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Learning Objectives

• Avogadro's Number Definition Chemistry
• Avogadro's Number Of Molecules
• Avogadro's Constant Is Defined As The Number Of Particles In
• How To Do Avogadro's Constant
• Number Of Particles In A Mole

Avogadro's Constant. Avogadro's number (or Avogadro's constant) is the number of elementary particles in a mole of any substance For most calculations, four significant figures for Avogadro's constant are enough: 6.022 x 10 23. A mole of any substance contains Avogadro's number of elementary particles. An Avogadro number of particles = 6.02 x 10 23 particles The Avogadro number or constant may be represented by the letter 'L' and when dealing with this number of particles we say that there is an 'amount' of 1 mole. 1 mole of any substance contains an Avogadro number of particles of that substance = 6.02 x 10 23 particles. The numeric value of the Avogadro constant expressed in reciprocal mole, a dimensionless number, is called the Avogadro number, sometimes denoted N or N 0, which is thus the number of particles that are contained in one mole, exactly 6.022 140 76 × 10 23. Avogadro's number is the number of particles in one gram of a carbon-12 atom. Avogadro's number is the number of atoms in 12 grams of carbon-12 atoms.

Avogadro's law states that 'equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.' 1 For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

• Use Avogadro's number to convert to moles and vice versa given the number of particles of an element.
• Know the definition of the mole.
• Determine the formula mass of an ionic or molecular compound.
• Determine the percent composition of each element in a compound from the chemical formula.

When objects are very small, it is often inconvenient or inefficient, or even impossible to deal with the objects one at a time. For these reasons, we often deal with very small objects in groups, and have even invented names for various numbers of objects. The most common of these is 'dozen' which refers to 12 objects. We frequently buy objects in groups of 12, like doughnuts or pencils. Even smaller objects such as straight pins or staples are usually sold in boxes of 144, or a dozen dozen. A group of 144 is called a 'gross'.

This problem of dealing with things that are too small to operate with as single items also occurs in chemistry. Atoms and molecules are too small to see, let alone to count or measure. Chemists needed to select a group of atoms or molecules that would be convenient to operate with.

Avogadro's Number:Counting Atoms

Owing to their tiny size, atoms and molecules cannot be counted by direct observation. But much as we do when 'counting' beans in a jar, we can estimate the number of particles in a sample of an element or compound if we have some idea of the volume occupied by each particle and the volume of the container. Once this has been done, we know the number of formula units (to use the most general term for any combination of atoms we wish to define) in any arbitrary weight of the substance. The number will of course depend both on the formula of the substance and on the weight of the sample. However, if we consider a weight of substance that is the same as its formula (molecular) weight expressed in grams, we have only one number to know: Avogadro's number.

Avogadro's number

Avogadro's number is known to ten significant digits:

[N_A = 6.022141527 times 10^{23}.]

However, you only need to know it to three significant figures:

[N_A approx 6.02 times 10^{23}. label{3.2.1}]

So (6.02 times 10^{23}) of what? Well, of anything you like: apples, stars in the sky, burritos. However, the only practical use for (N_A) is to have a more convenient way of expressing the huge numbers of the tiny particles such as atoms or molecules that we deal with in chemistry. Avogadro's number is a collective number, just like a dozen. Students can think of (6.02 times 10^{23}) as the 'chemist's dozen'.

Before getting into the use of Avogadro's number in problems, take a moment to convince yourself of the reasoning embodied in the following examples.

Things to understand about Avogadro's number

• It is a number, just as is 'dozen', and thus is dimensionless.
• It is a huge number, far greater in magnitude than we can visualize
• Its practical use is limited to counting tiny things like atoms, molecules, 'formula units', electrons, or photons.
• The value of N_A can be known only to the precision that the number of atoms in a measurable weight of a substance can be estimated. Because large numbers of atoms cannot be counted directly, a variety of ingenious indirect measurements have been made involving such things as Brownian motion and X-ray scattering.

