The average temperature of the atmosphere near the surface of the earth is about

Question

The average temperature of the atmosphere near the surface of the earth is about 20.0?C.

Part A

What is the root-mean-square speed of hydrogen molecules, H2 at this temperature?

Part B

The escape speed from the earth is about 11.0km/s . Is the average H2 molecule moving fast enough to escape?

Part C

Compare the rms speeds of oxygen (O2) and nitrogen (N2) with that of H2
vrmsO2 =

Part D

vrmsN2 =

Part E

So why has the hydrogen been able to escape the earth's gravity, but the heavier gases (such as O2 and N2) have not, even though none of these gases has an rms speed equal to the escape speed of the earth? (Hint: Do all the molecules have the rms speed, or are some moving faster? Since the rms speed for H2 is greater than that of O2and N2 which gas would have a higher percentage of its molecules moving fast enough to escape?)

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Explanation / Answer

Vrms = sqrt(3RT/M) = sqrt(3*8.314*293/0.002) = 1878.64 m/s

No, this is much less than escape speed.

Vrms of N2 = sqrt(3*8.314*293/0.028) = 510.88 m/s

Vrms O2 = sqrt(3*8.314*283/0.032) = 477.88 m/s

E)

Our atmosphere exists because of gravity. Lighter gasses, like hydrogen (the lightest) can escape from Earth's gravity and therefore move out into space. Gas molecule always spread out evenly inside a container. Since there is no container, and insufficient gravity to hold hydrogen down, it may escape into space. Given, not all of our atmosphere's hydrogen escapes. Heavier molecules such as Oxygen and Nitrogen can't escape Earth's gravity as easily. Again, some do escape, but the majority do not. That is the reason on going up the altitude, % of both N2 and O2 reduces.

The H2 molecules have higher %age of escape. This % age is directly proportional to velocity and inversely proportional to mass.

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