At 25°C and 760 mm of Hg pressure, a gas occupies 600 mL volume. What will be its pressure at a height where the temperature is 10°C and volume of the gas are 640 mL ?

Solution

Original conditions Final conditions.

straight V subscript 1 space equals space 600 space mL space space space space space space space space space space space space space space space space space space space space straight V subscript 2 space equals space 640 space mL straight P subscript 1 space equals space 760 space mm space Hg space space space space space space space space space space space space space space space space straight P subscript 2 space equals space ? straight T subscript 1 space equals space 273 plus 25 space equals space 298 space straight K space space space space space space space straight T subscript 2 space equals space 273 plus 10 space equals space 283 space straight K

Applying the gas equation,

fraction numerator straight P subscript 1 straight V subscript 1 over denominator straight T subscript 1 end fraction space equals space fraction numerator straight P subscript 2 straight V subscript 2 over denominator straight T subscript 2 end fraction

or space space space space space space space space straight P subscript 2 space equals space fraction numerator straight P subscript 1 straight V subscript 1 straight T subscript 2 over denominator straight V subscript 2 straight T subscript 1 end fraction

Substituting the values, we have

straight P subscript 2 space equals space fraction numerator 760 space mm space cross times space 600 space mL space cross times space 283 space straight K over denominator 640 space mL space cross times space 298 space straight K space end fraction space space space space space equals space 676.6 space mm space Hg

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