Study of Gas Laws — Question 3

(a) V₁ = Initial volume of the gas = 80 cm³
P₁ = Initial pressure of the gas = 100 mm of Hg
P₂ = Final pressure of the gas = 125 mm of Hg
V₂ = Final volume = ?

By Boyle's Law:

$\text{P}_1 \text{V}_1 = \text{P}_2 \text{V}_2$

Substituting the values :

$100 \times 80 = 125 \times \text{V}_2 \\[0.5em] \text{V}_2 = \dfrac{100 \times 80 }{125} \\[0.5em] \text{V}_2 = 64 \text{ cm}^3$

∴ x = 64 cm³

(b) V₁ = Initial volume of the gas = 40 cm³
P₁ = Initial pressure of the gas = 200 mm of Hg
V₂ = Final volume of the gas = 32 cm³
P₂ = Final pressure of the gas = ?

By Boyle's Law:

$\text{P}_1 \text{V}_1 = \text{P}_2 \text{V}_2$

Substituting the values :

$200 \times 40 = \text{P}_2 \times 32 \\[0.5em] \text{P}_2 = \dfrac{200 \times 40 }{32} \\[0.5em] \text{P}_2 = 250 \text{ mm of Hg}$

∴ y = 250 mm of Hg

(i) Graph of volume plotted against pressure :

(ii) Graph of PV plotted against pressure :