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States Of Matter

Question
CBSEENCH11005942

What will be the pressure of the gaseous mixture when 0.5 L of H2 at 0.8 bar and 2.0 L of dioxygen at 0.7 bar are introduced in a 1L vessel at 27°C? 

Solution
Calculation of partial pressure of H2.
straight V subscript 1 space equals space 0.5 space straight L semicolon space space space space space space space space straight V subscript 2 space equals space 1.0 space straight L
straight P subscript 1 space equals space 0.8 space bar space space space space space space space space straight P subscript 2 space equals space ?
According to Boyle's law
                      straight P subscript 1 straight V subscript 1 space equals space straight P subscript 2 straight V subscript 2 space space space or space space space straight P subscript 2 space equals space fraction numerator straight P subscript 1 straight V subscript 1 over denominator straight V subscript 2 end fraction
Substituting the values, we have
         
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Calculation of partial pressure of O2.
V1 = 2.0 L                     V2 = 1 L
P1 = 0.7 bar                    P2 = ?
According to Boyle's law
P1V1 = P2V2    or   straight P subscript 2 space equals space fraction numerator straight P subscript 1 straight V subscript 1 over denominator straight V subscript 2 end fraction
Substituting the values, we have
straight P subscript straight O subscript 2 end subscript space equals space fraction numerator 0.7 space bar space cross times space 2.0 space straight L over denominator 1 straight L end fraction space equals 1.4 space bar
therefore space space space Total space pressure space space equals space PH subscript 2 plus space PO subscript 2
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0.4 space bar space plus space 1.4 space bar space equals space 1.8 space bar