Written By Pavithra VG
Last Modified 25-01-2023

Avogadro’s Hypothesis: Avogadro’s Law, Examples, Formula, Applications

You will find the answer to all these interesting questions in this article about Avogadro’s Hypothesis. The atomicity of water \(\left( {{{\rm{H}}_2}{\rm{O}}} \right)\) is \(3\). A molecule of water is made up of \(2\) hydrogen atoms and \(1\) oxygen atom. Now, how many hydrogen and oxygen molecules make up a molecule of water? At constant temperature and pressure, is the number of molecules in different gases like hydrogen, oxygen, steam, ammonia, etc. the same or different?

The law is named after Amedeo Avogadro, who suggested in 1812 that two identical samples of an ideal gas with the same volume, temperature, and pressure have the same number of molecules. When equal amounts of gaseous hydrogen and nitrogen are at the same temperature and pressure, they contain the same number of atoms and exhibit perfect gas behaviour.

In this article, you will explore Avogadro’s law, examples of it, Avogadro’s constant its applications in detail and more. Continue reading for more information.

What is Avogadro’s Hypothesis?

The Italian chemist Amedeo Avogadro, established a relationship between the volume of a gas and the corresponding number of molecules under a given set of conditions of temperature and pressure. This hypothesis is called Avogadro’s hypothesis. It states that, under similar conditions of temperature and pressure, an equal volume of all gases contain an equal number of molecules.

\({\rm{V}} \propto {\rm{N}}\)

Where V is the volume of the gas and N is the number of molecules.

For example, if an equal volume of four gases hydrogen \(\left( {{{\rm{H}}_2}} \right)\), oxygen \(\left( {{{\rm{O}}_2}} \right)\), chlorine \(\left( {{\rm{C}}{{\rm{l}}_2}} \right)\) and ammonia \(\left( {{\rm{N}}{{\rm{H}}_3}} \right)\) is enclosed in the different flasks of the same capacity under similar conditions of temperature and pressure, then all flasks have the same number of molecules. However, these molecules may be different in size and mass.

Avogadro’s Hypothesis and Dalton’s Atomic Theory

Avogadro’s Hypothesis is a modification of the Berzelius hypothesis. According to the Berzelius hypothesis, an equal volume of all gases under similar conditions of temperature and pressure contains an equal number of atoms.

But this hypothesis is not applicable to the chemical reactions involving gases. It was found that even fractions of atoms were involved in some chemical reactions. But in the Dalton atomic theory half of an atom of an element cannot exist. This conflict was solved by Avogadro by making a clear distinction between atom and molecule.

According to Avogadro, an atom is the smallest particle of an element that may or may not have an independent existence. In contrast, a molecule is the smallest particle of a substance (element or compound) that can exist independently.

L earn Ideal Gas Equation

Example for Avogadro’s Hypothesis: Formation of HCl Gas

One volume of hydrogen and one volume of chlorine combine to give two volumes of hydrogen chloride gas and NTP (Normal Temperature Pressure) conditions.

\({\rm{Hydrogen}} + {\rm{Chlorine}} \to {\rm{Hydrogen}}\,{\rm{chloridegas}}\)

\(1\,{\rm{Volume}}\,1\,{\rm{Volume}}\,2\,{\rm{Volumes}} = {\rm{kn}}\)

Let \(1\) volume of each gas contain n molecules.

