Using the equation of state pV = nRT; show that at a given temperature density of a gas is proportional to gas pressure p.


The equation of state is given by,

pV = nRT ……….. (i)


Where,


p-Pressure of gas


V- Volume of gas


n- Number of moles of gas


R- Gas constant


T -Temperature of gas


From equation (i) we have,



Replacing n = m/M we have



because the number of moles is given as:


Where,


M - Mass of gas


M - Molar mass of gas


But,


(where, d = density of gas)


Thus, from equation (ii), we have




Molar mass (M) of a gas is always constant and therefore, at constant temperature T,


Hence, at a given temperature, the density (d) of gas is proportional to its pressure (p).


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