Ideal Gas Law

Basic Postulates (Assumptions)

The ideal gas law is based on several key assumptions about the behavior of gases. These assumptions simplify the complex interactions in real gases and allow for the development of a mathematical model.

• Gas particles are in constant, random motion. They move in straight lines until they collide with another particle or the walls of the container.

• The volume of individual gas particles is negligible compared to the volume of the container.

• No intermolecular forces exist between gas particles; they neither attract nor repel each other.

• Collisions between gas particles and with the container walls are perfectly elastic, meaning no energy is lost during collisions.

Additional info: These assumptions are most accurate under conditions of low pressure and high temperature, where real gases behave most like ideal gases.

Ideal Gas Equation

The ideal gas equation mathematically relates the pressure, volume, temperature, and amount of an ideal gas:

• Equation:

• P = pressure (in atmospheres, atm)

• V = volume (in liters, L)

• n = amount of substance (in moles, mol)

• R = ideal gas constant

• T = temperature (in kelvin, K)

Example: Calculate the volume occupied by 2.00 mol of an ideal gas at 1.00 atm and 273 K.

R – The Ideal Gas Constant

The ideal gas constant (R) is a proportionality constant that relates the units in the ideal gas equation. Its value depends on the units used for pressure and volume.

• Common value:

• Other values include (when using SI units).

Calculations Involving Ideal Gases

Calculations using the ideal gas law can determine unknown quantities such as pressure, volume, temperature, or amount of gas. Rearranging the equation allows for solving for any variable.

• To find pressure:

• To find volume:

• To find temperature:

• To find moles:

Example: If 0.50 mol of a gas occupies 10.0 L at 300 K, what is the pressure?

Dalton’s Law of Partial Pressures

Definition and Application

Dalton’s Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas.

• Equation:

• Partial pressure is the pressure that each gas would exert if it were alone in the container.

• This law is useful for calculating the pressure of gases collected over water or in mixtures.

Example: If a container holds oxygen at 0.50 atm and nitrogen at 0.75 atm, the total pressure is:

Absolute Zero

Definition

Absolute zero is the lowest possible temperature, where the motion of particles theoretically ceases. It is defined as 0 kelvin (K), which is equivalent to -273.15°C.

• At absolute zero, a system has minimum internal energy.

• No substance can be cooled to absolute zero by any finite number of processes (third law of thermodynamics).

Additional info: Absolute zero is a fundamental concept in thermodynamics and is the basis for the Kelvin temperature scale.