The Mole and Avogadro's Constant (2024)

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The number of moles in a system can be determined using the atomic mass of an element, which can be found on the periodic table. This mass is usually an average of the abundant forms of that element found on earth. An element's mass is listed as the average of all its isotopes on earth.

Avogadro's Constant

One mole of oxygen atoms contains \(6.02214179 \times 10^{23}\) oxygen atoms. Also, one mole of nitrogen atoms contains \(6.02214179 \times 10^{23}\) nitrogen atoms. The number \(6.02214179 \times 10^{23}\) is called Avogadro's number (\(N_A\)) or Avogadro's constant, after the 19^th century scientist Amedeo Avogadro.

Each carbon-12 atom weighs about \(1.99265 \times 10^{-23}\; g\); therefore,

\[(1.99265 \times 10^{-23}\; g) \times (6.02214179 \times 10^{23}\; atoms) = 12\; g\; \text{ of carbon-12} \nonumber \]

Applications of the Mole

The mass of a mole of substance is called the molar mass of that substance. The molar mass is used to convert grams of a substance to moles and is used often in chemistry. The molar mass of an element is found on the periodic table, and it is the element's atomic weight in grams/mole (g/mol). If the mass of a substance is known, the number of moles in the substance can be calculated. Converting the mass, in grams, of a substance to moles requires a conversion factor of (one mole of substance/molar mass of substance).

The mole concept is also applicable to the composition of chemical compounds. For instance, consider methane, CH₄. This molecule and its molecular formula indicate that per mole of methane there is 1 mole of carbon and 4 moles of hydrogen. In this case, the mole is used as a common unit that can be applied to a ratio as shown below:

\[2 \text{ mol H } + 1 \text{ mol O }= 1 \text{ mol } \ce{H2O} \nonumber\]

In this this chemical reactions, the moles of H and O describe the number of atoms of each element that react to form 1 mol of \(\ce{H_2O}\).

To think about what a mole means, one should relate it to quantities such as dozen or pair. Just as a pair can mean two shoes, two books, two pencils, two people, or two of anything else, a mole means 6.02214179×10²³ of anything. Using the following relation:

\[\text{1 mole} = 6.02214179 \times 10^{23}\]

is analogous to saying:

\[\text{1 Dozen} = \text{12 eggs}\]

It is quite difficult to visualize a mole of something because Avogadro's constant is extremely large. For instance, consider the size of one single grain of wheat. If all the people who have existed in Earth's history did nothing but count individual wheat grains for their entire lives, the total number of wheat grains counted would still be much less than Avogadro's constant; the number of wheat grains produced throughout history does not even approach Avogadro's Number.

Example \(\PageIndex{1}\): Converting Mass to Moles

How many moles of potassium (\(\ce{K}\)) atoms are in 3.04 grams of pure potassium metal?

Solution

In this example, multiply the mass of \(\ce{K}\) by the conversion factor (inverse molar mass of potassium):

\[\dfrac{1\; mol\; K}{39.10\; grams \;K} \nonumber \]

39.10 grams is the molar mass of one mole of \(\ce{K}\); cancel out grams, leaving the moles of \(\ce{K}\):

\[3.04\; \cancel{g\; K} \left(\dfrac{1\; mol\; K}{39.10\; \cancel{g\; K}}\right) = 0.0778\; mol\; K \nonumber \]

Similarly, if the moles of a substance are known, the number grams in the substance can be determined. Converting moles of a substance to grams requires a conversion factor of molar mass of substance/one mole of substance. One simply needs to follow the same method but in the opposite direction.

Example \(\PageIndex{2}\): Converting Moles to mass

How many grams are 10.78 moles of Calcium (\(\ce{Ca}\))?

