The word mole was first introduced by the german chemist Wilham Ostwald in 1896. This is the Latin word meaning ‘pile’. The mole can be converted into the mass, volume, and number of particles. To convert moles into mass the conversion factor is molar mass. However, for the particle-mole conversions, the conversion factor is Avogadro’s number.

## What is the mole?

” The atomic mass, formula mass, molecular mass, or ionic mass of the substance expressed in grams is called the mole of the substance.”

However, the mole can also be defined as the amount of the substance that consists of Avogadro’s number of particles (6.023× 10^{23}). This number is named in honor of Amedeo Avogadro(1776-1856).

## Mass-mole conversions

When we Interconverting the mass and mole the conversion factor is the molar mass. Which is expressed in the unit gram/mol. When we convert mass into moles divide the initial mass by the molar mass. However, when we convert moles into mass multiply the initial moles with molar mass. This is summarized in the image below:

**Example 1**

Calculate the mass of 10^{-2 }moles of MgSO_{4}.

**Solution **

**Step 1: Determine the formula mass **

Although MgSO_{4} is an ionic compound. Therefore, we use the term formula mass instead of molar mass.

Formula mass of the MgSO_{4 }= 24 × 1 + 32 × 1 + 16 × 4

= 120 g/mol

**Step 2: Multiply moles by formula mass**

No of moles of MgSO_{4} = 10^{-2} moles

Mass of MgSO_{4} = Number of moles of MgSO_{4} × formula mass of MgSO_{4}

Mass of MgSO_{4} = 10^{-2} × 120 = 1.2 g

**Example 2**

Calculate no of moles in 40g of H_{3}PO_{4}.

**Solution **

**Step 1: Determination of molecular mass **

The molecular mass of H_{3}PO_{4 }= 1 × 3 + 31 × 1 + 16 × 4

= 98 gmol^{-1}

**Step 2: Divide mass by the molecular mass **

Mass of the H_{3}PO_{4 }= 40g

No of moles = mass of the substance/molar mass of the substance

No of moles = 40g/ 98gmol^{-1} = 0.408 mol

## Volume-mole conversions

The mole quantities of gases can be expressed in terms of volume. According to Avogadro’s law, one mole of any gas at STP occupies a volume of 22.4dm^{3}. However, for the volume-mole conversions following conversion factor is used:

**Example 1**

Find the number of moles present in 11.2L of N_{2} gas at STP.

**Solution **

no of moles = vol given(STP)/22.4L

= 11.2/22.4 = 0.5 mol

## Particle-mole conversions

Avogadro’s number is the conversion factor for the particle-mole conversions. If we want to find the number of atoms in an element, multiply Avogadro’s number with the number of moles. If we know the number of particles and we want to find the number of moles. Hence, we divide the number of particles by Avogadro’s number.

**Example **

What is the number of silver atoms in the bracelet which contains 1.56 mol of Ag?

**Solution **

No of moles = 1.56

Avogadro’s No = 6.022 × 10^{23}

No of atoms = 1.56mol/6.022×10^{23}

= 9.39×10^{23}

## Concepts Berg

**How do you do a 3 step mole conversion?**

To convert the moles into mass we follow three steps. These are the following:

- Calculate the moles which are mentioned in the question.
- Find the molar mass of the substance.
- In the last step, multiply these two values.

**What is the conversion from moles to grams?**

When we want to convert the moles into grams. Multiply the number of moles with the molar mass to get grams.

**How are mass and mole related?**

**How is the mole ratio used in stoichiometry?**

In stoichiochemistry, the mole ratio is used to convert the number of moles of one substance into the number of moles of another substance.

**Reference Books **

**A Visual Analogy Guide to Chemistry, 2e**By**Paul A Krieger (**Grand Rapids Community College)**Chemistry: The Molecular Science**By**John Olmsted, Gregory M. Williams**

**Reference Links**

- Mole conversion tips for chemistry (dummies.com)