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Chemistry

Calculate the final volume of a gas 'X', if the original pressure of the gas, at S.T.P. is doubled and its temperature is increased three times.

Gas Laws

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Answer

Initial conditions [S.T.P.]Final conditions
P1 = Initial pressure of the gas = 760 mm HgP2 = Final pressure of the gas = (2 x 760) mm Hg
V1 = Initial volume of the gas = VV2 = Final volume of the gas = ?
T1 = Initial temperature of the gas = 273 KT2 = Final temperature of the gas = (3 x 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 :

760×V273=2×760×V23×273V2=32VV2=112V\dfrac{760 \times \text{V}}{273} = \dfrac{ 2 \times 760 \times\text{\text{V}}2}{3 \times 273} \\[1em] \text{V}2 =\dfrac{3 }{2}\text{V} \\[1em] \text{V}_2 = 1\dfrac{1}{2} \text{V}

∴ Final volume of the gas = 1121\dfrac{1}{2} times the original volume.

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