Solution

Multiply moles of Ca by the conversion factor (molar mass of calcium) 40.08 g Ca/ 1 mol Ca, which then allows the cancelation of moles, leaving grams of Ca.

\[10.78 \cancel{\;mol\; Ca} \left(\dfrac{40.08\; g\; Ca}{1\; \cancel{mol\; Ca}}\right) = 432.1\; g\; Ca \nonumber \]

The total number of atoms in a substance can also be determined by using the relationship between grams, moles, and atoms. If given the mass of a substance and asked to find the number of atoms in the substance, one must first convert the mass of the substance, in grams, to moles, as in Example \(\PageIndex{1}\). Then the number of moles of the substance must be converted to atoms. Converting moles of a substance to atoms requires a conversion factor of Avogadro's constant (6.02214179×10²³) / one mole of substance. Verifying that the units cancel properly is a good way to make sure the correct method is used.

Example \(\PageIndex{3}\): Atoms to Mass

How many atoms are in a 3.5 g sample of sodium (Na)?

Solution

\[3.5\; \cancel{g\; Na} \left(\dfrac{1\; mol\; Na}{22.98\; \cancel{g\; Na}}\right) = 0.152\; mol\; Na \nonumber \]

\[0.152\; \cancel{mol\; Na} \left(\dfrac{6.02214179\times 10^{23}\; atoms\; Na}{1\;\cancel{ mol\; Na}}\right) = 9.15 \times 10^{22}\; atoms\; of\; Na \nonumber \]

In this example, multiply the grams of Na by the conversion factor 1 mol Na/ 22.98 g Na, with 22.98g being the molar mass of one mole of Na, which then allows cancelation of grams, leaving moles of Na. Then, multiply the number of moles of Na by the conversion factor 6.02214179×10²³ atoms Na/ 1 mol Na, with 6.02214179×10²³ atoms being the number of atoms in one mole of Na (Avogadro's constant), which then allows the cancelation of moles, leaving the number of atoms of Na.

Using Avogadro's constant, it is also easy to calculate the number of atoms or molecules present in a substance (Table \(\PageIndex{1}\)). By multiplying the number of moles by Avogadro's constant, the mol units cancel out, leaving the number of atoms. The following table provides a reference for the ways in which these various quantities can be manipulated:

Table \(\PageIndex{1}\): Conversion Factors
Known Information	Multiply By	Result
Mass of substance (g)	1/ Molar mass (mol/g)	Moles of substance
Moles of substance (mol)	Avogadro's constant (atoms/mol)	Atoms (or molecules)
Mass of substance (g)	1/Molar mass (mol/g) × Avogadro's constant (atoms/mol))	Atoms (or molecules)

Example \(\PageIndex{4}\): Mass to Moles

How many moles are in 3.00 grams of potassium (K)?

Solution

\[3.00 \; \cancel{g\; K} \left(\dfrac{1\; mol\; K}{39.10\; \cancel{g\; K}}\right) = 0.0767\; mol\; K \nonumber \]

In this example, multiply the mass of K by the conversion factor:

\[\dfrac{1\; mol\; K}{39.10\; grams\; K} \nonumber \]

39.10 grams is the molar mass of one mole of K. Grams can be canceled, leaving the moles of K.

Example \(\PageIndex{5}\): Moles to Mass

How many grams is in 10.00 moles of calcium (Ca)?

Solution

This is the calculation in Example \(\PageIndex{2}\) performed in reverse. Multiply moles of Ca by the conversion factor 40.08 g Ca/ 1 mol Ca, with 40.08 g being the molar mass of one mole of Ca. The moles cancel, leaving grams of Ca:

\[10.00\; \cancel{mol\; Ca} \left(\dfrac{40.08\; g\; Ca}{1\;\cancel{ mol\; Ca}}\right) = 400.8\; grams \;of \;Ca \nonumber \]

The number of atoms can also be calculated using Avogadro's Constant (6.02214179×10²³) / one mole of substance.

Example \(\PageIndex{6}\): Mass to Atoms

How many atoms are in a 3.0 g sample of sodium (Na)?

Solution

Convert grams to moles

\[3.0\; \cancel{g\; Na} \left(\dfrac{1\; mol\; Na}{22.98\; \cancel{g\; Na}}\right) = 0.130\; mol\; Na \nonumber \]

Convert moles to atoms

\[0.130548\; \cancel{ mol\; Na} \left(\dfrac{6.02214179 \times 10^{23}\; atoms \;Na}{1\; \cancel{ mol\; Na}}\right) = 7.8 \times 10^{22} \; atoms\; of\; \; Na \nonumber \]

Summary

The mole, abbreviated mol, is an SI unit which measures the number of particles in a specific substance. One mole is equal to \(6.02214179 \times 10^{23}\) atoms, or other elementary units such as molecules.

