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Chemistry

Calculate the volume of a gas A at s.t.p., if at 37°C and 775 mm of mercury pressure, it occupies a volume of 9129\dfrac{1}{2} litres.

Gas Laws

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Answer

Initial conditionsFinal conditions [S.T.P.]
P1 = Initial pressure of the gas = 775 mm of HgP2 = Final pressure of the gas = 760 mm of Hg
V1 = Initial volume of the gas = 9.5 lit.V2 = Final volume of the gas = ?
T1 = Initial temperature of the gas = 37°C = 37 + 273 = 310 KT2 = Final temperature of the gas = 273 K

By Gas Law:

P1×V1T1=P2×V2T2\dfrac{\text{P}1\times\text{V}1}{\text{T}1} = \dfrac{\text{P}2\times\text{V}2}{\text{T}2}

Substituting the values :

775×9.5310=760×V2273V2=775×9.5×273310×760V2=20,09,962.52,35,600T2=8.53125 lit.\dfrac{775\times 9.5}{310} = \dfrac{760\times\text{\text{V}}2}{273} \\[0.5em] \text{V}2 =\dfrac{775\times 9.5\times 273}{310\times 760} \\[0.5em] \text{V}2 = \dfrac{20,09,962.5}{2,35,600} \\[0.5em] \text{T}2 = 8.53125 \text{ lit.}

Therefore, final volume of the gas = 8.5312 lit

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