# Avogadro's number explained with worked examples

### What is Avogadro's Number?

Avogadro's number refers to the number of particles or atoms or molecules present in one mole of a substance. This number is 6.02214076 × 1023. It is termed Avogadro's constant.

The calculations involving Avogadro's number may require us to find the number of particles, atoms or molecules. We should not be confused on these terms as they all point to the same thing. However, we may further be asked to find the moles, mass or molar mass of a substance in questions related to Avogadro's numbers.

Questions related to Avogadro's number, mole and molar mass will be solved in this article. Meanwhile, an understanding on the concept of mole and Avogadro's number is required.

Please read an introduction to mole and Avogadro's number here

### Questions and Answers on Avogadro's Number

• ##### Question 1

2H2(g) + O2(g) -> 2H2O(l)

From the above equation, calculate the number of atoms present in the reactants. (Avogadro's number is 6.02 × 1023).

• ##### Solution

The reactants present in the reaction are two moles of hydrogen molecules and one mole of oxygen molecule.

Worthy of note is the number present in front of the molecules involved in the reaction. This number is the mole itself. Hydrogen has 2 in front (that is, 2 moles of hydrogen) while oxygen has nothing, and this signifies 1 mole of oxygen. Water is the product from the reaction. It has 2 anteriorly and can be appropriately referred to as 2 moles of water.

Recall that one mole of any substance = 6.02 × 1023. These substances can be an atom, a molecule or a compound.

• From the question, two moles of hydrogen = 2 x 6.02 × 1023 = 12.04 × 1023

• One mole of oxygen = 1 x 6.02 × 1023 = 6.02 × 1023

Therefore, the reactant 2H2(g) contains 12.04 × 1023 atoms while O2(g) contains 6.02 × 1023

You can read on molecular mass and its calculations here

• ##### Question 2

How many moles are present in 120.4 × 1023 molecules. (Avogadro's number  is 6.02 × 1023).

• ##### Solution

Recall that one mole of any substance will always contain 6.02 × 1023 atoms, particles or molecules. The question uses 'molecules' in this instance, but regardless, it is still the same as atoms or particles.

• If 1 mole = 6.02 × 1023

• Then Z moles = 120.4 × 1023

• Cross multiply

• Z x  6.02 × 1023 = 1 x 120.4 × 1023

• Make Z the subject of the formula

• Z = 120.4 × 1023 / 6.02 × 1023

• Z = 20 moles

Therefore 20 moles of Z will contain 120.4 × 1023 molecules.

• ##### Question 3

3.01 × 1023 particles of sodium reacted with chlorine to produce sodium chloride. How many moles of sodium reacted and what is the molar mass of sodium according to the reaction. (Sodium = 23, Avogadro's number = 6.02 × 1023).

• ##### Solution

One mole of any substance contains = 6.02 × 1023.

• If 1 mole of sodium = 6.02 × 1023

• Then Y mole = 3.01 × 1023

• Cross multiply

• Y x 6.02 × 1023 = 1 x 3.01 × 1023

• Make Y the subject of the formula

• Y = 3.01 × 1023 / 6.02 × 1023

• Y = 1/2 mol

Therefore, 1/2 mol of sodium is equivalent to 3.01 × 1023 particles of sodium.

Molar mass of sodium = 23g/mol

• Since 1/2 mole reacted, the molar mass of sodium that reacted will be 1/2 x 23g/mol

• 11.5g/mol

You can read on Dalton's atomic theory and its modifications here

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