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.
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
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