An English Physicist, Robert Boyle in 1962 studied the effect of pressure change on gas volume. His observations led to Boyle’s Law.

### What is Boyle’s Law?

Boyle’s law states that the volume of a fixed mass of gas is inversely proportional to its pressure, provided temperature remains constant.

It means that at constant temperature, an increase in the pressure exerted on a fixed mass of gas leads to a decrease in the gas volume and vice versa.

Mathematically,

\( \scriptsize V \propto \normalsize \frac{1}{P} \)This proportionality can be converted into an equation by adding a constant, K.

i.e \( \scriptsize V = \normalsize \frac{1}{P}\scriptsize K \)

:- \( \scriptsize V = \normalsize \frac{K}{P} \)

Or PV = K

Where V = Volume

P = Pressure

K = Proportionality constant

Using the expression PV = K

For gas 1, we have P_{1}V_{1} = K

For gas 2, we have P_{2}V_{2} = K

Since K = K then,

P_{1}V_{1} = P_{2}V_{2} (at constant temperature)

Where P_{1} = Initial Pressure, P_{2} = Final Pressure

V_{1} = Initial Volume, V_{2} = Final volume

Boyle’s law can also be restated as the pressure of a given mass of gas inversely proportional to its volume, temperature remaining constant.

### Graphical Representation of Boyle’s Law

The following can be obtained from the graphical representation of Boyle’s law.

(a) A plot of P against V is a curve, which is asymptotic with the x-and y-axis.

(b) A plot of V against 1/V (or v against 1/P) gives a straight line passing through the origin.

(c) A plot of PV against Pressure P (or volume V) is a straight horizontal line graph.

### Pictorial Representation of Boyle’s Law

Figure above shows diagrammatically how kinetic theory of matter explains Boyle’s law which states that the volume of a gas is inversely proportional to its pressure.

### How kinetic theory explains Boyle’s Law

A constant temperature, if the pressure on a given amount of gas is doubled, its volume will decrease by one-half. Conversely, if the pressure is decreased by one-half, the volume will double.

### Calculations based on Boyle’s Law

1. A given mass of a gas occupies a volume of 300cm^{3} at 900mmHg pressure. Calculate the volume occupied by the same gas at 750mmHg if the temperature remains constant.

According to Boyle’s law

P_{1}V_{1} = P_{2}V_{2}

P_{1} =900mmHg

V_{I} = 300cm^{3}

P_{2} = 750mmHg

V_{2} = ?

V_{2 }= \(\frac{P_1 V_1}{P_2}\\ = \frac{900 \; \times \; 300}{750} \\ = \scriptsize 360cm^3 \)

2. A certain mass of gas occupies 200cm^{3} at 1.0 x 10^{5}Nm^{-2}, Calculate its volume when the pressure becomes 2.0 x 10^{5} Nm^{-2} at constant temperature.

P_{1} = 1.0×10^{5}Nm^{-2}

V_{1} = 200cm^{3}

P_{2} = 2.0 X 10^{5}Nm^{-2}

V_{2} = ?

V_{2} = \(\frac{P_1 V_1}{P_2}\\ = \frac{1.0 \; \times \; 10^5 \; \times \; 200}{2 \; \times \; 10^5} \\ = \scriptsize 100cm^3 \)

## Responses