# Ideal Gas Equation – Derivation, Definition, Equation

## Introduction to Ideal Gas Equation

Gas chemistry, a fascinating realm within the world of chemistry, delves deep into the mysterious behavior of gases that surround us every day. From the air we breathe to the unseen gases within chemical reactions, understanding their properties is essential. At the core of comprehending the behavior of gases lies the Ideal Gas Equation, a mathematical construct that has shaped our understanding of how gases interact with their surroundings. In this article, we embark on a journey to unveil the secrets of the Ideal Gas Equation, its derivation, and the fundamental laws that underpin it. Our quest will take us through the intricate language of chemistry, demystifying this essential equation that governs the behavior of gases. So, let’s embark on this expedition into the heart of gas chemistry!

## What is the Ideal Gas Equation?

The ideal gas equation is a fundamental concept in the field of chemistry and physics. It’s a mathematical formula that helps us understand how gases behave under various conditions. This equation is incredibly useful because it allows us to make predictions about the behavior of gases without having to observe them directly.

The ideal gas equation is also known as the ideal gas law, and it’s expressed as:

$$PV=nRT$$

In this equation:

• P represents the pressure of the gas.
• V is the volume of the gas.
• n stands for the number of moles of the gas.
• R is the universal gas constant.
• T represents the temperature of the gas in Kelvin.

## Ideal Gas Laws

Before we dive into the details of the ideal gas equation, let’s explore a few other gas laws that paved the way for its development.

#### Boyle’s Law

Boyle’s law, named after physicist Robert Boyle, states that the pressure and volume of a gas are inversely proportional when the temperature and the number of moles are held constant. In simpler terms, if you decrease the volume of a gas, its pressure will increase, and vice versa. This law is expressed as:

PV = constant

#### Charles’s Law

Charles’s law, named after French scientist Jacques Charles, deals with the relationship between the volume and temperature of a gas. It states that, at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin. This law can be expressed as:

V/T = constant

#### Gay-Lussac’s Law

Gay-Lussac’s law, named after French chemist Joseph Louis Gay-Lussac, focuses on the relationship between the pressure and temperature of a gas. According to this law, at constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin. The law can be expressed as:

P/T = constant

Avogadro’s law, named after Italian scientist Amedeo Avogadro, states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. In other words, the number of molecules in a gas is directly proportional to the volume. This law can be expressed as:

n/V = constant

## Ideal Gas Equation

Now that we’ve explored some of the essential gas laws, we can understand how they all come together in the ideal gas equation. Let’s break down the equation and understand what each variable represents.

The ideal gas equation is, $$PV=nRT$$

• P (Pressure): This is the force exerted by the gas on the walls of its container. It’s measured in Pascals (Pa) or atmospheres (atm).
• V (Volume): The volume of the gas is the space it occupies. It’s typically measured in liters (L) or cubic meters (m³).
• n (Number of Moles): Moles are a unit of measurement in chemistry that represents the amount of substance. It’s measured in moles (mol).
• R (Universal Gas Constant): The universal gas constant is a constant that relates the properties of gases. It’s a key factor in the ideal gas equation. Its value depends on the units used for pressure, volume, and temperature. One common value for R is 8.314 J/(mol·K) when pressure is in Pascals, volume is in cubic meters, and temperature is in Kelvin.
• T (Temperature in Kelvin): In the ideal gas equation, the temperature must be measured in Kelvin (K). To convert from Celsius to Kelvin, simply add 273.15 to the temperature in Celsius.

## Ideal Gas Equation Derivation

Now, let’s get into the nitty-gritty of how the ideal gas equation is derived. Brace yourself; we’re diving into some mathematical equations, but we’ll keep it as simple as possible!

Step 1: According to Boyle’s Law and Charles’s Law

We’ll start with the combination of Boyle’s law and Charles’s law. These two laws can be combined to give us an intermediate equation:

$$\frac{ P_{1} V_{1} }{ T_{1} } = \frac{ P_{2} V_{2} }{ T_{2}}$$

In this equation, the subscripts 1 and 2 represent two different states of the gas, each with its own set of pressure (P), volume (V), and temperature (T).

