Monatomic Gases: Noble Gases, Ideal Gas, General Gas Law

Gases that are made up of molecules that consist of a single atom are known as monatomic gases. Gases such as helium or sodium vapor are examples of monatomic gases. They can be quite easily distinguished from diatomic or polyatomic gases. In this article, we will learn more about monatomic gases, gas law, important formulae, and noble gases.

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What are Monatomic gases?

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Monatomic gases are the gases with a single atom. They do not consist of rotational and energy vibrational components which make their thermodynamic behavior in the normal temperature range extremely simple. There are only three translational degrees of freedom in monatomic gases. (\(\frac{3}{2}\))K_BT is the average energy of a monatomic gas in temperature T. All the chemical elements at a high temperature and a gaseous phase act as monatomic gases. 

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General gas law

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The gas that follows a physical behavior by maintaining a particular idealized relation between temperature, pressure, and volume is known as a perfect or ideal gas. This law that they follow is known as general gas law. The law consists of both Boyle's law and the Charle's law’. Boyle's law states that the volume of gas is indirectly proportional to the pressure and Charles' law states that the volume of gas is directly proportional to the pressure. The law describes the behavior of ideal gas as well as real gases. 

An ideal gas is whose molecules show no interaction but go through elastic collision with the wall of the container or with each other. Any gas according to Avogadro's law follows the general law if the constant specified quantity of gas is expressed in terms of molecules of gases. The gram mole and the mass of the unit are used where the molecular weight is expressed in grams. 

Equation of state

Equation of state describes the states of matter under temperature, volume, or pressure. 

Assumptions of general gas law

Kinetic theory of gases is helpful while deducing general gas law. Some of the assumptions of general gas law are as follows:

• The gas follows newton's law of motion and contains a large number of molecules that are in random motion.
• The volume occupied by the gas is significantly higher than the volume of the molecules. 

Even though there are no such gases that show these properties, the general gas law explains the behavior of the real gases at a high temperature. A gas does not follow the equation when conditions are such that the gas in the mixture liquefies at the temperature. 

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Noble gases

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One of the properties of monatomic gases is that they are unreactive; noble gases also show similar properties. In monatomic gases, atoms are not hurdled to each other. Argon, krypton, and xenon are noble gases that are listed as monatomic gases. It should be noted that all the chemical elements are considered to be monatomic gases at a significantly high temperature. As there is no rotational and vibrational energy, the monatomic gases show thermodynamic behavior which is extremely simple if compared to polyatomic gases. 

Noble gases are the only gases that can stay stable for an atom molecule at a definite standard temperature and pressure. Noble gases such as argon, neon, helium, xenon, krypton, and radon have a powerful outer shell which makes them non-reactive elements. All these elements have been recognized as totally inert elements except helium and neon.

Elemental or molecular gases are noble gases that are bought together with the homonuclear diatomic gases to differentiate them from the molecules that are also regarded as chemical compounds. Eg, nitrogen (N₂).

Use of noble gases in daily life

• Because of the unreactive nature of the noble gas, argon is used in light bulbs to avoid burning the filament.
• Neon gas glows when electricity is passed through it which is why they are used for making advertising signs.
• The gas helium has a lower density than air because of which they are used to fill balloons. 

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Diatomic molecules

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The molecules are made of only two atoms are known as diatomic. Nitrogen (78%) and oxygen (21%) are the two elements on the earth that have diatomic molecules. 

Diagram

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Important Formulae

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• PV = n R T

Where, P = Pressure

V= volume

n = amount of substance

R = ideal gas constant

T = temperature

• PV=\(\frac{1}{3}\) Nmv² (where v² is constant)
• \(\frac{P_v}{t}\) = Nr

Where, n = gram moles of a perfect gas

R = universal gas constant

• Cp = (\(\frac{5}{2}\)) R 

Where, Cp = Molar specific heat at constant pressure

• The ratio of specific heat = \(\frac{C_p}{C_v}\) = \(\frac{5}{3}\)

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Things to Remember

• Gases that are made up of molecules that consist of a single atom are known as monatomic gases.
• Example: Helium or Sodium Vapor
• The gas that follows a physical behavior by maintaining a particular idealized relation between temperature, pressure, and volume is known as a perfect or ideal gas.
• PV = n R T
• Monatomic gases are unreactive like noble gases.
• The molecules are made of only two atoms are known as diatomic.