ICSE Questions Set in Previous Years — Question 39

Initial conditions [S.T.P.] :

P₁ = Initial pressure of the gas = 760 mm Hg
V₁ = Initial volume of the gas = 100 cm³
T₁ = Initial temperature of the gas = 0°C = 273 K

Final conditions:

P₂ (Final pressure) = increased by one-fifth of P₁
= (1 + $\dfrac{1}{5}$) of 760
= $\dfrac{6}{5}$ x 760
= 912
V₂ (Final volume) = ?
T₂ (Final temperature) = increased by one-fifth of 273 K = 1 + $\dfrac{1}{5}$ of 273
= $\dfrac{6}{5}$ x 273 = $\dfrac{1638}{5}$

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 :

$\dfrac{760 \times 100 }{273} = \dfrac{912\times \text{V}_2}{\dfrac{1638}{5}} \\[1em] \dfrac{760 \times 100 }{273} = \dfrac{5 \times 912 \times \text{V}_2}{1638} \\[1em] \text{V}_2 = \dfrac{760 \times 100 \times 1638}{273 \times 5 \times 912} \\[1em] \text{V}_2 = 100\text{ cm}^3$

∴ The final volume of the gas = 100 cm³