Amount of Substance and the Mole Revision Notes for OCR A-Level Chemistry A

Amount of substance and the mole

Introduction: counting particles in chemistry

Chemical reactions happen at the atomic level, involving individual atoms, molecules, or ions. However, we measure chemicals using mass (grams) or volume. This creates a challenge: how do we connect the mass we can measure to the actual number of particles taking part in a reaction?

The answer lies in using a concept called amount of substance, which gives us a way to count particles indirectly by weighing them.

The mole and Avogadro constant

What is a mole?

In chemistry, the term amount of substance (symbol: $n$ ) represents the quantity of particles present in a sample. This is measured using a unit called the mole (symbol: mol).

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A mole is defined as the quantity of substance that contains exactly $6.02 \times 10^{23}$ particles. These particles could be atoms, molecules, ions, or electrons - the mole simply counts them.

The Avogadro constant

The number $6.02 \times 10^{23}$ is called the Avogadro constant and is given the symbol $N_\text{A}$ . Its units are $\text{mol}^{-1}$ , meaning "per mole".

$N_\text{A} = 6.02 \times 10^{23} \text{ mol}^{-1}$

This represents the number of particles in each mole of any substance.

Why this specific number?

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The Avogadro constant is directly linked to carbon-12, which serves as the standard for measuring atomic masses. Exactly 12 g of carbon-12 contains precisely $6.02 \times 10^{23}$ atoms. This provides the foundation for the mole concept.

The Avogadro constant is an incredibly large number. To put it in perspective: if $6.02 \times 10^{23}$ pennies were distributed evenly among every person on Earth, each person could spend $1 million every hour for their entire lifetime and still have money left over!

Molar mass

Definition and units

Molar mass (symbol: $M$ ) acts as a conversion factor between moles and mass. It is defined as the mass of one mole of a substance.

The units of molar mass are always grams per mole ( $\text{g mol}^{-1}$ ).

Molar mass of elements

For elements, there's a simple rule:

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The mass of one mole of atoms of an element equals the relative atomic mass in grams.

This means you can find the molar mass of any element directly from the periodic table by taking the relative atomic mass value and adding "g mol⁻¹" as the unit.

Examples of molar masses for common elements:

One mole of carbon (C) atoms has a mass of $12.0 \text{ g}$ , so $M(\text{C}) = 12.0 \text{ g mol}^{-1}$
One mole of hydrogen (H) atoms has a mass of $1.0 \text{ g}$ , so $M(\text{H}) = 1.0 \text{ g mol}^{-1}$
One mole of magnesium (Mg) atoms has a mass of $24.3 \text{ g}$ , so $M(\text{Mg}) = 24.3 \text{ g mol}^{-1}$
One mole of iron (Fe) atoms has a mass of $55.8 \text{ g}$ , so $M(\text{Fe}) = 55.8 \text{ g mol}^{-1}$

The image above shows equal numbers of atoms (equal moles) of different elements. Notice how their masses differ even though each sample contains the same number of atoms - this is because different elements have different molar masses.

Molar mass of compounds

For compounds, calculate the molar mass by adding together the relative atomic masses of all the atoms in the formula.

Examples:

Nitrogen dioxide ( $\text{NO}_2$ ): $M(\text{NO}_2) = 14.0 + (16.0 \times 2) = 46.0 \text{ g mol}^{-1}$
Sodium carbonate ( $\text{Na}_2\text{CO}_3$ ): $M(\text{Na}_2\text{CO}_3) = (23.0 \times 2) + 12.0 + (16.0 \times 3) = 106.0 \text{ g mol}^{-1}$

The importance of molar mass

Knowing the molar mass of a substance means that if you have a sample and know its mass, you can work out the number of moles present, and therefore the number of particles. This is fundamental to all chemical calculations involving amounts.

