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States Of Matter

Question
CBSEENCH11005930

Density of a gas is found to be 5.46 g/dm3 at 7°C at 2 bar pressure. What will be its density at STP? 

Solution
We know,
straight d space equals space MP over RT
For the same gas at different temperature and pressure,
              straight d subscript 1 over straight d subscript 2 space equals space straight P subscript 1 over straight T subscript 1 cross times straight T subscript 2 over straight P subscript 2                     ...(1)
Initial conditions,                  STP conditions
straight d subscript 1 space equals space 5.46 space straight g space dm to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space space space space space space space straight d subscript 2 space equals space ?
straight T subscript 1 space equals space 273 plus 27 space equals space 300 straight K space space space space space space space space space space space space space space space space space straight T subscript 2 space equals space 273 space straight K
straight P subscript 1 space equals space 2 space bar 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 space space space space space space space straight P subscript 2 space equals space 1 space bar 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
Substituting the values, we have 
fraction numerator 5.46 space straight g space dm to the power of negative 3 end exponent over denominator straight d subscript 2 end fraction space equals space fraction numerator 2 space bar space cross times space 273 space straight K over denominator 300 straight K space cross times 1 space bar end fraction space space space or space space straight d subscript 2 space equals space 3 straight g space dm to the power of negative 3 end exponent