By applying Avogadro’s hypothesis

\({\rm{Hydrogen}} + {\rm{Chlorine}} \to {\rm{Hydrogen}}\,{\rm{chloridegas}}\)
\({\rm{n}}\,{\mkern 1mu} {\rm{molecules}}\,\,{\rm{n}}\,{\mkern 1mu} {\rm{molecules}}{\mkern 1mu} \,\,2{\rm{n}}{\mkern 1mu} \,{\rm{molecules}}\)
\(1\,{\mkern 1mu} {\rm{molecules}}\,{\mkern 1mu} 1\,{\mkern 1mu} {\rm{molecules}}{\mkern 1mu} \,2{\mkern 1mu} \,{\rm{molecules}}\)
\(\frac{1}{2}{\mkern 1mu} \,{\rm{molecules}}{\mkern 1mu} \,\frac{1}{2}{\mkern 1mu} \,{\rm{molecules}}{\mkern 1mu} \,1{\mkern 1mu} \,{\rm{molecules}}\)

This means that \(1\) molecule of hydrogen chloride contains ½ molecule of hydrogen and \(1/2\) molecule of chlorine. Now, \(1/2\) molecule of hydrogen can exist because one molecule of hydrogen contains two atoms of hydrogen, and \(1/2\) molecules of hydrogen mean one atom of hydrogen. Similarly, \(1/2\) molecule of chlorine contains an atom of chlorine because chlorine is also a diatomic molecule. Thus, one molecule of hydrogen chloride is formed from \(1\) atom of hydrogen and \(1\) atom of chlorine. This agrees with Dalton theory.

What is the Value of Avogadro Constant?

The number of molecules in one mole of gas has been determined to be \(6.022 \times {10^{23}}\). This value is known as Avogadro Constant.

According to Avagadro, all gases containing an equal amount of substances occupy the same volume at the same temperature and pressure.

\({\rm{V}} \propto {\rm{n}}\)

\({\rm{V = kn}}\)

Where \({\rm{k}}\) is the proportionality constant.

One mole, each gas at standard temperature and pressure, will have the same volume. This is known as molar volume \(\left( {{{\rm{V}}_{\rm{m}}}} \right)\). \(1\) mole of any gas at the \(273.15\;{\rm{K}}\) and \(1\) bar pressure occupies \({22.7110^{ – 3}}\;{{\rm{m}}^3}\) or \(22.71\;{\rm{L}}\).

The number of moles can be calculated by the equation,

\({\rm{V = kn}}\)

We know that, \({\rm{n}} = \frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{gas}}}}{{{\rm{Molar}}\,{\rm{mass}}}} = \frac{{\rm{m}}}{{\rm{M}}}\)

\({\rm{V}} = {\rm{k}}\frac{{\rm{m}}}{{\rm{M}}}\)

\({\rm{M}} = {\rm{k}}\frac{{\rm{m}}}{{\rm{V}}}\)

We know that density, \({\rm{d}} = \frac{{\rm{m}}}{{\rm{v}}}\)

On rearranging,

\({\rm{M = kd}}\)

Hence, the density of a gas is directly proportional to its molar mass.

Applications of Avogadro’s Law

1. Deduction of atomicity of Elementary Gases: Atomicity of an elementary substance is defined as the number of atoms of the element present in one molecule of a substance.
Example: Atomicity of oxygen \(\left( {{{\rm{O}}_{\rm{2}}}} \right)\) is \(2\) while that of ozone \(\left( {{{\rm{O}}_{\rm{3}}}} \right)\) is \(3\).
Avogadro’s law helps in determining the atomicity of elementary gases such as hydrogen, oxygen, chlorine, etc.
Example: Calculation of atomicity of oxygen.
Consider the reaction between hydrogen and oxygen to form water vapour. Two volumes of hydrogen combined with \(1\) volume of oxygen to form two volumes of water vapour.
\({\rm{Hydrogen}} + {\rm{Oxygen}} \to {\rm{Water}}\,{\rm{Vapour}}\)
\(2\,{\rm{Volumes}}\,1\,{\rm{Volume}}\,2\,{\rm{Volumes}}\)
Applying Avogadro’s hypothesis
\({\rm{Hydrogen}} + {\rm{Oxygen}} \to {\rm{Water Vapour }}\)
\(2{\rm{n}}\,{\rm{molecules}}\,{\rm{n}}\,{\rm{molecules}}\,2{\rm{n}}\,{\rm{molecules}}\)
\(1\,{\rm{molecules}}\,\frac{1}{2}\,{\rm{molecules}}\,1\,{\rm{molecules}}\)
Thus, \(1\) molecule of water contains \(\frac{1}{2}\) molecule of oxygen. But \(1\) molecule of water contains \(1\) atom of oxygen. Hence, \(\frac{1}{2}\) molecules of oxygen \( = 1\) atom of oxygen
Or \(1\) molecule of oxygen \(= 2\) atoms of oxygen, i.e., atomicity of oxygen \(= 2\).

