# Ideal Gas Laws and Equation

###### Habish Ribin Haneef
Updated on

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. An ideal gas is also called a perfect gas. Based on the ideal gas law and the simplified equation of state, the ideal gas concept can be analyzed under statistical mechanics. Many gases behave qualitatively like an ideal gas under various conditions of temperature and pressure and the gas molecules play the role of ideal particles. Over a considerable parameter range around standard temperature and pressure, gases like nitrogen, oxygen, hydrogen, carbon dioxide, noble gases, and mixtures like air can be considered as ideal gases. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure. This is because, the potential energy due to intermolecular forces becomes less significant compared with the kinetic energy of the particle and the size of the molecules becomes less significant compared to the empty space between them. According to International Union of Pure and Applied Chemistry(IUPAC), one mole of an ideal gas has a volume of 22.710947 litres at standard temperature and pressure. But on the other hand, at lower temperature and higher pressure, the ideal gas model fails. A real gas often has a lower pressure than an ideal gas at lower temperatures. A real gas often have a larger volume than ideal gases at high pressures. The real gases also undergo a phase transition like liquid to solid at some point of low temperature and high pressure. But, phase transitions are not found or described in an ideal gas model.

## Ideal Gas Laws:

The laws that deals with ideal gases are called ideal gas laws. These laws include Charles law, Boyles law, and Avagadro law.

Charles law was discovered by French physicist Jacques Charles in the year 1780. Charles law is also known as the “law of volumes”. It is an experimental gas law that describes how gases tend to expand when heated. Charles law states that at constant pressure, the volume of an ideal gas is directly proportional to the absolute temperature.

The formula for Charles law is,

VI /TI=VF /TF

Where, VI= Initial volume

VF= Final volume

TI= Initial absolute temperature

TF= Final absolute temperature

Now let’s see some examples of Charles law in our everyday life. The working of a hot air balloon is based on Charles law. As per Charles law, the temperature and pressure is directly proportional to each other. When a gas is heated, it expands and as a result of this, it becomes less denser and hence the balloon is lifted in the air. Another important example of Charles law is a deodorant bottle. In the bottle of a deodorant you might have noticed some warning signs stating the bottle should be kept away from sunlight and high temperature. Ever imagined the reason behind this? This is because, at high temperatures, the air molecules inside the bottle will expand which can lead to the bursting of the bottle.

Boyles law was formulated by the Anglo-Irish chemist Robert Boyle in the year 1662. Boyles law is an experimental gas law that describes the relationship between the pressure and volume of a confined gas. Boyles law states that the pressure exerted by a gas is inversely proportional to the volume occupied by it. This means that the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of the gas are kept constant.

Boyles law can be mathematically expressed as,

P1V1 = P2V2

Where, P1= Initial pressure exerted by the gas

P2= Final pressure exerted by the gas

V1= Initial volume occupied by the gas

V2= Final volume occupied by the gas

Now, let’s see some real life examples of Boyles law. Can you believe, the process of human respiration have the traces of Boyles law. During the process of inhaling, the lungs are filled with air and hence they expand. Here, the volume increases and pressure decreases. Similarly, while exhaling, the lungs are free of air and hence they shrink. Here, the volume decreases and pressure increases. The change in pressure and volume is momentary and periodic in nature. Another daily life example of Boyles law is the working of a syringe. As you know, a syringe is a medical equipment used to insert or withdraw fluids. A syringe consists of a cylinder for storing the fluid and a plunger for varying the pressure. If the plunger is pushed down, the volume of the fluid decreases and the pressure of the fluid increases. If the plunger is pulled up, the volume of the fluid increases and the pressure of the fluid decreases.

Avogadro’s law is an experimental gas law relating the volume of a gas to the amount of substance of gas present. Avogadro’s law is named after the Italian scientist Amedeo Carlo Avogadro. Avogadro suggested that two dissimilar ideal gases occupying the same volume at a given temperature and pressure must contain an equal number of molecules. Avogadro’s law states that at constant temperature and pressure, the total number of atoms or molecules of a gas is directly proportional to the volume occupied by the gas.

Avogadro’s law can be mathematically expressed as,

V/n = k

Where, V= Volume occupied by the gas

n= The amount of gaseous substance

k= a constant

Now, let’s see some examples of Avogardro’s law in our everyday life. A common example of Avogadro’s law is filling air inside a balloon. This process can either be done using our mouth or using a pump. If you reduce the amount of air contained by the balloon, you will observe a significant decrease in the volume or size of the balloon. Therefore, this process follows Avogadro’s law. Another common example of Avogadro’s law is the working of a bicycle pump. The pump collects air from the environment and inserts the air into the deflated object. Now, there will be an increase in the number of gas molecules in the object and this will lead to the change of shape of the object and it ultimately gets expanded. Hence, the bicycle pump also follows Avogadro’s law.

## Ideal Gas Equation:

The ideal gas equation describes the behaviour of a gas. The ideal gas equation is also known as “general equation of gas.” This expression shows the relationship between pressure, temperature, volume, and amount of gas. According to ideal gas equation, ideal gas is the one whose volume is proportional to the number of moles and temperature and inversely proportional to the pressure. The ideal gas equation is true only for ideal gases.

The ideal gas equation is given below,

PV= nRT

Where, P= Pressure of the ideal gas

V= Volume of the ideal gas

n= Amount of ideal gas measured in terms of moles

R= Universal gas constant

T= Temperature

In the ideal gas equation, R is a universal gas constant. It is the molar equivalent of boltzmann constant having the units of energy increased per temperature per mole. The universal gas constant is denoted by “R”. The value of universal gas constant is 8.314 kj/mole.K

According to ideal gas equation, the product of pressure and volume of a gas holds a constant relation with the product of the universal gas constant, number of moles of gas and temperature.

## Derivation of Ideal Gas Equation:

Let, p= Pressure exerted by the gas

v= Volume of the gas

T= Temperature

n= Number of moles of gas

R= Universal gas constant

Now, according to Boyles law, at constant n and T, the volume has an inverse relation with the pressure exerted by a gas.

v 1/p —> 1

According to Charles law, at constant p and n, the volume of a gas has a direct relation with the temperature.

v T —> 2

According to Avogadro’s law, at constant p and T, the volume of a gas has a direct relation with the number of moles of gas.

v n —> 3

Now, combining equations 1, 2, and 3, we have,

v nT/p

Therefore, PV= nRT

Where R is the universal gas constant with value 8.314 J/mol-K

Answer. An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions.

Answer. Charles law states that at constant pressure, the volume of an ideal gas is directly proportional to the absolute temperature.

Answer. Boyles law states that the pressure exerted by a gas is inversely proportional to the volume occupied by it.

Answer.  Avogadro’s law states that at constant temperature and pressure, the total number of atoms or molecules of a gas is directly proportional to the volume occupied by the gas.

PV= nRT

Where, P= Pressure of the ideal gas

V= Volume of the ideal gas

n= Amount of ideal gas measured in terms of moles

R= Universal gas constant

T= Temperature

Answer.  The universal gas constant is the molar equivalent of boltzmann constant having the units of energy increased per temperature per mole. The universal gas constant is denoted by “R”. The value of universal gas constant is 8.314 kj/mole.K

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