**Instructions:**

- Enter values for Pressure, Volume, and Temperature along with their respective units.
- Click "Calculate" to calculate the result based on the Ideal Gas Law.
- Click "Clear" to clear the input fields and results.
- Click "Copy" to copy the result to the clipboard.

**Results:**

**Calculation and Explanation:**

**Calculation History:**

## Introduction

The Ideal Gas Law Calculator is a valuable tool for scientists, engineers, and students alike. It is used to analyze and predict the behavior of gases under various conditions.

## The Ideal Gas Law

The Ideal Gas Law, denoted as PV = nRT, relates the pressure (P), volume (V), amount of substance (n), and temperature (T) of an ideal gas. This law is a fundamental concept in thermodynamics and is a close approximation for many real gases under certain conditions. The equation is as follows:

**PV = nRT**

Where:

- P is the pressure of the gas (in Pascals, Pa)
- V is the volume of the gas (in cubic meters, m³)
- n is the number of moles of gas (in moles, mol)
- R is the ideal gas constant (in J/(mol·K))
- T is the temperature of the gas (in Kelvin, K)

## Related Formulae

### Gas Constant (R)

The ideal gas constant, R, is a key component of the Ideal Gas Law and is defined as:

**R = 8.314 J/(mol·K)**

### Moles (n)

The number of moles of a gas can be calculated using the following formula:

**n = (PV) / (RT)**

### Pressure (P)

Pressure can be calculated by rearranging the Ideal Gas Law:

**P = (nRT) / V**

### Volume (V)

Volume can be calculated by rearranging the Ideal Gas Law:

**V = (nRT) / P**

### Temperature (T)

Temperature can be calculated by rearranging the Ideal Gas Law:

**T = (PV) / (nR)**

## Example Calculations

Let’s walk through a couple of example calculations to illustrate the use of the Ideal Gas Law Calculator.

### Example 1: Calculating Pressure

Suppose we have a container with a volume of 2.5 m³, containing 5 moles of an ideal gas at a temperature of 300 K. Using the Ideal Gas Law, we can calculate the pressure:

**P = (nRT) / V** **P = (5 mol * 8.314 J/(mol·K) * 300 K) / 2.5 m³** **P = 3985.04 Pa**

So, the pressure inside the container is approximately 3985.04 Pascals.

### Example 2: Calculating Volume

Let’s say we have 3 moles of gas at a pressure of 5000 Pa and a temperature of 400 K. We can calculate the volume using the Ideal Gas Law:

**V = (nRT) / P** **V = (3 mol * 8.314 J/(mol·K) * 400 K) / 5000 Pa** **V = 199.37 m³**

The volume of the gas is approximately 199.37 cubic meters.

## Real-World Use Cases

The Ideal Gas Law and its calculator find applications in various fields:

### Chemistry and Chemical Engineering

- Used to predict the behavior of gases in chemical reactions and industrial processes.
- Helps in designing and optimizing chemical reactors and distillation columns.

### Meteorology

- Used to model the behavior of gases in the Earth’s atmosphere, aiding in weather predictions.
- Essential for understanding phenomena like the ideal gas law’s effect on weather balloons.

### Automotive Engineering

- Employed in engine design and emissions control systems.
- Helps engineers calculate gas properties within internal combustion engines.

### Environmental Science

- Used to study the behavior of gases in natural environments and pollutants in the atmosphere.
- Helps in understanding air quality and climate change.

### Physics

- Fundamental in gas kinetic theory, providing insights into the motion of gas particles.
- Applied in high-energy physics experiments involving particle collisions.

## Conclusion

The Ideal Gas Law Calculator is a versatile tool that enables scientists and engineers to understand and predict the behavior of gases in various real-world scenarios. By applying the Ideal Gas Law and its related formulae, professionals from different fields can make informed decisions and optimize processes.