2. Determination of the relationship between vapour density and molar mass of a gas:
The vapour density of a gas is the ratio between the mass of a certain volume of the gas to the mass of the same volume of hydrogen gas under the similar conditions of temperature and pressure.
\({\rm{Vapour}}\,{\rm{density}}\,({\rm{V}}.{\rm{D}}.)\,{\rm{of}}\,{\rm{gas}} = \frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{certain}}\,{\rm{volume}}\,{\rm{of}}\,{\rm{gas}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{same}}\,{\rm{volume}}\,{\rm{of}}\,{\rm{hydrogen}}}}\)
According to Avogadro’s hypothesis, equal volume of all gases under similar conditions of temperature and pressure contains equal number of molecules.
Let the given volume of the gas and hydrogen contain n molecule at STP conditions.
\({\rm{Vapour}}\,{\rm{density}} = \frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{n}}\,{\rm{molecules}}\,{\rm{of}}\,{\rm{gas}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{n}}\,{\rm{molecules}}\,{\rm{of}}\,{\rm{hydrogen}}}}\)
\({\rm{Vapour}}\,{\rm{density}} = \frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{1}}\,{\rm{molecules}}\,{\rm{of}}\,{\rm{gas}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{1}}\,{\rm{molecules}}\,{\rm{of}}\,{\rm{hydrogen}}}}\)
The ratio of the mass of one molecule of gas to the mass of an atom of hydrogen is called molar mass.
Therefore, \({\rm{Vapour}}\,{\rm{density}} = \frac{{{\rm{Molar}}\,{\rm{Mass}}}}{{\rm{2}}}\)
\({\rm{Molar}}\,{\rm{Mass}} = 2 \times {\rm{Vapour}}\,{\rm{density}}\)
Vapour density is also called relative density of the gas.

3. Determination of relationship between mass and volume of the gas:

\({\rm{Molar}}\,{\rm{Mass}} = 2 \times {\rm{Vapour}}\,{\rm{density}}\)

\({\rm{Molar}}\,{\rm{Mass}} = 2 \times \frac{{{\rm{Mass}}\,{\rm{of}}\,{\rm{certain}}\,{\rm{volume}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}}}{{{\rm{Mass}}\,{\rm{of}}\,{\rm{same}}\,{\rm{volume}}\,{\rm{of}}\,{\rm{hydroen}}\,{\rm{at}}\,{\rm{STP}}}}\)

\({\rm{Molar}}\,{\rm{Mass}} = 2 \times \frac{{{\rm{Mass}}\,{\rm{of}}\,1{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}}}{{{\rm{Mass}}\,{\rm{of}}\,1{\rm{L}}\,{\rm{of}}\,{\rm{hydroen}}\,{\rm{at}}\,{\rm{STP}}}}\)

But, the mass of \({1{\rm{L }}}\) of hydrogen gas is \({\rm{0}}{\rm{.089 g}}\)

Therefore, \({\rm{Molar}}\,{\rm{Mass}} = 2 \times \frac{{{\rm{Mass}}\,{\rm{of}}\,1{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}}}{{0.089}}\)

\({\rm{Molar}}\,{\rm{Mass}} = \frac{2}{{0.089}} \times {\rm{Mass}}\,{\rm{of}}\,1{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}\)

\({\rm{Molar}}\,{\rm{Mass}} = 22.4 \times {\rm{Mass}}\,{\rm{of}}\,1{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}\)

\({\rm{Molar}}\,{\rm{Mass}} = {\rm{Mass}}\,{\rm{of}}\,22.4{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{at}}\,{\rm{STP}}\)

Thus, \(22.4{\rm{L}}\) of any gas at \({\rm{STP}}\) weighs equal to the molar mass of gas expressed in grams. This is called gram molecular volume.

