The **main difference between ideal gas law and combined gas law** is that ideal gas law is a fundamental equation that relates the pressure (P), volume (V), and temperature (T) of an ideal gas, along with the gas constant (R), whereas combined gas law is derived from the ideal gas law and combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single equation.

The ideal gas law and the combined gas law are fundamental principles in thermodynamics and fluid dynamics, offering crucial insights into the behavior of gases.

### Key Areas Covered

**1. What is the Ideal Gas Law **

* – Definition, Calculation, Role*

**2. What is Combined Gas Law**

* – Definition, Calculation, Role*

**3. Similarities Between Ideal Gas Law and Combined Gas Law**

* – Outline of Common Features*

**4. Difference Between Ideal Gas Law and Combined Gas Law**

* – Comparison of Key Differences*

**5. FAQ: Ideal Gas Law and Combined Gas Law**

* – Frequently Asked Questions*

### Key Terms

* Ideal Gas Law, Ideal Gas, Combined Gas Law*

## What is Ideal Gas Law

The ideal gas law is a fundamental equation describing gas behavior under various conditions. Expressed as PV = nRT, it’s a powerful tool for understanding the relationships between key gas properties: pressure (P), volume (V), temperature (T), the number of moles (n), and the gas constant (R). Moreover, this law combines individual gas laws into a single equation, providing insight into the interactions between these variables.

**P (Pressure)**: Pressure is a measure of the force exerted by gas molecules on the walls of their container. It is typically measured in pascals (Pa) or atmospheres (atm).

**V (Volume)**: Volume represents the physical space occupied by the gas. It is generally measured in liters (L) or cubic meters (m³).

**n (Number of Moles)**: The number of moles represents the quantity of gas particles in a given sample. It is measured in moles (mol).

**T (Temperature)**: Temperature is a measure of the average kinetic energy of gas particles. It is typically measured in kelvin (K).

**R (Gas Constant)**: The gas constant is a proportionality constant that relates the pressure, volume, number of moles, and temperature. Its value depends on the units used for other variables. The most common gas constant is 8.314 J/(mol·K).

### Role of Ideal Gas Law

The ideal gas law is applicable to ideal gases, which are theoretical gases that follow the ideal gas behavior perfectly. Negligible molecular volumes and weak intermolecular forces characterize these gases. In reality, no gas is truly ideal, but the ideal gas law serves as a useful approximation for real gases under many conditions. The ideal gas law can be derived from Boyle’s Law, Charles’s Law, and Avogadro’s hypothesis. Let’s examine the derivation:

Boyle’s Law: PV = constant (at constant temperature and number of moles)

Charles’s Law: V/T = constant (at constant pressure and number of moles)

Avogadro’s Hypothesis: V/n = constant (at constant pressure and temperature)

By combining these three relationships, we get:

(PV) / (nT) = constant

This constant is denoted as R, the gas constant. Thus, we have derived the Ideal Gas Law:

PV = nRT

In fact, the ideal gas law is a versatile equation that can be used to predict and describe the behavior of gases under a wide range of conditions. It is particularly useful for understanding how changes in pressure, volume, temperature, or the number of moles affect gas properties.

The ideal gas law is paramount in science and engineering, finding practical applications in various fields. It defines the characteristics of ideal gases, offering a fundamental model for real gases and serving as a cornerstone for understanding gas behavior. Additionally, it helps to predict gas behavior in diverse situations, calculate properties of gas mixtures, determine reactant or product quantities in chemical reactions, calibrate instruments like barometers, and establish the value of the gas constant (R), which is a fundamental constant in thermodynamics and essential for various scientific calculations.

## What is Combined Gas Law

The combined gas law is a fundamental equation in the field of thermodynamics, connecting the individual gas laws—Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law. It combines these individual gas laws into a single equation that describes the behavior of gases under changing conditions. Moreover, it provides a versatile tool for understanding how changes in pressure, volume, and temperature affect gas properties.

The mathematical representation of the combined gas law is as follows:

(P_{1}∗V_{1})/T_{1} = (P_{2}∗V_{2})/T_{2}

In this equation:

P_{1} and P_{2} represent the initial and final pressures of the gas, respectively.

V_{1} and V_{2} represent the initial and final volumes of the gas, respectively.

T_{1} and T_{2} represent the initial and final temperatures of the gas, respectively.

The combined gas law allows you to relate the initial and final states of a gas when changes in pressure, volume, and temperature occur while keeping the number of moles and the gas constant constant. In fact, it is a powerful tool for solving a wide range of gas-related problems and for predicting the behavior of gases under varying conditions.

The combined gas law plays a significant role in science and engineering with a range of practical applications. It also helps comprehend how gases react to simultaneous changes in pressure, volume, and temperature, making it valuable for understanding gas behavior. Industries such as chemical manufacturing and energy production rely on it for gas storage and transportation, especially when conditions vary. Furthermore, in the context of gas mixtures, the law is useful in calculations involving partial pressures, molar fractions, and volume alterations in mixed gases.

## Similarities Between Ideal Gas Law and Combined Gas Law

- These laws are rooted in the understanding of how gases behave under different conditions.
- Both laws involve the three primary variables of gases: pressure (P), volume (V), and temperature (T).

## Difference Between Ideal Gas Law And Combined Gas Law

### Definition

Ideal gas law is a fundamental equation describing the behavior of ideal gases under varying conditions, relating pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). On the other hand, combined gas law is an equation that combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law to describe how the pressure, volume, and temperature of a gas change when multiple variables are altered simultaneously.

### Equation

The ideal gas law is described by the equation PV = nRT, while the combined gas law is expressed as P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}, where the initial pressure (P_{1}) times initial volume (V_{1}) divided by initial temperature (T_{1}) equals the final pressure (P_{2}) times final volume (V_{2}) divided by final temperature (T_{2}).

### Variables

Ideal gas law involves pressure (P), volume (V), the number of moles (n), the gas constant (R), and temperature (T) in an ideal gas system. Meanwhile, the combined gas law involves the initial and final values of pressure, volume, and temperature in a gas system where changes are occurring.

### Main Purpose

The ideal gas law primarily describes the behavior of ideal gases, offering a foundation for understanding how gases respond to changes in pressure, volume, and temperature, while the combined gas law combines the individual gas laws (Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law) into a single equation.

## FAQ: Ideal Gas Law And Combined Gas Law

### What is the ideal gas equation?

PV = nRT is the equation for the ideal gas law.

### What is the combined gas equation?

(P_{1}V_{1})/T_{1} = (P_{2}V_{2})/T_{2} is the equation for the combined gas law.

### How do we know when to use the combined gas law?

You should typically use the combined gas law when you have a constant amount of gas and you’re dealing with changing variables such as temperature, pressure, and volume.

## Conclusion

Ideal gas law is a fundamental equation that relates the pressure (P), volume (V), and temperature (T) of an ideal gas, along with the gas constant (R), whereas combined gas law is derived from the ideal gas law and combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single equation. Thus, this is the main difference between ideal gas law and combined gas law.

##### Reference:

1. “Combined Gas Law Formula.” Byju’s.

2. “Ideal Gas Law.” Wikipedia. Wikipedia Foundation.

##### Image Courtesy:

1. “Ideal gas law” By Dtvardovskyi – Own work (CC BY-SA 4.0) via Commons Wikimedia

2. “2314 Boyles Law” By OpenStax College – Anatomy & Physiology, Connexions Web site, Jun 19, 2013. (CC BY 3.0) via Commons Wikimedia

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