The key equation: $n = \frac{m}{M}$

Understanding the relationship

Amount of substance ( $n$ ), mass ( $m$ ), and molar mass ( $M$ ) are connected by a key equation:

$n = \frac{m}{M}$

Where:

$n$ = amount of substance in moles (mol)
$m$ = mass in grams (g)
$M$ = molar mass in grams per mole (g mol⁻¹)

This equation can be rearranged to find any of the three variables if you know the other two:

To find mass: $m = n \times M$
To find molar mass: $M = \frac{m}{n}$

The triangle method

A useful way to remember these rearrangements is the triangle method:

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Using the triangle method:

Place $m$ at the top, and $n$ and $M$ at the bottom. To find any variable, cover it up, and what remains shows you the calculation:

Cover $n$ : you get $\frac{m}{M}$ (so $n = \frac{m}{M}$ )
Cover $m$ : you get $n \times M$ (so $m = n \times M$ )
Cover $M$ : you get $\frac{m}{n}$ (so $M = \frac{m}{n}$ )

Make sure you're comfortable rearranging this equation - it's essential for almost all mole calculations in chemistry.

Worked examples

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Worked Example 1: Finding amount of substance from mass

Question: Calculate the amount of substance, in moles, in 96.0 g of carbon (C).

Solution: Use $n = \frac{m}{M}$ where $m = 96.0 \text{ g}$ and $M(\text{C}) = 12.0 \text{ g mol}^{-1}$

$n = \frac{96.0}{12.0} = 8.0 \text{ mol}$

Answer: 8.0 mol

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Worked Example 2: Finding mass from amount of substance

Question: Calculate the mass, in g, of 0.050 mol of nitrogen dioxide ( $\text{NO}_2$ ).

Solution: Step 1: Find the molar mass $M(\text{NO}_2) = 14.0 + (16.0 \times 2) = 46.0 \text{ g mol}^{-1}$

Step 2: Rearrange $n = \frac{m}{M}$ to give $m = n \times M$

Step 3: Calculate the mass $m = 0.050 \times 46.0 = 2.3 \text{ g}$

Answer: 2.3 g

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Worked Example 3: Finding molar mass from mass and amount

Question: Calculate the molar mass when 2.65 g contains 0.025 mol of a substance.

Solution: Step 1: Identify the known values We have $n = 0.025 \text{ mol}$ and $m = 2.65 \text{ g}$

Step 2: Rearrange the equation From $n = \frac{m}{M}$ , rearrange to find $M$ : $M = \frac{m}{n}$

Step 3: Calculate $M = \frac{2.65}{0.025} = 106.0 \text{ g mol}^{-1}$

Answer: 106.0 g mol⁻¹

Particles matter: atoms vs molecules

When working with moles, it's crucial to use the correct formula for the substance you're dealing with. The formula tells you what type of particle you're counting.

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Understanding the difference between atoms and molecules:

Consider hydrogen:

1 mol of H means 1 mole of hydrogen atoms (individual H atoms)
1 mol of H₂ means 1 mole of hydrogen molecules (H₂ molecules, each containing 2 H atoms)

These are different quantities! One mole of H₂ molecules contains twice as many hydrogen atoms as one mole of H atoms.

Always check whether you're working with:

Individual atoms (e.g., C, Mg, Fe)
Molecules (e.g., H₂, O₂, CO₂, H₂O)
Ions in ionic compounds (e.g., Na⁺, Cl⁻ in NaCl)

Using the unambiguous name or correct formula ensures clarity in your calculations and prevents errors.

Remember!

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Key Takeaways:

The mole is the unit for amount of substance; one mole contains $6.02 \times 10^{23}$ particles (Avogadro constant)
Molar mass is the mass of one mole of a substance in g mol⁻¹; for elements, it equals the relative atomic mass in grams
The key equation is $n = \frac{m}{M}$ , which you must be able to rearrange to find $m = n \times M$ or $M = \frac{m}{n}$
Always check whether you're working with atoms, molecules, or formula units - use the correct formula (e.g., H vs H₂)
Units matter: amount ( $n$ ) in mol, mass ( $m$ ) in g, molar mass ( $M$ ) in g mol⁻¹

Exam Focus Checklist:

✓ Can you define the mole and state the value of the Avogadro constant?

✓ Can you explain why the mass of one mole of atoms equals the relative atomic mass in grams?

✓ Can you calculate the molar mass of a compound from its formula?

✓ Can you confidently use and rearrange $n = \frac{m}{M}$ to solve problems?

✓ Can you distinguish between atoms and molecules when working with moles?

✓ Do you always include correct units in your calculations?

Amount of Substance and the Mole (OCR A-Level Chemistry A): Revision Notes