A sample of 0.177 g of an ideal gas occupies 1000 cm3 at STP. Calculate the rms speed of the gas molecules.

STP means standard temperature-273.15K and pressure 101.325 kPa.


We know that rms speed of gas is given by



Where R=gas constant 8.31J/molK


T=temperature of gas


M=molar mass of gas


Given


Temperature T=273.15K


Pressure P=101.325Pa


Mass =0.177g =0.17710-3kg


Volume = 1000cm3


1cm=10-2m


1cm3=10-6m3


1000cm3=10-3m3


Density =


We know that ideal gas equation is


PV=nRT


Where V= volume of gas


R=gas constant=8.31J/molK


T=temperature


N=number of moles of gas


So, we can write .


Putting the value of RT in vrms we get


vrms =


nM= total mass of gas ‘m’


and density =


Putting the value of density and m in vrms, we get


vrms =


Putting the value of P and in above equation we get



The rms speed of the gas molecules at STP is 1310.4ms-1.


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