4.64 x 10^-26 kg)

v_mp = [(8.28 x 10^-21 J) / (4.64 x 10^-26 kg)]

v_mp = 422.4 m/s

Now, we will twice the most probable speed of a gas.

Then, we get

v'_mp = 2 v_mp 2 (422.4 m/s)

v_'mp = 844.8 m/s