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States Of Matter

Question
CBSEENCH11005941

300 mL of a gas A at a pressure of 600 mm is mixed with 200mL of another gas B at a pressure of 700 mm in a vessel of 2-litre capacity. What will be the total pressure of the resulting mixture, if the temperature is kept constant?

Solution

Let the partial pressure of the gases A and B be represented by PA and PBrespectively.
(i) Partial pressure of gas A in 2 litre flask:
   V1 = 300 mL;      P2 = 600 mm
   V2 = 2 L = 2 x 1000 = 2000 mL;  PA = ?
According to Boyle's law,  P1V1 = P2V2
i.e.  600 x 300 = PA x 2000
therefore space space space space space space straight P subscript straight A space equals space fraction numerator 600 space cross times space 300 over denominator 2000 end fraction space equals space 90 space nm
(ii) Partial pressure of gas B in 2 litre flask:
       V1 = 200 mL,   P1 = 700 mL
       V2 = 2 litre = 2 x 1000 = 2000 mL
       PB = ?
According to Boyle's law,
              P1V1 = P2V2
i.e.     700 x 200 = PB X 2000
therefore space space space space straight P subscript straight B space equals space fraction numerator 700 space cross times space 200 over denominator 2000 end fraction space equals space 70 space mm
therefore  Total pressure exerted by the mixture
      straight P space equals space straight P subscript straight A plus straight P subscript straight B
space space space space space space space space left square bracket By space Dalton apostrophe straight s space law space of space partial space pressure right square bracket
space space space space space space space space space space space space space space equals space 90 plus 70 space equals space 160 space mm