The Mole: 'A Dozen Eggs and a Mole of Sugar, Please'

The mole (symbol: mol) is the base unit of amount of substance ('number of substance') in the International System of Units or System International (SI), defined as exactly 6.02214076×10²³ particles, e.g., atoms, molecules, ions or electrons. The current definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (¹²C) (the isotope of carbon with relative atomic mass 12 Daltons by definition).

It is not obvious why eggs come in dozens rather than 10s or 14s, or why a ream of paper contains 500 sheets rather than 400 or 600. The definition of a mole—that is, the decision to base it on 12 g of carbon-12—is also arbitrary. The important point is that 1 mole of carbon—or of anything else, whether atoms, compact discs, or houses—always has the same number of objects: 6.02 × 10²³.

The Mole

Video (PageIndex{1}) How big is a mole?

Converting Between Number of Atoms to Moles and Vice Versa

We can use Avogadro's number as a conversion factor, or ratio, in dimensional analysis problems. If we are given the number of atoms of an element X, we can convert it into moles of by using the relationship

[text{1 mol X} = 6.022 times 10^{23} text{ X atoms}.]

An example on the use of Avogadro's number as a conversion factor is given below for carbon.

Example (PageIndex{1}): Moles of Carbon

The element carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is (4.72 times 10^{24}) atoms of carbon?

Solution

Formula Mass

One skill needed in future chapters is the ability to determine the mass of the formula of various chemical substances. This quantity is called the formula mass. The formula mass is obtained by adding the masses of each individual atom in the formula of the substance. Because a proper formula is electrically neutral (with no net electrons gained or lost), the ions can be considered atoms for the purpose of calculating the formula mass.

Let us start by calculating the formula mass of sodium chloride (NaCl). This formula mass is the sum of the atomic masses of one sodium atom and one chlorine atom, which we find from the periodic table; here, we use the masses to two decimal places:

To two decimal places, the formula mass of NaCl is 58.44 amu.

For covalent substances, the formula represents the numbers and types of atoms composing a single molecule of the substance; therefore, the formula mass may be correctly referred to as a molecular mass. Consider chloroform (CHCl₃), a covalent compound once used as a surgical anesthetic and now primarily used in the production of tetrafluoroethylene, the building block for the “anti-stick” polymer, Teflon. The molecular formula of chloroform indicates that a single molecule contains one carbon atom, one hydrogen atom, and three chlorine atoms. The average molecular mass of a chloroform molecule is therefore equal to the sum of the average atomic masses of these atoms.

For ionic compounds with polyatomic ions, the sum must include the number and mass of each atom in the formula for the polyatomic ion. as shown in the example below for aluminum sulfate, Al₂(SO₄)₃.

Example (PageIndex{2}) Formula Mass for an Ionic Compound

Aluminum sulfate, Al₂(SO₄)₃, is an ionic compound that is used in the manufacture of paper and in various water purification processes. What is the formula mass (amu) of this compound?

Solution

The formula for this compound indicates it contains Al³⁺ and SO₄²⁻ ions combined in a 2:3 ratio. For purposes of computing a formula mass, it is helpful to rewrite the formula in the simpler format, Al₂S₃O₁₂. Following the approach outlined above, the formula mass for this compound is calculated as follows:

The formula mass for Al₂(SO₄)₃, is 342.14 amu.

Exercise (PageIndex{1})

Use the atomic masses (rounded to two decimal places) to determine the formula mass for each ionic compound.

1. TiO₂
2. AgBr
3. Au(NO₃)₃
4. Fe₃(PO₄)₂

Answer

a. 79.87 amu

b. 187.77 amu

c. 383.0 amu

Percent Composition of a Compound from a Chemical Formula

The percent composition of a compound can also be determined from the formula of the compound. The subscripts in the formula are first used to calculate the mass of each element in one mole of the compound. That is divided by the molar mass of the compound and multiplied by (100%).

