Lesson 2, Topic 3
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# Boyle’s Law

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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 P1V1 = K

For gas 2, we have P2V2 = K

Since K = K then,

P1V1 = P2V2 (at constant temperature)

Where P1 = Initial Pressure, P2 = Final Pressure

V1 = Initial Volume, V2 = 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 300cm3 at 900mmHg pressure. Calculate the volume occupied by the same gas at 750mmHg if the temperature remains constant.

According to Boyle’s law

P1V1 = P2V2

P1 =900mmHg
VI = 300cm3
P2 = 750mmHg
V2 = ?

V2 = $$\frac{P_1 V_1}{P_2}\\ = \frac{900 \; \times \; 300}{750} \\ = \scriptsize 360cm^3$$

2. A certain mass of gas occupies 200cm3 at 1.0 x 105Nm-2, Calculate its volume when the pressure becomes 2.0 x 105 Nm-2 at constant temperature.

P1 = 1.0×105Nm-2
V1 = 200cm3
P2 = 2.0 X 105Nm-2
V2 = ?

V2 = $$\frac{P_1 V_1}{P_2}\\ = \frac{1.0 \; \times \; 10^5 \; \times \; 200}{2 \; \times \; 10^5} \\ = \scriptsize 100cm^3$$

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