Moles and Molar Mass

This is part of Year 11 HSC Chemistry course under the topic of Mole Concept.

HSC Chemistry Syllabus

• Explore the concept of the mole and relate this to Avogadro’s constant to describe, calculate and manipulate masses, chemical amounts and numbers of particles in: (ACSCH008, ACSCH039)
– Moles of elements and compounds n = \frac{m}{MM} (n = chemical amount in moles, m = mass in grams, MM = molar mass in g mol-1
– Percentage composition calculations and empirical formulae
– Limiting reagent reactions

What is a Mole?

The mole, denoted as (mol), is the SI unit representing an amount of substance. Specifically, it is defined by the number of particles present in 12 g of carbon-12. This specific quantity is known as Avogadro's number and is approximately:

$$6.022 \times 10^{23} \text{particles per mole}$$

It's essential to realise that the mole, akin to the term "dozen" which signifies 12, only provides a count and does not convey any information about the mass of those entities. For instance, having one mole of water in a container means that there are approximately 6.022 \times 10^{23} water molecules in that particular volume.

Determining Molar Mass

The molar mass (MM) of a substance represents the mass of exactly one mole of that substance. This is equivalent to the mass of 6.022 \times 10^{23} particles of that substance.

The periodic table is a vital tool for calculating molar mass.

1. To determine the molar mass of an element, we must first identify whether it exists in monatomic or molecular form.
• The molar mass of a monatomic element is the atomic mass given on the periodic table, expressed in grams per mole. For instance, iron has a molar has of 55.85 g/mol, whereas gold is 107.9 g/mol.
• For molecular elements, the formula must be known to determine the molar mass. As an example, oxygen typically exists as a diatomic element O_2. Therefore, the molar mass of O_2 would be double that of an oxygen atom which is 16.00 g/mol.

$$\text{Molar mass (MM) of } O_2 = 2 \times \text{MM of O} = 2 \times 16.00 = 32.00 \text{g/mol}$$

1. The molar mass of a compound is the summation of the molar masses of the atoms in its formula. For example, iron and oxygen react to form iron oxide, often referred to as rust, with the chemical formula Fe_2O_3.

$$\text{Molar mass (MM) of }Fe_2O_3 = 2 \times \text{MM of Fe} + 3 \times \text{MM of O} = 159.7 \text{g/mol}.$$

Moles in Calculation

In Chemistry, when we combine different substances to execute a reaction, it is essential to know the amount of substance in moles, its mass in grams, and the total number of its constituent particles. Intriguingly, the relationship between atomic-scale and macroscopic scale measurements remains consistent for both elements and compounds.

• An atom's mass in atomic mass units (amu) is numerically equivalent to the mass (in grams) of 1 mole of atoms of that element.

It is important to recognise that atoms, molecules, and particles are the same concept referring to monatomic or molecular substances respectively.

1 atom of Fe = 55.85 amu & 1 mole of Fe = 55.85 g
1 molecule of O_2 = 32.00 amu & 1 mole of O_2 = 32.00 g

Given the relativity of atomic mass, an atom of Fe is \frac{55.85}{32.00} times heavier than 1 mole of oxygen gas.

• The mass of a molecule (or formula unit) of a compound in atomic mass units (amu) corresponds numerically to the mass in grams (g) of 1 mole of the compound.

1 molecule of H_2O = 18.016 amu & 1 mole of H_2O = 18.016 g
1 molecule of Fe_2O_3 = 159.7 amu & 1 mole of Fe_2O_3 = 159.7 g

Considering atomic mass relativity, a molecule of H_2O is \frac{18.016}{159.7} times lighter than a molecule of Fe_2O_3.

By extrapolating from our knowledge on moles, a 63.55 g mass of copper implies that there is 1 mole of copper, amounting to 6.022 \times 10^{23} copper particles.

Converting between moles, mass, and number of particles

One of the most important skills in chemical calculations is the conversion between he amount of a substance (in moles) and its mass (in grams). The bridge between these two quantities is the molar mass (mm), which provides the weight in grams of 1 mole of a given substance. Mathematically, this relation can be expressed as

$$\frac{\text{no. of grams}}{1 \text{ mol}} \text{ or } \frac{1 \text{ mol}}{\text{no. of grams}}$$

• If we are converting from amount (in mol) to mass (in g), we utilise the molar mass to determine the mass

$$\text{Mass(g) = amount (mol)} \times \frac{\text{no. of grams}}{1 \text{mol}}$$

• Conversely, when converting from mass (in g) to amount (in mol), we either divide the molar mass or multiply its reciprocal to nullify the mass unit:

$$\text{Amount (mol)} = \text{mass (g)} \times \frac{1 \text{mol}}{\text {no. of grams}}$$