# The time of diffusion of a gas mixture containing ozone and oxygen is 105 seconds & that of same volume of oxygen under same condition of temp. & pressure is 100 s. Calculate the percentage by volume of ozone in the mixture of relative density of ozone is 24.

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2015-06-04T20:14:10+05:30

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The time of diffusion is inversely proportional to the square root of the density of gas.  or the molar mass..

P, V and T are same.  So the number of moles are same for both the mixture and Oxygen.  Let us say there are 1 mole of each gas.

density d = mass M / volume V

M2 = molar mass of oxygen = 32
T2 = 105 sec
T1 = 100 sec.

T2² / T1² = d1 / d2 = M1 / M2

105² / 100² = M1 / 32        =>    M1 = mass of mixture = 35.28

Molar mass of ozone = 48

x = proportion of ozone by volume in the mixture.

mass of mixture = 35.28 =  (1 - x) * 32 +  x  48
=> x = 3.28 / 16 = 0.205
=>  proportion by volume of Ozone  = 20.5%