Chapter 5: Unit 4. Mole and Avogadro’s Number

Mole and Avogadro’s Number

The chemical changes observed in any reaction involve the rearrangement of billions of atoms. It is impractical to try to count or visualize all these atoms, but scientists need some way to refer to the entire quantity. They also need a way to compare these numbers and relate them to the weights of the substances, which they can measure and observe. The solution is the concept of the mole, which is very important in quantitative chemistry.

Avogadro’s Number

Amadeo Avogadro first proposed that the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules, regardless of the type of gas. Although he did not determine the exact proportion, he is credited for the idea.

A mole is a quantity that contains 6.02 *10²³   atoms, molecules and ions.

Avogadro’s number is the number of particles in a mole 6.02 *10²³

The mole (or mol) represents a certain number of objects. The amount of a substance that contains the same number of entities as there are atoms in 12 g of carbon-12. One mole of H₂O molecules contains 6.022 x 10²³ molecules. • 1 mole contains 6.022 x 10²³ entities (Avogadro’s number). One mole of NaCl contains 6.022 x 10²³ NaCl formula units.

Exactly 12 g of carbon-12 contains 6.022 x 10 23 atoms. Here are some examples of 1 mol of a substance.

*** There is a new definition of mole available at C & EN article

https://cen.acs.org/content/cen/articles/96/web/2018/11/New-definitions-kilogram-mole.html

The meaning and usefulness of the mole: number of moles of elements in a compound can also be determined from the chemical formula. For example,

the chemical formula of water is H₂O. Therefor in 1 mole of H₂O contains 2 mols of H and 1 mol of O from the subscript of the chemical formula.

Mol and number of particles can be easily calculated by using the conversion factor:

1mol
6.022 x 10²³       or vice versa

Examples:
How many atoms are present in 3.0 mols of Ag?

Ans:   Since it is mols to atoms, Avogadro’s number is the conversion factor.

3.0 mols of Ag * 6.022 x 10²³  atoms of Ag     = 18.067 * 10²³  atoms or 1.8 *10²⁴atoms Ag

1 mol Ag

1. How many molecules are present in 2.93 mols of H₂O?

Since it is mols to molecules, Avogadro’s number is the conversion factor.

Ans:  2.93 mols of H₂O * 6.022 x 10²³  molecules of H₂O    = 18.067 * 10²³  atoms or 1.8 *10²⁴

1 mol H₂O

2. How many mols of Hydrogen are in 1.56 mols of CH₄?

Since it is mols from a compound to mols of an element, we will use chemical formula.

1.56 mols of CH₄ *  4 mols H      = 6.24 mols of H

• mol CH₄
  4)     How many hydrogen atoms are there in 2.50 mol of glucose (C₆H₁₂O₆)?
• We will use both chemical formula and avogadro’s number to solve this problem.
  2.50 mol C₆H₁₂O_{6 *}12 mols H *       6.022 x 10²³  atoms of H =180.66 x 10²³  or 1.81 x 10²³ atoms
  1 mol C₆H₁₂O₆            1 mol H

Watch the following video:

Questions:

1. How many atoms are present in 5.5 mol of Fe?

2. How many mols of each element present in 2 .00 mols of the following compound?

C₉H₈O₄ (aspirin)

4. How many molecules are present in 7.29 mols of the compound below?

5. 11* 10²⁴ molecules are present in a glass of water. How many mols of H₂O are present?

Ans: 1. 3.31*10²⁴ atoms

2.18 mols of C, 16 mols H, 8.0 mols O

3. 3. 77 *10²⁵ atoms of oxygen

4. 4.39*10²⁴ molecules

5. 5.17 mols