Two gasses are in thermal equilibrium in a closed container: 2 moles of N2 (Nitr

Question

Two gasses are in thermal equilibrium in a closed container: 2 moles of N2 (Nitrogen has atomic mass 14) and 5 moles of Argon (noble gas, atomic mass 40). a) Explain which substance has more total thermal energy. Assume that each molecule of N2has 7 active modes. b) Explain which is moving faster, a N2 molecule or an Argon 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 in detail.

Explanation / Answer

a) Kinetic energy of each N2 molecule = (7/2)*k*T ( 7 --- > active modes)

Total kinetic energy of N2, KE_N2 = N*(7/2)*k*T (where N is the total number of molecules)

= n*Na*(7/2)*k*T (n is number of moles and Na is avagadros number)

= 2*Na*(7/2)*k*T

= 7*Na*k*T

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

Total kinetic energy of Ar, KE_Ar = 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)

= 5*Na*(3/2)*k*T

= 7.5*Na*k*T

clearly, KE_Ar > KE_N2

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

we know, M_Ar = 40 gram/mole

M_N2 = 28 gram/mole

so, N2 molecules have more speed than Ar molecules.

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

It has already been explained in part 1.

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