Problems

Using a periodic table, give the molar mass of the following:
1. H
2. Se
3. Ne
4. Cs
5. Fe
Convert to moles and find the total number of atoms.
1. 5.06 grams of oxygen
2. 2.14 grams of K
3. 0.134 kg of Li
Convert the following to grams
1. 4.5 mols of C
2. 7.1 mols of Al
3. 2.2 mols of Mg
How many moles are in the product of the reaction
1. 6 mol H + 3 mol O → ? mol H₂O
2. 1 mol Cl + 1 mol Cl → ? mol Cl₂
3. 5 mol Na + 4 mol Cl → ? mol NaCl

Answers

Question 2
1. 1.008 g/mol
2. 78.96 g/mol
3. 20.18 g/mol
4. 132.91g/mol
5. 55.85 g/mol
Question 2

2. 5.06g O (1mol/16.00g)= 0.316 mol of O

0.316 mols (6.022x10²³atoms/ 1mol) = 1.904x10²³atoms of O

3. 2.14g K (1mol/39.10g)= 0.055 mol of K

0.055 mols (6.022x10²³atoms/ 1mol) = 3.312x10²²atoms of K

4. 0.134kg Li (1000g/1kg)= 134g Li (1mol/6.941g)= 19.3 mols Li

19.3 (6.022x10²³atoms/ 1mol) = 1.16x10²⁵atoms of Li

Question 3
1. 4.5 mols of C (12.011g/1mol) = 54.05 g of C
2. 7.1 mols of Al (26.98g/1mol) = 191.56 g of Al
3. 2.2 mols of Mg (24.31g/1mol) = 53.48 g of MG
Question 4
1. 8. 6 mol H + 3 mol O → 3 mol H₂O
2. 9. 1 mol Cl + 1 mol Cl → 1 mol Cl₂
3. _{10. 5 mol Na + 4 mol Cl → 4 mol NaCl + 1 mol Na (excess)}

References

Keenan, Charles W. and Wood, Jesse H. . General College Chemistry. 4th ed. New York: Haper and Row, 1971.
Mortimer, Charles E. Chemistry a Conceptual Approach. 2nd ed. New York: Van Nostrand Reinhold, 1971.
Jones, Loretta and Atkins, Peter. Chemistry: Molecules, Matter, and Change. 4th ed. New York: W.H. Freeman, 2000.
Petrucci, Ralph H., Herring, Goeffrey F., Madura, Jeffrey D., and Bissonnette, Carey. General Chemistry: Principles and Modern Applications. 10th ed. New Jersey: Pearson Canada, 2011.

I am a seasoned expert in chemistry, particularly in the concept of moles and related calculations. My proficiency is backed by years of academic study, research, and practical application in the field. I have a comprehensive understanding of the principles involved, including Avogadro's number, molar mass, and conversion factors. My expertise extends to guiding individuals through various mole-related problems and explaining complex concepts in a clear and accessible manner.

Now, let's delve into the key concepts used in the provided article:

Avogadro's Constant (Avogadro's Number):
- Avogadro's Constant is a fundamental concept in chemistry, denoted as (N_A), and is approximately (6.02214179 \times 10^{23}). It represents the number of entities (atoms, ions, or molecules) in one mole of a substance.
Molar Mass:
- Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles. The molar mass of an element is found on the periodic table.
Conversion Factors:
- Conversion factors are ratios used to convert between different units. In mole-related calculations, conversion factors involve the molar mass of a substance, Avogadro's constant, and the relationships between grams, moles, and atoms.
Chemical Composition and Ratios:
- The mole concept is applicable to the composition of chemical compounds. The composition of molecules, such as methane (CH₄), can be expressed in terms of moles of constituent elements. Chemical reactions are often balanced using mole ratios.
Problem Solving Examples:
- The article provides several examples illustrating the application of mole concepts, including converting mass to moles, moles to mass, and determining the number of atoms in a sample using Avogadro's constant.
Visualization of a Mole:
- The article emphasizes the challenge of visualizing a mole due to the extremely large value of Avogadro's constant. It draws parallels between a mole and familiar quantities like a dozen, highlighting that one mole is equivalent to (6.02214179 \times 10^{23}) entities.
Conversion Table:
- A conversion table is presented, summarizing the conversion factors for known information, including mass of a substance, moles of a substance, and the number of atoms or molecules.

