A student performed an experiment to measure pressure and volume of a gas at constant temperature and noted the following:

Pressure (mm of Hg)	Volume (cm3)
100	80
125	x
200	40
y	32

Calculate the value of x and y. Which law was used in the calculations? Draw graphs to show:

(i) volume plotted against pressure.

(ii) PV plotted against pressure

(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 :