Gas Laws & Ideal Gas Equation

Introduction to Gas Laws

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. These laws help us understand and predict the behavior of gases in various situations.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are held constant. Mathematically, it is expressed as:

$$P_1V_1 = P_2V_2$$

• P = Pressure
• V = Volume

If the volume increases, the pressure decreases, and vice versa.

Charles' Law

Charles' Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure and the amount of gas are constant. It is expressed as:

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

• V = Volume
• T = Temperature (in Kelvin)

As the temperature increases, the volume increases.

Avogadro's Law

Avogadro's Law states that the volume of a gas is directly proportional to the number of moles of gas when the pressure and temperature are constant. It can be written as:

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

• V = Volume
• n = Number of moles

More moles of gas mean a larger volume.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases. It is expressed as:

$$P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$$

Each gas in a mixture exerts pressure as if it were alone in the container.

Ideal Gas Equation

The Ideal Gas Equation combines all the gas laws into one equation. It is expressed as:

$$PV = nRT$$

• P = Pressure
• V = Volume
• n = Number of moles
• R = Ideal gas constant (8.314 J/mol·K)
• T = Temperature (in Kelvin)

This equation allows us to calculate any one of the variables if the others are known.