# Boyle's Law

This is part of Year 11 HSC Chemistry course under the topic of Gas Laws.

### HSC Chemistry Syllabus

• Conduct investigations and solve problems to determine the relationship between the Ideal Gas Law and:
• Boyle's Law

### Gas Laws

Boyle's law is one of the four individual gas laws which were combined to describe the ideal gas law.

The gas laws describe the behaviour of gases under ideal circumstances and assume their properties that ideal gases:

• Have a low density since the spaces between the particles of gas are large
• Are free flowing/forming meaning that they fill the volumes of their containers and can leak through cracks
• Are compressible and expandable
• Are diffusive meaning that they travel from areas of higher concentration to areas of lower concentration.

Boyle's law focuses on the inversely proportional relationship between pressure and volume when temperature and amount of gas are kept constant.

### Boyle's Law

Boyle's Law is named after Robert Boyle, a 17th-century chemist who was one of the first to pioneer the modern scientific method.

Boyle's law states that the pressure of a gas is inversely proportional to its volume when temperature and amount of gas are kept constant. Mathematically the relationship described by Boyle's Law can be expressed as

$$P \propto \frac{1}{V}$$

and thus

$$PV = k$$

or

$$P_1V_1 = P_2V_2$$

Where:

P_1 and V_1 represent the initial pressure and volume

P_2 and V_2 represent the pressure and volume after a change has been imparted on the gas system.

In the context of Boyle's Law, pressure refers to the force that is experienced by particles of gas while volume refers to the space that is occupied by those gas particles.

Units of Measurement:

• Pressure:
• Pascal (Pa)
• 1 Kilopascal (kPa) = 1000 Pa
• 1 Atmosphere (atm) = 101325 Pa.

• Volume
• Millilitre (mL)
• 1 Litre (L) = 1000 mL

### Deriving and understanding Boyle's Law

The ideal gas law is given by the formula:

$$PV = nRT$$

Where:

• P is pressure (in kPa)
• V is volume (in L)
• n is the number of moles of gas
• R is the universal gas constant = 8.314 J mol–1 K–1
• T is temperature (in Kelvin)

When temperature and amount are held constant, the expression nRT is equivalent to a constant k. Thus the following mathematical equation can also be obtained:

$$PV = k$$

For this relationship to be true, an increase in pressure must lead to an equivalent decrease in volume and a decrease in pressure must lead to an equivalent increase in temperature. Thus when temperature and amount are held constant, according to the ideal gas law

$$P \propto \frac{1}{V}$$

The relationship described by Boyle's Law is demonstrated in the graph below.

### Real-World Examples & Practical Applications

Understanding Boyle's law is crucial not just in academic settings but also for everyday applications including lung, syringe, and balloon functions.

1. Lungs: below the lungs lie a muscle called the diaphragm. This muscle moves up and down to increase and decrease the pressure in the lungs. When breathing in, the lung expands – volume increases and pressure decreases as predicted by Boyle's law. At this point, the external pressure is greater than the internal pressure of the lungs which is the mechanism which allows air to travel into the lungs. When we exhale, the volume of the lung decreases. According to Boyle's law, we expect that the pressure also increases. Contrary to inhalation, the internal pressure is now greater than the external pressure, so particles of pas then travel outwards from the lungs to decrease the internal pressure.

2. Syringe: Pushing a syringe, assuming that it is sealed, will decrease volume and increase pressure much like a bicycle pump. Initially, the molecules of gas are moving around randomly inside the syringe. Once the plunger is pushed however, the amount of space available for those molecules of gas to move is diminished. Despite this decrease in volume, the molecules continue to vibrate as usually meaning that there are much more collisions between the gas and the walls of the syringe. Thus we observe Boyle's law in action as an increase in the pressure of the system occurs when volume is decreased.

3. Balloon: When a balloon is squeezed, the volume available for gas particles decreases just like with the syringe. Similarly, the particles of gas which are inside the container are initially vibrating and moving with a certain amount of kinetic energy. After the balloon has shrunk indicating a decrease in volume, the particles begin colliding with a greater frequency and force. Thus with a decrease in volume, the system experiences an increase in internal pressure.