Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at 0°C. Mass of a helium molecule = 6.64 × 10^–27 kg and Boltzmann constant = 1.38 × 10^–23 J K^–1.

Question

Philoid · Accepted Answer

In kinetic theory of ideal gas, the average energy is given by

Where R=gas constant=8.31Jmol^-1K^-1

T-temperature of gas

M=molar mass of gas

Given

Temperature T=0

T(K)=T ()+273.15

T=T(K)=0+273.15=273.15K

Mass of helium molecule m =6.64 × 10^–27 kg

We know that,

Gas constant R=k_BN_A

Where k_B= Boltzmann constant = 1.38 × 10^–23 J K^–1.

And N_A=Avogadro number=6.02310^-23 mol^-1

Molar mass of gas molecule M= Avogadro numbermass of gas molecule

M=N_Am

So average velocity becomes

We know that

Momentum=massvelocity

Momentum=6.64 × 10^–271202.31=8kgms^-1

Average magnitude of momentum of helium at 0 is 8kgms^-1.

Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at 0°C. Mass of a helium molecule = 6.64 × 10–27 kg and Boltzmann constant = 1.38 × 10–23 J K–1.