Study of Gas Laws — Question 23

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) = 27°C = 27 + 273 = 300 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 :

$\dfrac{1 \times 22.4}{273} = \dfrac{4 \times \text{V}_2}{300} \\[1em] \text{V}_2 = \dfrac{300 \times 22.4}{273 \times 4} \\[1em] \text{V}_2 = 6.15 \text{ l} \\[1em]$

∴ Volume occupied = 6.15 l