Gas Laws

The behavior of gases can be explained using three fundamental laws: Boyle's Law, Charles's Law, and the Ideal Gas Law. These laws relate pressure, volume, and temperature of gases under different conditions.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.

Formula: P₁V₁ = P₂V₂

Examples:

Example 1: If a gas at 2 atm occupies 5 L, what will its volume be at 4 atm?

Solution: V₂ = (P₁V₁) / P₂ = (2 × 5) / 4 = 2.5 L

Example 2: A gas occupies 10 L at 1 atm. What is its pressure if its volume is reduced to 2 L?

Solution: P₂ = (P₁V₁) / V₂ = (1 × 10) / 2 = 5 atm

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature at constant pressure.

Formula: V₁ / T₁ = V₂ / T₂

Examples:

Example 1: A gas has a volume of 3 L at 300 K. What is its volume at 600 K?

Solution: V₂ = (V₁T₂) / T₁ = (3 × 600) / 300 = 6 L

Example 2: A gas occupies 4 L at 200 K. What is its temperature when its volume becomes 8 L?

Solution: T₂ = (V₂T₁) / V₁ = (8 × 200) / 4 = 400 K

Ideal Gas Law

The Ideal Gas Law relates pressure, volume, temperature, and the number of moles of a gas.

Formula: PV = nRT

Where: P = Pressure, V = Volume, n = Moles of gas, R = Gas constant, T = Temperature (in Kelvin).

Examples:

Example 1: Find the volume of 1 mole of a gas at 1 atm and 273 K. R = 0.0821 L·atm/mol·K

Solution: V = (nRT) / P = (1 × 0.0821 × 273) / 1 = 22.4 L

Example 2: Calculate the pressure of 2 moles of gas in a 10 L container at 300 K. R = 0.0821 L·atm/mol·K

Solution: P = (nRT) / V = (2 × 0.0821 × 300) / 10 = 4.93 atm