[% : text{by mass} = frac{text{mass of element in} : 1 : text{mol}}{text{molar mass of compound}} times 100%]

The percent composition of a given compound is always the same as long as the compound is pure.

Example (PageIndex{3})

Dichlorine heptoxide (left( ce{Cl_2O_7} right)) is a highly reactive compound used in some organic synthesis reactions. Calculate the percent composition of dichlorine heptoxide.

Solution

Avogadro's Number Definition Chemistry

Percent composition can also be used to determine the mass of a certain element that is contained in any mass of a compound. In the previous sample problem, it was found that the percent composition of dichlorine heptoxide is (38.76% : ce{Cl}) and (61.24% : ce{O}). Suppose that you needed to know the masses of chlorine and oxygen present in a (12.50 : text{g}) sample of dichlorine heptoxide. You can set up a conversion factor based on the percent by mass of each element.

[12.50 : text{g} : ce{Cl_2O_7} times frac{38.76 : text{g} : ce{Cl}}{100 : text{g} : ce{Cl_2O_7}} = 4.845 : text{g} : ce{Cl}]

[12.50 : text{g} : ce{Cl_2O_7} times frac{61.24 : text{g} : ce{O}}{100 : text{g} : ce{Cl_2O_7}} = 7.655 : text{g} : ce{O}]

The sum of the two masses is (12.50 : text{g}), the mass of the sample size.

Exercise (PageIndex{2})

Barium fluoride is a transparent crystal that can be found in nature as the mineral frankdicksonite. Determine the percent composition of barium fluoride.

Answer a:

78.32% Ba and 21.67% F

Summary

• The mole (symbol: mol) is the base unit of amount of substance ('number of substance') in the International System of Units or System International (SI), defined as exactly 6.02214076×10²³ particles, e.g., atoms, molecules, ions or electrons.
• Avogadro's number is related to moles of any substance X as follows:

[text{1 mol X} = 6.022 times 10^{23} text{ X atoms}.]

Avogadro's Number Of Molecules

• Formula masses of ionic and molecular compounds can be determined from the masses of the atoms in their formulas.
• Processes are described for calculating the percent composition of a compound based on the chemical formula.

• Anonymous

• Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).

• Stephen Lower, Professor Emeritus (Simon Fraser U.) Chem1 Virtual Textbook

• Marisa Alviar-Agnew (Sacramento City College)

• Henry Agnew (UC Davis)

• Wikipedia

Main Difference – Avogadro’s Constant vs Avogadro’s Number

The terms, mole, Avogadro’s number and Avogadro’s constant are related to each other. A mole is a unit used to measure the amount of a substance. It can be used to measure any type of chemical substance. The value of one mole is 6.022 x 10²³. This is called the Avogadro’s number. Avogadro’s number is the number of particles present in one mole of a substance. The mole of any substance is equal to this number of particles. These particles can be atoms, molecules, colloids or anything. Therefore, it is a constant number that is independent of the type of substance that is considered and is called the Avogadro’s constant. The main difference between Avogadro’s number and Avogadro’s constant is that Avogadro’s number is given as a number that has no units whereas the Avogadro’s constant is given in the unit of per mole (mol^-1).

Key Areas Covered

1. What is Avogadro’s Constant
– Definition, Historical Background, Units, Applications
2. What is Avogadro’s Number
– Definition, Historical Background, Applications
3. What is the Relationship Between Avogadro’s Constant and Avogadro’s Number
– Avogadro’s Constant and Avogadro’s Number
4. What is the Difference Between Avogadro’s Constant and Avogadro’s Number
– Comparison of Key Differences

Key Terms: Avogadro, Avogadro’s Constant, Avogadro’s Number, Mole

What is Avogadro’s Constant

Avogadro’s constant is the number of particles present in one mole of a substance. This is named after the scientist Amedeo Avogadro. This Avogadro’s constant was invented because scientists wanted to relate the amount of microscopic matter to the amount of macroscopic matter. For example, in a particular chemical reaction, the amount of a substance used should be related to the number of atoms or molecules that is present in that substance. Only then can we identify and predict the amount of product that is going to be given by that reaction.