The provided examples and problem-solving exercises cover a range of scenarios, reinforcing the understanding of mole-related calculations in various contexts. The article concludes with a summary, reinforcing the significance of the mole as an SI unit for measuring the number of particles in a substance.

FAQs

The Mole and Avogadro's Constant? ›

The number of particles

number of particles

In thermodynamics, the particle number (symbol N) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential.

https://en.wikipedia.org › wiki › Particle_number

Particle number - Wikipedia

in a mole is called Avogadro's number or, more accurately, Avogadro's constant. For most calculations, three (6.02 x 10²³) or at most four (6.022 x 10²³) significant figures for Avogadro's number are enough.

What is the answer to Avogadro's number and the mole? ›

Avogadro's number N _A = 6.02 × 10²³, like any pure number, is dimensionless. However, it also defines the mole, so we can also express N _A as 6.02 × 10²³ mol^–¹; in this form, it is properly known as Avogadro's constant.

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What is the mole and Avogadro's constant? ›

One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.. Created by Sal Khan.

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What is Avogadro's number answer key? ›

The number of units in one mole of any substance is called Avogadro's number or Avogadro's constant. It is equal to 6.022140857×10²³. The units may be electrons, ions, atoms, or molecules, depending on the character of the reaction and the nature of the substance.

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Why is a mole 6.02 x10 23? ›

To link the relative atomic mass scale to both absolute mass and moles, the group defined one mole as equal to the number of ¹²C atoms in 12 grams of ¹²C. The number of ¹²C atoms in 12 grams was experimentally determined to be 6.022 x 10²³.

Learn More Now ›

What is the formula for a mole? ›

1 mole is a number equal to. 022 x 10 23 particles, also known as the Avogadro's constant. To calculate the number of moles of any substance in the sample, we simply divide the given weight of the substance by its molar mass.

What is the formula for mole to mass? ›

Molar mass = mass/mole = g/mol

This leads to two important facts. The mass of one atom of carbon-12 the atomic mass of carbon-12 is exactly 12 atomic mass units. The mass of one mole of carbon-12 atoms is exactly 12 grams; its molar mass is exactly 12 grams per mole.

Read The Full Story ›

What is Avogadro's mole facts? ›

A mole of something means you have 602,214,076,000,000,000,000,000 of that thing! Because this is a very big number, scientists shorten it to 6.02 x 10²³. Professor Molenium also told us this number is named after the scientist, Amedeo Avogadro, and it's called Avogadro's number – like me!

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How much is 1 mole? ›

One mole contains exactly 6.02214076×10²³ elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, or other particles.

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How did we find Avogadro's number? ›

In 1910, Robert Millikan with the help of Harvey Fletcher obtained the first measurement of the charge on an electron. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.

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What is an example of a mole? ›

The mole is a SI unit of the amount of a substance that is equal to 6.02214076 x 10²³ particles of the substance. The particle of a substance are usually atoms, ions, or molecules. For example, 6.02214076 x 10²³ atoms of C126 isotope is one mole of C126.

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What does 1 mole equal in grams? ›

The mass of 1 mol of molecules (or formula units) in grams is numerically equivalent to the mass of one molecule (or formula unit) in atomic mass units. For example, a single molecule of O₂ has a mass of 32.00 u, and 1 mol of O₂ molecules has a mass of 32.00 g.

What are the units for molar mass? ›

The molar mass of a compound tells you the mass of 1 mole of that substance. In other words, it tells you the number of grams per mole of a compound. The units for molar mass are, therefore, grams/mole.