The Ideal Gas Law and Its Components

Learning Objectives

Define pressure, volume, temperature, and moles in the context of gases.

State and apply Boyle's Law, Charles's Law, and Gay-Lussac's Law.

Use the Ideal Gas Law (PV=nRT) to solve for unknown variables.

Understand the conditions under which real gases deviate from ideal behavior.

Understanding the Gaseous State

Gases are unique because their particles are far apart and in constant, random motion. This allows them to be compressed and to fill any container they occupy. To describe the state of a gas, we use four variables:

Pressure (P): The force exerted by the gas per unit area. Common units are atmospheres (atm), kilopascals (kPa), or millimeters of mercury (mmHg).

Volume (V): The space the gas occupies, usually in liters (L) or milliliters (mL).

Temperature (T): A measure of the average kinetic energy of the gas particles. In gas law calculations, temperature must always be in Kelvin (K). K = °C + 273.15.

Moles (n): The amount of gas, representing a specific number of particles (6.022 x 10²³ particles per mole).

The Simple Gas Laws

Several laws describe the relationships between pairs of these variables when others are held constant.

Boyle's Law: At constant temperature, the pressure of a gas is inversely proportional to its volume. (P₁V₁ = P₂V₂)

Charles's Law: At constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). (V₁/T₁ = V₂/T₂)

Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its absolute temperature (in Kelvin). (P₁/T₁ = P₂/T₂)

These can be combined into the Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂. This is useful for problems where P, V, and T are all changing.

The Ideal Gas Law

The Ideal Gas Law incorporates all four variables into a single, powerful equation:

PV = nRT

Where:

P, V, n, T are pressure, volume, moles, and temperature as defined above.

R is the ideal gas constant. Its value depends on the units used for pressure.

R = 0.0821 L·atm / (mol·K) (most common in chemistry)

R = 8.314 J / (mol·K) or L·kPa / (mol·K) (common in physics and physical chemistry)

It is crucial to use the correct value of R that matches the units of your other variables.

When are Gases Not Ideal?

The Ideal Gas Law works well under most conditions, but it assumes that gas particles have no volume and do not exert attractive or repulsive forces on each other. Real gases deviate from this ideal behavior under two main conditions:

1.High Pressure: Particles are forced close together, so their individual volume becomes significant compared to the container volume.

2.Low Temperature: Particles move more slowly, allowing intermolecular attractive forces to become significant.

The van der Waals equation is a modified version of the ideal gas law that accounts for these factors.

Key Terms

Ideal Gas Law: The equation of state of a hypothetical ideal gas, expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the absolute temperature in Kelvin.
Boyle's Law: A gas law stating that the pressure and volume of a gas have an inverse relationship when temperature is held constant (P₁V₁ = P₂V₂).
Charles's Law: A gas law stating that the volume of an ideal gas is directly proportional to its absolute temperature (in Kelvin) when pressure is held constant (V₁/T₁ = V₂/T₂).
Absolute Temperature: Temperature measured on a scale where zero represents the absolute minimum temperature possible (absolute zero). The Kelvin scale is an absolute temperature scale.
Standard Temperature and Pressure (STP): A standard set of conditions for experimental measurements, defined as a temperature of 273.15 K (0 °C) and an absolute pressure of exactly 1 atm (101.325 kPa).