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ICSE Class 9 Chemistry Question 19 of 24

Model Question Paper — 1 — Question 18

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18
Question

Question 7(b)

What temperature in degree centigrade would be necessary to double the volume of a gas (initially at STP), if the pressure is reduced to half ?

Answer
Initial conditions [S.T.P.]Final conditions
P1 = Initial pressure of the gas = 1 atmP2 = Final pressure of the gas = 0.5 atm
V1 = Initial volume of the gas = VV2 = Final volume of the gas = 2V
T1 = Initial temperature of the gas = 273 KT2 = Final temperature of the gas = ?

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 :

1×V273=0.5×2VT2T2=0.5×2×273T2=273K\dfrac{1\times \text{V}}{273} = \dfrac{0.5\times\text{2\text{V}}}{\text{T}_2} \\[0.5em] \text{T}_2 = 0.5\times 2 \times 273\\[0.5em] \text{T}_2 = 273\text{K}

∴ Final temperature of the gas = 273 K = 0 °C