In the field of chemistry, we have fundamental concepts that are foundational. One such fundamental is gas and the role it plays in understanding the behavior of matter. In the previous article, we have dipped our toes into gas laws. We discussed the three main gas laws – Boyles’s law, Charles’s Law, and Avogadro’s Law as well as learned how to solve problems on each law.

Now, it is time for us to delve deep into broader principles that govern gas behavior. In this article we will be learning about the General Gas Law and the Ideal Gas Law. These laws gives us a framework to predict and analyze the various properties of gases under changing conditions.

## Fundamentals

Before we delve into the General Gas Law and the Ideal Gas Law, lets first refresh our units and what they represent.

**Pressure (P):**Pressure can be defined as the force applied per unit area. When it comes to the context of gases, pressure refers to the force applied by gas molecules colliding with the walls of the container. Pressure can be measured either in Pascals(Pa) or atmospheres (atm).**Volume (V):**In a gas context, volume represents the space occupied by a gas. Volume varies depending on the shape and size of its container. It is measured liters (L) or cubic meters (m^{3}).**Temperature (T):**This is the measure of the average kinetic energy of gas particles. The SI unit of temperature is Kelvin (K) but it can also be measured in Fahrenheit (F) and Celsius (C).**Amount of Gas (n):**This represents the quantity of gas particles present in a system. The amount of gas is typically measured in moles(mol).**Ideal Gas Constant (R):**This is a proportionality constant which can vary depending on the units that are used for pressure, volume, and temperature. The value of the Ideal Gas Constant is……….

Let’s try to keep the above mentioned measurements in mind, as they will help us in understanding the General Gas Law and Ideal Gas Law.

## The General Gas Law

The General Gas Law, merges the principles of Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single equation. As such it is also popularly known as the Combined Gas Law. It offers a unique unified method to describing the relationship between pressure, volume, temperature, as well as the amount of gas. The General Gas Law equation is written in the following:

$$

PV = nRT

$$

It can also be written as:

$$

\frac{P_1 V_1}{n_1 T_1}=\frac{P_2 V_2}{n_2 T_2}

$$

**Where:**

P = Pressure of gas in Pascals (Pa).

V = Volume of the gas in cubic meters (m^{3}).

n = Number of moles of the gas.

R = Ideal gas constant with the value of 8.314J/K⋅mol

T = Temperature of the gas in Kelvin (K).

Breaking this law down we discover that provided the quantity of gas and the conditions remain constant, the product of the pressure and volume of a gas will always be directly proportional to the number of moles of the gas as well as its temperature. This equation can be especially useful when breaking down the behavior of gases when undergoing changes in multiple variables all at the same time.

### Example problem

Lets try solving a problem using the General Gas Law. So a scuba diver has a tank with a volume of 12.0 liters. The temperature of the tank is 25.0^C and contains oxygen gas at a pressure of 3.00 atm. What will be the new volume of the gas inside the tank if the diver descends to a depth where the temperature drops to 10.0^C and the pressure increases to 4.50 atm.

#### Solution:

Using the General Gas Law, we can determine the given values as below:

V1 = 12.0 L

T1 = 25.0^{o}C = 25.0^{o}C + 273.15 K

P1 = 3.0 atm

V2 = ?

T2 = 10.0^{o}C = 10.0^{o}C + 273.15 K

P2 = 4.50 atm

Thanks to the givens above, we can rearrange the General Gas Law equation to find the new volume of the gas inside the tank or V2.

$$

{V_2}=\frac{P_1 V_1 T_2}{P_2 T_1}

$$

Put in the values as follows:

$$

{V_2}=\frac{3.00atm\cdot12.0L\cdot283.15K}{4.50atm\cdot298.15K}

$$

$$

{V_2}=\frac{10176.6L/K}{1341.675atm/K}

$$

$$

{V_2}\approx {7.59L}

$$

And so, the new volume of the gas inside of the tank when the diver descends will be approximately 7.59 L.

## The Ideal Gas Law

Ideal Gas Law is actually a special case of the General Gas Law. Ideal Gas Law as implied, only applies to idea gases. Ideal gases are theoretical gases that occupy no space, so negligible volume as well as exert no intermolecular forces. This is problematic because no gas actually fits this model, but in a low pressure and high temperature circumstance, many gases behave close to ideal gases. The equation for the Ideal Gas Law is written below:

$$

PV= nRT

$$

As you can see, the Ideal Gas Law equation mirrors the General Gas Law equation. They are different in that the Ideal Gas Law equation can only be applied to ideal gases. It gives us the relationship between the pressure, volume, temperature, and amount of an ideal gas. This all provides a straightforward and easy tool to analyze gas behavior in different situations.

### Example problem

If a container with the pressure of 3.0 atm at a temperature of 25.0^{o}C holds a 2.5 L sample of gas, What will be the number of moles of the gas in the container?

#### Solution:

Using the formula for the Ideal Gas Law equation, we can solve the problem above. Let’s find the givens first.

P = 3.0 atm

V = 2.5 L

n = ?

R = 8.314J/K⋅mol

T = 25.0^{o}C = 25.0^{o}C + 273.15

We can then rearrange the formula to solve for n:

$$

{n}=\frac{PV}{RT}

$$

$$

{n}=\frac{3.0atm\cdot2.5L}{8.314J/K⋅mol\cdot298.15K}

$$

$$

{n}=\frac{7.5atm/L}{24.485atm/mol}

$$

$$

{n}\approx{0.307mol}

$$

So the number of moles of gas in the container is approximately 0.307 moles.

In finality, both the General and Ideal Gas laws are important when it comes to understanding the behavior of gases. From analyzing pressure, volume, temperature, or the amount of gas, both these laws encompass all operations pertaining to gases. While ideal gases may basically be non existent, the Idea Gas Law can serve as a indispensable tool for approximating many real-world scenarios. Understanding these two laws along with the other three fundamental gas laws discussed in the previous article will give you concrete understanding into gas laws.

## Frequently asked questions (FAQs)

### Q1 – What is the general gas law?

The General Gas Law, merges the principles of Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single equation.

### Q2 – What is the Ideal gas law?

Ideal Gas Law as implied, only applies to idea gases. Ideal gases are theoretical gases that occupy no space, so negligible volume as well as exert no intermolecular forces.

### Q3 – What is the difference between the general gas law and the ideal gas law?

Both the General Gas Law and the Ideal Gas Law use the same equation but they are different in that Ideal Gas Law only applies to ideal gases where as General Gas Law applies to more real world gases.