Lesson 2.4: Amount of Substance and the Mole

Introduction

In this lesson, we will explore the fundamental concept of the mole and how it serves as a unit of measurement in both chemistry and physics. The mole is essential for understanding the quantities of substances we work with. By the end of this lesson, you will be able to:

• Understand relative atomic and formula mass and the mole as a counting unit.
• Use the Avogadro constant and convert between mass, moles, and the number of particles.
• Calculate the concentration of a solution in moles per cubic decimetre.
• Accurately determine the relative formula mass of a compound.
• Convert between mass, moles, and the number of particles for various substances.

Understanding Relative Atomic and Formula Mass

1.1 What is Atomic Mass?

Atomic mass is the weighted average mass of an element's isotopes relative to the mass of carbon-12, defined as exactly 12 atomic mass units (amu). Usually, atomic masses are listed on the periodic table. For instance, the atomic mass of carbon (C) is approximately 12.01 amu.

Worked Example

Consider chlorine (Cl), which has an atomic mass of approximately 35.45 amu. If you have 2 moles of chlorine, how many grams do you have?

1. Use the formula Mass = Moles × Atomic Mass.
2. Substitute the values:

$Mass = 2 \, \text{moles} \times 35.45 \, \text{g/mol} = 70.90 \, \text{g}$

So, 2 moles of chlorine weigh approximately 70.90 grams.

1.2 Understanding Formula Mass

The formula mass (or molar mass) of a compound is found by adding together the atomic masses of the constituent elements in a compound, multiplied by the number of times each element appears in the formula.

Worked Example

Calculate the formula mass of water ($H_2O$).

1. Identify the atomic masses:

• Hydrogen (H): 1.01 amu
• Oxygen (O): 16.00 amu

1. Calculate using the formula:

$ \text{Formula Mass} = (2 \times 1.01) + (1 \times 16.00) = 2.02 + 16.00 = 18.02 \, \text{g/mol} $

The formula mass of water is approximately 18.02 g/mol.

The Mole as a Counting Unit

2.1 What is a Mole?

A mole is a unit that allows chemists to count particles (atoms, molecules, ions) in a sample. One mole of any substance contains exactly $6.022 \times 10^{23}$ particles, a number known as Avogadro's number.

2.2 The Importance of the Mole

The mole is crucial because it provides a bridge between the atomic scale and the macroscopic scale. Instead of counting individual atoms or molecules, chemists use moles to quantify substances conveniently.

2.3 Using Avogadro's Constant

Avogadro's constant allows us to convert between the number of particles and moles. If you know the number of particles, you can calculate moles using:

$$ \text{Moles} = \frac{\text{Number of Particles}}{6.022 \times 10^{23}} $$

Worked Example

If you have $1.2044 \times 10^{24}$ molecules of water, how many moles do you have?

1. Use the formula:

$ \text{Moles} = \frac{1.2044 \times 10^{24}}{6.022 \times 10^{23}} = 2.00 \, \text{moles} $

You have 2 moles of water molecules.

Converting Between Mass, Moles, and Number of Particles

3.1 Using Molar Mass for Conversions

To convert between mass and moles, you can use the formula:

$$ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} $$

Worked Example

How many moles are in 36 grams of water?

1. Use the molar mass of water: 18.02 g/mol.
2. Substitute into the formula:

$ \text{Moles} = \frac{36 \, \text{g}}{18.02 \, \text{g/mol}} = 1.996 \approx 2.00 \, \text{moles} $

You have about 2 moles of water in a 36-gram sample.

3.2 Converting from Moles to Mass

To find the mass from moles, rearrange the formula:

$$ \text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)} $$

Worked Example

What is the mass of 3 moles of sodium chloride ($NaCl$)?

1. Determine the molar mass: $Na \approx 22.99 \text{ g/mol}$, $Cl \approx 35.45 \text{ g/mol}$ so,

$ \text{Molar Mass} = 22.99 + 35.45 = 58.44 \, \text{g/mol} $

1. Use the formula to find mass:

$ \text{Mass} = 3 \, \text{moles} \times 58.44 \, \text{g/mol} = 175.32 \, \text{g} $

So, the mass of 3 moles of sodium chloride is approximately 175.32 grams.

The Concept of Concentration

4.1 Understanding Concentration

Concentration expresses the amount of a substance (in moles) within a certain volume (in cubic decimeters). The unit of concentration is moles per cubic decimetre (mol/dm³).

4.2 Calculating Concentration

To calculate concentration, the formula is:

$$ \text{Concentration (mol/dm}^3\text{)} = \frac{\text{Moles of solute}}{\text{Volume of solution (dm}^3\text{)}} $$

Worked Example

If you dissolve 2 moles of sodium chloride in 1 dm³ of water, what is the concentration?

1. Use the concentration formula:

$ \text{Concentration} = \frac{2 \, \text{moles}}{1 \, \text{dm}^3} = 2 \, \text{mol/dm}^3 $

The concentration of the solution is 2 mol/dm³.

Conclusion

In this lesson, we have learned about the mole as a counting unit, how to calculate relative atomic and formula mass, and how to convert between mass, moles, and number of particles. This foundational knowledge is essential for further studies in chemistry and understanding the behavior of substances in various states of matter.

Study Notes

• Atomic mass is the weighted average mass of isotopes of an element.
• The mole is defined as $6.022 \times 10^{23}$ particles of a substance.
• Molar mass is the mass of one mole of a substance in grams.
• To convert between mass, moles, and number of particles, use molar mass and Avogadro's constant.
• Concentration is measured in moles per cubic decimetre (mol/dm³).