What is the General Gas Equation? PV = nRT Best Explained with Real-World Examples(1662)

The General Gas Equation, also known as the Ideal Gas Law, is one of the most foundational and widely used equations in physical chemistry. It describes how gases behave under varying conditions of pressure, temperature, volume, and the amount of substance (moles). Whether you’re a chemistry student, an educator, or a professional working in engineering or thermodynamics, understanding this equation is vital for analyzing gas systems.

What is the General Gas Equation?

The General Gas Equation is written as:

PV = nRT

Where:

• P = Pressure of the gas
• V = Volume of the gas
• n = Number of moles of the gas
• R = Universal Gas Constant
• T = Absolute Temperature (in Kelvin)

This equation forms the ideal gas law, which models the behavior of an ideal gas—a hypothetical gas composed of randomly moving point particles that do not interact except when they collide elastically.

Background: The Evolution of Gas Laws

Before the General Gas Equation was formulated, several independent gas laws were discovered. Each law describes a unique relationship between two variables of a gas, assuming the other variables remain constant.

1. Boyle’s Law (1662)

Pressure and Volume

At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume.

P ∝ 1/V → PV = constant

2. Charles’s Law (1787)

Volume and Temperature

At constant pressure, the volume of a gas is directly proportional to its absolute temperature.

V ∝ T → V/T = constant

3. Gay-Lussac’s Law (1809)

Pressure and Temperature

At constant volume, the pressure of a gas is directly proportional to its temperature.

P ∝ T → P/T = constant

4. Avogadro’s Law (1811)

Volume and Moles

Equal volumes of gases at the same temperature and pressure contain the same number of particles.

V ∝ n → V/n = constant

➕ Combining All Four Laws

By combining these laws, we get the proportional relationship:

PV ∝ nT

This leads us to introduce a proportionality constant, R (the universal gas constant), giving the full equation:

PV = nRT

Variables and Units in the General Gas Equation

Correctly using the ideal gas law requires using consistent units. Here’s a summary of the variables and their standard units:

Important: Temperature must always be converted to Kelvin before using the formula. Conversion: K = °C + 273.15

Values of the Universal Gas Constant (R)

The gas constant R can take different numerical values depending on the units used in your calculations:

Tip: Choose the appropriate value of R based on the units of pressure and volume in your question to avoid conversion errors.

Derivation of the General Gas Equation

Let’s derive the ideal gas law by combining the earlier gas laws:

1. From Boyle’s Law:
   P ∝ 1/V at constant T and n
2. From Charles’s Law:
   V ∝ T at constant P and n
3. From Avogadro’s Law:
   V ∝ n at constant P and T

Combining all three:

V ∝ nT / P

Rewriting this, we get:

PV ∝ nT

Adding the proportionality constant R:

PV = nRT

This equation provides a mathematical model for gas behavior under the assumption that the gas behaves ideally.

Assumptions of the Ideal Gas Law

The general gas equation assumes the following:

1. Gas particles do not attract or repel each other (no intermolecular forces).
2. Gas particles have negligible volume compared to the container’s volume.
3. Collisions between gas particles are perfectly elastic—no energy is lost.
4. The gas is in random motion and evenly distributed.

Real gases deviate from this behavior under high pressure or low temperature conditions, where particle volume and intermolecular forces become significant.

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