# The Gas Laws

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:
• Gay-Lussac's Law (Temperature)
• Boyle's Law
• Charles' Law

### The Gas laws

The gas laws describe the relationship between pressure, volume, temperature and amount of ideal gases. These laws were developed by four distinguished scientists – Robert Boyle, Jacques Charles, Joseph Louis Gay-Lussac, and Amedeo Avogadro – into the late 18th century. Ideal gases follow predicted mathematical relationships under specified circumstances. These gas laws can be represented by a single equation - the ideal gas equation:

$$PV = nRT$$

In the context of gas laws:

Pressure: The amount of force exerted by gas particles onto one another and the walls in a system

Common pressure units:

• Pascal (Pa)
• 1 Kilopascal (kPa) = 1000 Pa
• 1 atmosphere (atm) = 101325 Pa

Volume: The space occupied by gas particles in a system

Common volume units:

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

Amount: The number of specified entities in a system (atoms, molecules, etc.)

Common ways to describe quantity of gas:
• number of particles/molecules
• number of moles (divided by Avogadro’s number)

Temperature: The average kinetic energy of gas particles in a system

Common Temperature units:

• Kelvin (K) - Absolute temperature. Zero Kelvin is defined as the temperature at which the average kinetic energy of gas molecules is zero, meaning there is no movement of molecules.
• Degrees Celcius (℃) - +273.15 to convert to Kelvin

### Gay-Lussac's Law: Pressure and Temperature

Gay-Lussac’s Law states that the pressure of a gas is directly proportional to its temperature, provided the volume and the amount of gas remain constant. This means that if the temperature of a gaseous system increases, so does the temperature and vice versa.

The mathematical representation of the relationship described by Gay-Lussac's law can be derived from the ideal gas law as shown:

$$PV = nRT$$

$$\frac{P}{T} = k \text{ (where } k \text{ is a constant at constant temperature and amount)}$$

$$P \propto T$$

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

The relationship between pressure and temperature as described by Gay-Lussac's law is demonstrated on the graph below.

Real-World Applications of Gay-Lussac's Law:

• Pressure cooker – food is sealed in steam which increases the pressure inside the cooker. As the temperature rises so does the pressure
• Aerosol Cans – have warnings to avoid open fires. Increase in temperature builds pressure in the can which can cause explosions.

### Boyle's Law

Boyle's law states the volume of a given amount of gas is inversely proportional to the applied pressure when temperature and amount are held constant. This means that as the pressure of a gas increases, its volume decreases since the gas particles are forced closer together

Conversely, when pressure decreases, the volume increases as the particles have more space to move apart. An example of this phenomenon can be seen in weather balloons, which expand as they rise to higher altitudes where pressure is lower.

The mathematical representation of the relationship described by Boyle's law can be derived from the ideal gas law as shown:

$$PV = nRT$$

$$PV = k \text{ (where } k \text{ is a constant when amount and temperature are constant )}$$

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

$$P_1V_1 = P_2V_2$$

The relationship between volume and pressure as described by Boyle's Law is demonstrated on the following graph.

Real-World Applications of Boyle's Law:

• Breathing and lung function – diaphragm moves down to increase volume and decrease pressure in lungs
• Syringe – pushing plunger decreases volume to increase pressure (like bike pump)
• Balloon – when balloons are squeezed, volume decreases so pressure inside increases.

### Charles's Law: Volume and Temperature

Charles's Law states that if the volume of a container of gas increases at constant pressure and mass, the temperature must also increase, and vice versa. Hot air balloons rise because gases expand when heated. This is why warm air collects near the ceiling while cooler air settles at ground level.

The mathematical representation of the relationship described by Charles's law can be derived from the ideal gas law as shown:

$$PV = nRT$$

$$V = kT \text{ (where } k \text{ is a constant when amount and pressure are constant)}$$

$$V \propto T$$

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

The relationship between volume and temperature as described by Charles's Law is demonstrated on the following graph.

Real-World Applications of Charles's Law:

Hot air balloon – increasing the temperature of air causes it to increase its volume and become less dense than surrounding air

Bread baking – increasing temperature causes gas to expand in dough.

### Avogadro's Law: Volume and Amount of Gas

Avogadro's Law states ideal gases containing the same number of molecules occupy an equal volume at the same pressure and temperature. In addition, volume is directly proportional to the quantity of gas when pressure and temperature are kept constant.

The mathematical representation of the relationship described by Avogadro's law can be derived from the ideal gas equation as shown:

$$PV = nRT$$

$$V \propto n \text{ (where } n \text{ is the amount of gas, and pressure } P \text{ and temperature } T \text{ are fixed and constant)}$$

$$V = k \times n \text{ where }k \text{ is a constant at a given temperature}$$

The relationship between volume and amount as described by Avogadro's law is demonstrated on the following graph