18 - Ideal Gas Law

Ideal Gas Law Overview

  • Ideal Gas Law: Describes the behavior of gases under various conditions.

  • Gases must be contained to apply the law.

Four Key Properties

  • Volume: The space occupied by the gas.

  • Temperature: Must be in Kelvin for calculations (0 K = absolute zero).

  • Pressure: Measured in various units depending on the context (atmospheres, mmHg).

  • Amount of Moles (n): Represents the quantity of gas.

Assumptions of the Ideal Gas Law

  1. Volume of gas << Volume of container.

  2. No intermolecular forces affecting the gas.

  3. Collisions between gas particles are perfectly elastic (kinetic energy is conserved).

Understanding Pressure

  • Pressure (P) = Force / Area

  • Example: Pressure increases when the area of contact decreases (e.g., wearing high heels).

Root Mean Squared Velocity

  • Root mean squared velocity indicates the average speed of gas particles.

  • Depends on temperature: As temperature increases, root mean squared velocity increases.

  • Formula: v_rms = sqrt((3RT)/M) where R = gas constant, T = temperature (K), M = molar mass.

Key Gas Laws

  • Boyle's Law: ( P_1V_1 = P_2V_2 ) (Pressure inversely related to volume at constant n and T).

  • Charles's Law: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} ) (Volume directly related to temperature at constant n and P).

  • Amonton's Law: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} ) (Pressure directly related to temperature at constant n and V).

  • Avogadro's Law: ( \frac{V_1}{n_1} = \frac{V_2}{n_2} ) (Volume directly related to number of moles at constant P and T).

Ideal Gas Law Formula

  • Combined gas law: ( PV = nRT )

  • R values:

    • 0.08206 atm L/(mol K)

    • 62.4 mmHg L/(mol K)

  • Choose R based on units given in problems.

Dalton's Law of Partial Pressure

  • Total pressure of a gas mixture = sum of the partial pressures of individual gases.

  • Each gas contributes to the overall pressure in proportion to its amount.

Problem Example

  • Balloon with initial volume of 785 mL at 21°C; temperature drops to 0°C. Calculate new volume while keeping pressure constant.

  • Use Charles's Law: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )

    • Convert temperatures to Kelvin (21°C = 294 K, 0°C = 273 K).

    • Solve for ( V_2 ): Results show volume decreases with temperature drop.