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1) Consider a sealed container with a volume of 2 m3 filled with 3 × 1023 helium atoms and 6 × 1023 molecules of nitrogen. Recall that helium is a monatomic gas, nitrogen is a diatomic gas. The atomic mass of He is 4 g/mol and of N2 is 28 g/mol. The temperature of the gas mixture is unknown, but high enough that for diatomic molecules the translational and rotational motion is described by equipartition. Calculate the ratio of the r.m.s. velocity of the helium atoms to the r.m.s. velocity of the nitrogen molecules.

Answer :

Answer:

Given the following gas particles:

He = 3 × 1023 atoms and N = 6 × 1023 molecules

Note : The speed of sound in a gas is roughly equal to the average speed of the  particles. Comparing the speed of a typical helium atom (Molar mass He = 4 atomic mass units) to  that of a typical nitrogen molecule (Molar mass of N2 = 2 x 14 atomic mass units) in a gas container mixture in  thermal equilibrium.

we will expect to be the ratio of sound speeds in  pure helium and nitrogen?

<KEtran>He = <KEtran>N2    due to Equipartition of translational kinetic energy.

Note : The rotational energy of nitrogen  molecules is not important here.

molar mass He/molar mass N2 = 4/28 = 0.143, Helium doesn’t form molecules.

velocity of He/velocity of N2 = (28/4)1/2 = 2.65 KE = mv2/2 so the speed ratio is the  inverse square root of the mass ratio.

The ratio of sound speeds  should be approximately - The actual the ratio of the r.m.s. velocity of the helium atoms to the r.m.s. velocity of the nitrogen molecules = 2.76.

Parrain

Based on the atomic masses of Helium and Nitrogen, the ratio of the r.m.s. velocity of the Helium atoms to that of Nitrogen will be 2.65.

What is the ratio?

The ratio can be found as:

= √(3RT / Atomic mass of Helium) x √ (Atomic mass of Nitrogen / 3RT)

Cross multiplying leaves:
= √ (Atomic mass of Helium / Atomic mass of Nitrogen)

Solving gives:

= √(28 /4)

= 2.645

= 2.65

Find out more on r.m.s. velocity at https://brainly.com/question/15995507.

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