Two gasses are in thermal equilibrium in a closed container: 2 moles of H2 (Hydr

ID: 1782426 • Letter: T

Question

Two gasses are in thermal equilibrium in a closed container: 2 moles of H2 (Hydrogen has atomic mass 1) and 4 moles of He (noble gas, atomic mass 4).

a) Explain which substance has more total thermal energy. Assume that each molecule of H2 has 5 active modes.

b) Explain which is moving faster, a H2 molecule or a Helium atom?

c) If you have two types of molecules and one has twice as many ways of absorbing energy as the other, what can you

say about their relative thermal energies per molecule at a given temperature? Please explain step by step process in detail.

a) Kinetic energy of each H2 molecule = (5/2)*k*T ( 5 --- > active modes)

Total kinetic energy of H2, KE_H2 = N*(5/2)*k*T (where N is the total number of molecules)

= n*Na*(5/2)*k*T (n is number of moles and Na is avagadros number)

= 2*Na*(5/2)*k*T

= 5*Na*k*T

Kinetic energy of each He molecule = (3/2)*k*T (3 ---> active modes)

Total kinetic energy of He, KE_He = N*(3/2)*k*T (where N is the total number of molecules)

= n*Na*(3/2)*k*T (n is number of moles and Na is avagadros number)

= 4*Na*(3/2)*k*T

= 6*Na*k*T

clearly, KE_He > KE_H2

b) we know, V_rms = sqrt(3*R*T/M) (Where M is the molar mass)

so rms speed is inversly proportional to molar mass of the gas.

we know, M_He = 4 gram/mole

M_H2 = 2 gram/mole

so, H2 molecules have more speed than He molecules.

c) One gas will have twice the energy of ther gas.

It has already been explained in part 1.

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