Summary

You will be able to recollect Avogadro’s hypothesis, Avogadro’s law, and a comparison of Dalton’s theory after reading this article. Avogadro’s constant and applications of Avogadro’s hypothesis in identifying atomicity of elementary gases, determining a relationship between vapour density and molar mass of gas, and determining a relationship between mass and volume of the gas are all things you’re familiar with.

FAQs

We have provided some frequently asked questions on Avogadro’s Hypothesis here:

Q.1. What is Avogadro’s equation?
Ans: Avogadro’s equation is \({\rm{V}} = {\rm{kn}}\)

Where \({\rm{V}}\) is the volume of gas, \({\rm{n}}\) is the number of moles of gas and \({\rm{k}}\) is the proportionality constant.

Q.2. What are the applications of Avogadro’s Hypothesis?
Ans: The applications of Avogadro’s Hypothesis are

Avogadro’s law helps in determining the atomicity of elementary gases such as hydrogen, oxygen, chlorine, etc.
It helps in the determination of the relationship between vapour density and molar mass of a gas.
\({\rm{Vapour}}\,{\rm{density}} = \frac{{{\rm{Molar}}\,{\rm{mass}}}}{2}\)
It helps in the determination of the relationship between mass and volume of the gas.
\({\rm{Molar}}\,{\rm{mass}} = {\rm{Mass}}\,{\rm{of}}\,22.4{\rm{L}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{STP}}\)

Thus, \({\rm{22}}{\rm{.4L}}\) of any gas at \({\rm{STP}}\) weighs equal to the molar mass of gas expressed in grams. This is called gram molecular volume.

Q.3. Why is Avogadro’s law important?
Ans: Avogadro’s law is important for the calculation of the amount of gas present in a particular volume.

According to Avogadro’s law

\({\rm{V = kn}}\)

Where \({\rm{V}}\) is the volume of gas, \({\rm{n}}\) is the number of moles of gas and \({\rm{k}}\) is the proportionality constant.

Q.4. What is Avogadro’s hypothesis in chemistry?
Ans: The Italian chemist Amedeo Avogadro established a relationship between the volume of a gas and the corresponding number of molecules under a given set of conditions of temperature and pressure. This hypothesis is called Avogadro’s hypothesis. It states that, under similar conditions of temperature and pressure, an equal volume of all gases contain an equal number of molecules.

\({\rm{V}} \propto {\rm{N}}\)

Where \({\rm{V}}\) is the volume of the gas and \({\rm{N}}\) is the number of molecules.

Q.5. What does Avogadro’s law state?
Ans: Avogadro’s law states that under similar conditions of temperature and pressure, the equal volume of all gases contains an equal number of molecules.

\({\rm{V}} \propto {\rm{N}}\)

Where \({\rm{V}}\) is the volume of the gas and \({\rm{N}}\) is the number of molecules.

Q.6. What is Avogadro’s law example?
Ans: An example for Avogadro’s Hypothesis is the formation of \({\rm{HCl}}\) gas. One volume of hydrogen and one volume of chlorine combine to give two volumes of hydrogen chloride gas at \({\rm{NTP}}\) (Normal Temperature Pressure) condition.

\({\rm{Hydrogen}} + {\rm{Chlorine}} \to {\rm{Hydrogen}}\,{\rm{chloride}}\,{\rm{gas}}\)

\(1\,{\rm{Volmue}}\,1\,{\rm{Volume}}\,2\,{\rm{Volumes}}\)

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