# The Gas Laws

This is part of Year 11 HSC Chemistry course under the topic of Molarity

### 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 relationships between pressure, volume, and temperature of ideal gases. These laws were developed by four distinguished scientists – Robert Boyle, Jacques Charles, Joseph Louis Gay-Lussac, and Amedeo Avogadro – in the late 18th century. Ideal gases follow these mathematical relationships under perfect circumstances. The gas laws culminated in the Ideal Gas Law, a combined expression representing these relationships.

### Boyle's Law

Boyle's law states that at a constant temperature, the volume of a given amount of gas varies inversely with the applied pressure. As the pressure on a gas increases, the volume decreases since the gas particles are forces 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.

$$PV = k \text{ (where } k \text{ is a constant at a given temperature)}$$

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

$$P_1V_1 = P_2V_2$$

### Charle'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.

$$V = kT \text{ (where } k \text{ is a constant at a given temperature)}$$

$$V \propto T$$

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

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

Gay-Lussac's Law states that at constant volume, the pressure of a given amount of gas is proportional to the temperature in Kelvin. Volume and pressure are interdependent, and so are temperature and pressure. For example, tire pressure is greater on hotter days or after a ride.

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

$$P \propto T$$

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

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

Avogadro's Law states that equal volumes of all gases at the same temperature and pressure have the same number of molecules.

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

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