Step 2: According to Avogadro’s Law

Next, let’s introduce Avogadro’s law into the equation. Remember, Avogadro’s law states that the number of moles (n) is directly proportional to the volume (V) at a constant temperature and pressure. This allows us to rewrite the equation as:

$$\frac{ P_{1} V_{1} }{ n_{1} T_{1} } = \frac{ P_{2} V_{2} }{ n_{2} T_{2}}$$

Step 3: Universal Gas Constant

To get to the ideal gas equation, we need to introduce the universal gas constant (R). We can do this by making R the subject of the equation. To do this, we multiply both sides by n₁R and rearrange the terms:

$$n_{1}R= \frac{ P_{1} V_{1} }{ T_{1} }$$

Step 4: Ideal Gas Equation

Now, we can replace the left side of the equation (n₁R) with the right side of the equation from Step 3. This gives us the ideal gas equation:

$$n_{1}R= \frac{ P_{1} V_{1} }{ T_{1} }$$

This equation can also be written as:

$$PV=nRT$$

And there it is! The ideal gas equation in all its glory. This equation helps us understand the behavior of gases under different conditions.

## Ideal Gas Equation Summary

In the realm of chemical exploration, the Ideal Gas Equation emerges as an invaluable tool. It elegantly weaves together various gas laws, including Boyle’s law, Charles’s law, and Avogadro’s law, to offer a comprehensive understanding of gas behavior. This equation, PV = nRT, captures the essence of gas chemistry, enabling scientists and researchers to predict and manipulate gas behavior under a range of conditions.

The equation itself is a testament to the beauty of chemical relationships. Pressure (P), volume (V), the number of moles (n), and temperature (T) harmoniously converge, guided by the universal gas constant (R), to provide a mathematical framework for the study of gases. Through this lens, we can peer into the intricate dance of gas molecules, gaining insights into their responses to changes in their environment.

## Final Notes

In conclusion, the Ideal Gas Equation serves as a cornerstone in the world of chemistry. It empowers us to navigate the complex world of gases, from the laboratory to industrial processes, and from understanding the behavior of gases in the Earth’s atmosphere to the engineering of innovative technologies. As we unravel the mysteries of gases, the Ideal Gas Equation stands as an enduring beacon of understanding, illuminating the path for countless scientific endeavors.

This is all about the Ideal Gas Equation, the in-depth article helps in understanding the ideal gas equation derivation, and ideal gas laws. If you want to learn complex concepts in a simple way visit our blogs section and if you are looking for the best online home tutor then Tutoroot will be the ultimate choice. Our experienced faculty helps in understand complex concepts in a simple way. Click here to book a FREE DEMO now!!

## FAQ’s

What is the Universal Gas Constant?

The universal gas constant (R) is a fundamental constant in chemistry and physics. It relates to the properties of gases and is a key component of the ideal gas equation (PV = nRT). The value of R depends on the units used for pressure, volume, and temperature. One common value for R is 8.314 J/(mol·K) when pressure is in Pascals, volume is in cubic meters, and temperature is in Kelvin.

Define Ideal Gas Equation

The ideal gas equation, also known as the ideal gas law, is a fundamental formula that describes the behavior of gases. It is expressed as PV = nRT, where P represents the pressure of the gas, V is the volume of the gas, n stands for the number of moles of the gas, R is the universal gas constant, and T represents the temperature of the gas in Kelvin. This equation allows us to make predictions about how gases will behave under different conditions.

What are the 3 Gas Laws?

The three fundamental gas laws are:

• Boyle’s Law: This law states that the pressure and volume of a gas are inversely proportional when the temperature and the number of moles are held constant. It is expressed as PV = constant.
• Charles’s Law: Charles’s law explores the connection between a gas’s volume and its temperature under unchanging pressure conditions. It articulates that as the temperature of a gas is measured in Kelvin increases, its volume also increases in direct proportion. This law can be expressed as V/T = constant.
• Gay-Lussac’s Law: Gay-Lussac’s law focuses on the relationship between the pressure and temperature of a gas at constant volume. This law asserts that the pressure of a gas increases directly in proportion to its temperature when measured in Kelvin. This law can be expressed as P/T = constant.

These three laws, along with Avogadro’s law, serve as the basis for the ideal gas equation, which unifies them into a single formula (PV = nRT) that describes the behavior of gases comprehensively.