At a height of 200 km above the earth\'s surface, in the thermosphere, the atmos

Question

At a height of 200 km above the earth's surface, in the thermosphere, the atmosphere is almost entirely nitrogen (N_2). The pressure is approximately 70 nPa (7 times 10^-8 Pa) and the temperature approximately 900 K. The earth's escape velocity is 11.2 km s^-1. How many nitrogen molecules will there be in a 1 km thick shell of the thermosphere, if the inner distance of the shell from the earth's surface is 200 km? (The earth's radius is 6353 km) Express your answer using three significant figures.

Explanation / Answer

The volume of the 1 Km shell at 200 Km in the thermosphere is

volume of a sphere is 4/3 pi r3

r = 500 m

volume = 5.24 x 108 m3

PV = nRT

7 x 10-8 Pa x 5.24 x 108 m3= n x 8.314 x 900

n = 0.0049 moles

so number of molecules will be 6.023 x 1023 x 0.0049 = 2.95 x 1021 molecules of nitrogen in a 1Km shell

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