The value of this constant was first calculated by the German scientist Jean-Baptiste Perrin. The value given for the Avogadro’s constant was 6.022 x 10²³. This number was given a name “mole”. One mole of a substance is composed of 6.022 x 10²³particles. For example, one mole of Sodium is composed of 6.022 x 10²³ of sodium atoms. One mole of sodium chloride is composed of 6.022 x 10²³of sodium chloride molecules. Therefore, the unit for Avogadro’s constant is mol^-1. The Avogadro’s constant for one mole is 6.022 x 10²³mol^-1.

The Avogadro’s constant is useful in determining the amount of a substance that reacts in a particular chemical reaction. It is also helpful in determining the amount of product that is given by that reaction. Moreover, we can also predict whether that reaction would happen or not. The Avogadro’s constant is used in determining the atomic mass, molecular mass, and other related concepts.

What is Avogadro’s Number

Avogadro’s number is 6.022 x 10²³. It is the value given for the Avogadro’s Constant. The same thing represented by the Avogadro’s number was first calculated by a German scientist Johann Loschmidt but in different units. However, the real Avogadro’s number was calculated by the scientist Jean-Baptiste Perrin who gave this value a name Avogadro’s number in honor of Avogadro who first gave the concept about the mole. Later, the concepts regarding Avogadro’s number developed rapidly with the development of the science and technology.

One mole of a substance is composed of an Avogadro’s number of particles. These particles can be atoms, ions, molecules, colloids, etc. The particle that is being considered depends on the nature of the substance that is being considered. This term is useful in determining the atomic masses and molecular masses since Avogadro’s number indicates the number of atoms present in one mole of a chemical element or the number of molecules present in a particular compound.

Relationship Between Avogadro’s Constant and Avogadro’s Number

• Avogadro’s number is the value of the Avogadro’s constant.

Difference Between Avogadro’s Constant and Avogadro’s Number

Definition

Avogadro’s Constant:Avogadro’s constant is the number of particles present in one mole of a substance.

Avogadro’s Number:Avogadro’s number is 6.022 x 10²³.

Other Definitions

Avogadro’s Constant:Avogadro’s constant states that the number of basic units present in a mole of a particular compound is a constant value for any compound.

Avogadro’s Number:Avogadro’s number is the number of hydrogen atoms present in one gram of ¹H or number of carbon atoms present in one gram of ¹²C sample.

Units

Avogadro’s Constant:Avogadro’s constant has the unit mol^-1 (per mole).

Avogadro’s Number:Avogadro’s number has no units.

Conclusion

Both Avogadro’s number and Avogadro’s constant describes the same concept. Both these concepts describe the number of particles present in one mole of a particular substance. They have the same value. However, they differ from each other according to their units. The main difference between Avogadro’s number and the Avogadro’s constant is that Avogadro’s number is given as a number that has no units whereas the Avogadro’s constant is given in the unit of per mole (mol^-1).

References:

Avogadro's Constant Is Defined As The Number Of Particles In

1. “The Mole and Avogadro’s Constant.” Chemistry LibreTexts, Libretexts, 21 July 2016, Available here. Accessed 18 Sept. 2017.
2. “Avogadro constant.” Wikipedia, Wikimedia Foundation, 10 Sept. 2017, Available here. Accessed 18 Sept. 2017.
3. The Editors of Encyclopædia Britannica. “Avogadro’s number.” Encyclopædia Britannica, Encyclopædia Britannica, inc., 10 June 2016, Available here. Accessed 18 Sept. 2017.

How To Do Avogadro's Constant

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Number Of Particles In A Mole

1.”Nombre avogadro” By From Joanjoc – Done by myself using PD image; Image:Amedeo Avogadro.gif (Public Domain) via Commons Wikimedia