Model Question Paper — 1 — Question 7

(i) Boyle's law — Temperature remaining constant the volume of a given mass of dry gas is inversely proportional to it's pressure.

V ∝ $\dfrac{1}{\text{P}}$ [T = constant]

(ii) Initial conditions [S.T.P.] :

P₁ = Initial pressure of the gas = 1 atm

V₁ = Initial volume of the gas = 22.4 l

T₁ = Initial temperature of the gas = 273 K

Final conditions :

P₂ (Final pressure) = 4 atm

T₂ (Final temperature) = 270°C = 270 + 273 = 543 K

V₂ (Final volume) = ?

By Gas Law:

$\dfrac{\text{P}_1\times\text{V}_1}{\text{T}_1} = \dfrac{\text{P}_2\times\text{V}_2}{\text{T}_2}$

Substituting the values :

$\dfrac{1 \times 22.4}{273} = \dfrac{4 \times \text{V}_2}{543} \\[1em] \text{V}_2 = \dfrac{543 \times 22.4}{273 \times 4} \\[1em] \text{V}_2 = \dfrac{12163.2}{1092} \\[1em] \text{V}_2 = 11.13 \text{ l} \\[1em]$

∴ Volume occupied = 11.13 l