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

  1. 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 C6H12O6 *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?
  1. How many mols of each element present in 2 .00 mols of the following compound?

C9H8O4 (aspirin)

3.    How many oxygen atoms are present in 5.20 mol of Al2(SO4)3?
  1. 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