Q. 53.8( 91 Votes )

Pressure of 1 g of an ideal gas A at 27°C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

Answer :

For ideal gas A, the ideal gas equation is given by,

PaV = naRT


Where, Pa and na represent the pressure and number of moles of gas A.


For ideal gas B, the ideal gas equation is given by,


PbV = nbRT


Where,Pa and nb represent the pressure and number of moles of gas B.


[V and T are constants for gases A and B]


Therefore, we have,



Where, Ma and Mb are the molecular masses of gases A and B respectively.


Now, we have


Substituting the values


ma = 1 g


Pa = 2 bar


mb = 2 g


Pb = 1 bar.


Given,


(Since total pressure is 3 bar)


Substituting these values in equation we have



Thus, a relationship between the molecular masses of A and B is given by


4Ma = Mb


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