Gas Pressure Formula: Ideal Gas Equation & Derivation

Gas is one of the most common states of matter along with solids and liquids. Like other states of matter, it is also composed of constituent molecules and atoms. These molecules and atoms exert a force on their adjacent molecules or atoms. This force exerted by the particles is known as pressure. The pressure exerted by the gaseous molecules/atoms on each other is known as gaseous pressure. And the formula to determine the gaseous pressure is known as the Gas Pressure Formula. 

Also read: Behaviour of Gas Molecules

Key Terms: Gas, Pressure,Gas Pressure Formula,States of Matter

---

What is Gaseous State of Matter?

[Click Here for Sample Questions]

Gaseous state of matter is one of the three most common states of matter, along with solids and liquids. Matter is defined as anything which occupies space and possesses mass. In the gaseous state, the particles are the farthest from each other, are arranged randomly, and are in constant motion throughout space. 

Properties of Matter

The interatomic attraction between the particles is the lowest in this state, thus the interatomic distance is the largest as compared to solids and liquids. They don't have any fixed shape, but they have a fixed volume and occupy the volume of any container by spreading rapidly. Gases can be compressed greatly.

For example, Helium gas, Oxygen, Nitrogen, Sulphur, etc.

---

What is Pressure?

[Click Here for Sample Questions]

Pressure is defined as the force applied by the particles of a substance, on any surface per square unit area. The force applied by the particles is perpendicular to the surface of the container. 

Pressure = Force/ Area

Pressure is denoted by P and has an S.I Unit of atm.

There are different types of pressure, fluid pressure, stagnation pressure, vapor pressure, liquid pressure, one of these is ideal gas pressure or gas pressure.

Read More:

---

What is Gas Pressure Formula?

[Click Here for Sample Questions]

Before understanding the gas pressure formula for ideal gases, we need to know about the different relations that lead up to the main equation. There are three gas laws that combine together and make up the ideal gas pressure equation. These three laws are:

• Boyle’s Law

• Charles Law

• Avogadro’s Law

Boyle’s Law

Robert Boyle performed several experiments and concluded that at a constant temperature, the pressure of a fixed amount of gas varies inversely with its volume. This is known as Boyle’s law. The amount of gas is given by the number of moles of gas. Boyle's law can be represented as:

Pressure ∝ 1/ Volume of gas

P ∝ 1/ V

P= k x 1/V (k is a constant)

PV = k (a constant)

Thus this law states a relationship between pressure and volume of the gas.

Boyle’s Law

Charles's Law

Robert Boyle performed several experiments and concluded that at a fixed pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature. This is known as Charles’s law. The amount of gas is given by the number of moles of gas. Charles's law can be represented as:

Volume ∝ Temperature

V ∝ T

V = K²T (K is a constant)

V/T = K

Thus this law states a relationship between temperature and volume of the gas.

Charle’s Law

Read More:

Avogadro’s Law

Avogadro’s law states that equal volumes of all gases under the same conditions of temperature and pressure contain equal numbers of molecules. Avogadro's law can be represented as:

Volume ∝ number of moles of gas

V ∝ n

V = k³n

V/n = k³

Avogadro’s Law

Combining the three laws we get:

At constant T and n;

V ∝ 1/p (Boyle’s Law) 

At constant P and number of moles;

V ∝ T (Charles’ Law) 

At constant p and T; 

V ∝ n (Avogadro Law)

Thus,

V ∝ nTp

pV = nRT 

Where,

R = proportionality constant.

P = pressure of gas

V = volume of gas

n = number of moles

T = temperature

Read More:

---

Things to Remember

• The gaseous state of matter is one of the three most common states of matter, along with solids and liquids.
• Pressure is defined as the force applied by the particles of a substance, on any surface per square unit area.
• There are three gas laws that combine together and make up the ideal gas pressure equation. These three laws are:
  • Boyle’s Law
  • Charles Law
  • Avogadro’s Law
• At constant T and n; V ∝ 1/p (Boyle’s Law) 
• At constant p and n; V ∝ T (Charles’ Law) 
• At constant p and T; V ∝ n (Avogadro Law)
• At constant V; p ∝ T (Gay Lussac’s Law) 
• Thus the ideal gas law is, pV = nRT