Clouds of hydrogen molecules have been detected deep in inte

Clouds of hydrogen molecules have been detected deep in interstellar space. It is estimated that these clouds contain about 1 x 1010 hydrogen molecules per m3 and have a temperature of just 25 K Using these data, find the approximate pressure in such a cloud. atm

Solution

1 mole of any substance contains 6.023*10²³ molecules

so 1*10¹⁰ molecules per m3 contains 1*10¹⁰/(6.023*10²³) moles/ m3=1.6603*10^-14 moles/m3

1m3= 1000L, hence moles/m3= 1.6603*10^-14/ 1000 moles/L=1.6603*10^-17 moles/L

from gas law, PV= nRT, n= no of moles, V= volume and R= gas constant = 0.0821 L.atm/mole.K and T is temperatrue in K=25K

P=(n/V)*RT= 1.6603*10^-17* 0.0821*25 atm=3.41*10^-17 atm