The density of a mixture of nitrogen gas and oxygen gasses is 1.15g/L at 750mm of Hg at 27 degree centigrade. Calculate the percentage of the of gas in the gas mixture.

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Solution

$F r o m a n i d e a l g a s e q u a t i o n p V = n R T p V = \frac{W}{M} R T p = \frac{W}{V} \frac{R T}{M} = \frac{d R T}{M} M = \frac{d R T}{p} = \frac{1.15 \times 0.0821 \times 300}{\frac{750}{760}} (\sin c e 760 m m = 1 a t m) = 28.70 g A c c o r d i n g t o A v e r a g e a t o m i c m a s s A v e r a g e a t o m i c m a s s = \frac{X_{1} M_{1} + X_{2} M_{2}}{X_{1} + X_{2}} (w h e r e X - r e l a t i v e a b u n d a n c e a n d M - a t o m i c m a s s) X_{1} - r e l a t i v e a b u n d a n c e o f N i t r o g e n X_{2} - r e l a t i v e a b u n d a n c e o f o x y g e n X_{1} + X_{2} = 100 X_{2} = 100 - X_{1} S u b s t i t u t e a l l t h e s e 28.70 = \frac{X_{1} \times 28 + (100 - X_{1}) \times 32}{100} 2870 = 28 X_{1} + 3200 - 32 X_{1} 4 X_{1} = 330 X_{1} - 82.5 % S o X_{2} - 17.5 % T h u s t h e % o f N i t r o g e n = 82.5 % T h u s t h e % o f o x y g e n = 17.5 %$

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