The number density of atoms (chiefly hydrogen) in interstellar space is about 10

Question

The number density of atoms (chiefly hydrogen) in interstellar space is about 10 per cubic centimeter, and the temperature is about 100 K. (a) Calculate the pressure of the gas in interstellar space, and express it in atmospheres. (b) Under these conditions, an atom of hydrogen collides with another atom once every 1×109 seconds (that is, once every 30 years). By using the average speed, estimate the distance travelled by a H atom between collisions. Compare this distance with the distance from the earth to the sun (150 million km (or 93 million miles)).

Explanation / Answer

For the first part, use PV = nRT

P = nRT/V

P = 10 atom/cm3 * 1 mol / 6.02x1023 atom * 82.1 cm3 atm/ K mol * 100 K = 1.36x10-19 atm

For the second part, use the mean root square velocity which is:

v = (3RT/MM)1/2

v = (3*8.3144 kg m2/s2 K mol * 100 K / 0.001 kg/mol)1/2

v = 1579.34 m/s

d = v*t = 1579.34 m/s * 1x109 s =1.5793x1012 m

This is way farther than Earth to sun.

Hope this helps

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