Q.29. The pressure of interstellar space is about 4.0 × 10 - 22 atm. If the temperature is 3 K, how many molecules are present per litre?
(R = 0.08 l-atm/K-mol)
(a) 2430
(b) 1420
(c) 845
(d) 1002

Dear Student, 

According to the gas law:
                                  PV = nRT                        [ p = pressure, V = volume, n = no. of moles,                                               T = temperature]
P = 4 x 10-22 atm. 
T = 3 K 
V is to considered as unity as no. of molecules is to be calculated per unit volume.
Putting these values: 
                            4 × 10 -22 × 1= n × 0.08 × 3n = 4 × 10-220.08 ×3    = 503× 10-22 mol

As 1 mol = 6 x 1023  molecules.
so, 
       50/3 x 10-22 mol will contain = 6 x 1023 x 50/3 x 10-22 molecules
                                                    =  100.2 x 10 
                                                    = 1002 molecules 

So, 1002 molecules are present per unit volume of the interstellar space.
So, the option ( d ) is correct .


Regards.

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