Chemistry (9701) | Relative masses of atoms and molecules

AS & A Level Chemistry (9701) Study Notes

Chapter 2.1: Relative Masses of Atoms and Molecules

Welcome to stoichiometry! This chapter is absolutely fundamental because it teaches you how to count and weigh atoms and molecules—the essential building blocks of all chemical calculations.

Don't worry if measuring atoms sounds impossible. It is! Atoms are incredibly tiny. Instead of trying to weigh one atom directly, chemists use a system of relative masses, comparing everything back to one agreed-upon standard. Ready to tackle the standard? Let's go!

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1. The Universal Standard: Carbon-12

When you buy a bag of sugar, the weight is compared to a standard kilogram. In chemistry, we need a standard atom to compare all other atoms against.

Key Definition: Unified Atomic Mass Unit (u)

The standard reference atom chosen is the most common isotope of Carbon, Carbon-12.

Definition: The unified atomic mass unit (u) (sometimes called the Dalton, Da) is defined as exactly one twelfth (\(1/12\)) of the mass of a single atom of the carbon-12 isotope.

Think of it this way: You take one Carbon-12 atom and chop its mass into 12 equal slices. One slice is 1 u.
Therefore, the mass of one Carbon-12 atom is exactly 12 u.

Why Carbon-12? It's stable, abundant, and was historically useful for setting the standard scale.

2. Defining Relative Isotopic Mass

The first type of relative mass we define is for a single, specific type of atom (an isotope).

Definition: Relative Isotopic Mass

The relative isotopic mass is the mass of one specific isotope of an element compared to \(1/12\) of the mass of a carbon-12 atom.

This value is essentially equal to the mass number (nucleon number) of that isotope.

• Example: A single atom of Chlorine-35 has a relative isotopic mass of 35.0.
• Example: A single atom of Oxygen-16 has a relative isotopic mass of 16.0.

Crucial Point: Relative masses are dimensionless (they have no units, like g or kg) because they are a ratio—a comparison to the standard. They are just numbers.

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3. The Average Mass: Relative Atomic Mass (\(A_r\))

In nature, elements almost always exist as a mixture of several isotopes. For instance, Chlorine exists as 75% Chlorine-35 and 25% Chlorine-37.

If we weighed a natural sample of chlorine, it wouldn't weigh exactly 35 or 37. It would be an average. This average is the Relative Atomic Mass.

Definition: Relative Atomic Mass (\(A_r\))

The relative atomic mass (\(A_r\)) is the weighted average mass of all the isotopes of an element present in a natural sample, compared to \(1/12\) of the mass of a carbon-12 atom.

The word weighted is vital! This means that more abundant isotopes contribute more to the average mass than rare ones.

Step-by-Step: Calculating Relative Atomic Mass (\(A_r\))

This calculation is the most common application of this concept, often using data derived from mass spectrometry.

If an element X has isotopes \(I_1\), \(I_2\), ... with masses \(M_1\), \(M_2\), ... and corresponding natural abundances \(A_1\), \(A_2\), ... (expressed as percentages or fractions), the \(A_r\) is calculated using this formula:

\[A_r = \frac{(M_1 \times A_1) + (M_2 \times A_2) + \dots}{100}\]

(If abundances are given as percentages, divide by 100. If given as fractions, you do not need to divide by 100.)

Example: Copper exists as Copper-63 (69.2% abundance) and Copper-65 (30.8% abundance).
\[A_r(Cu) = \frac{(63.0 \times 69.2) + (65.0 \times 30.8)}{100}\]
\[A_r(Cu) = 63.6\]

Did you know? The \(A_r\) value is what you see on the Periodic Table! The number 35.5 for chlorine or 63.6 for copper reflects the natural mixture found on Earth.

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4. Relative Masses of Compounds

Atoms rarely exist alone; they bond together to form molecules or large lattices. We can calculate the mass of these compounds by adding up the \(A_r\) values of the constituent atoms.

Definition: Relative Molecular Mass (\(M_r\))

The relative molecular mass (\(M_r\)) is the sum of the relative atomic masses of all the atoms in a molecule, compared to \(1/12\) of the mass of a carbon-12 atom.

This term is used specifically for substances that exist as discrete, covalently bonded molecules (like \(\text{H}_2\text{O}\), \(\text{CO}_2\), \(\text{C}_6\text{H}_{12}\text{O}_6\)).

Calculation Example for Water (\(\text{H}_2\text{O}\)):
\(A_r(\text{H}) = 1.0\), \(A_r(\text{O}) = 16.0\).
\(M_r(\text{H}_2\text{O}) = (2 \times 1.0) + 16.0 = 18.0\)

Definition: Relative Formula Mass (\(F_r\))

The relative formula mass (\(F_r\)) is the sum of the relative atomic masses of the atoms in an ionic compound (or giant molecular structure), using the simplest formula (the formula unit), compared to \(1/12\) of the mass of a carbon-12 atom.

This term is generally used for ionic compounds (like \(\text{NaCl}\), \(\text{Mg}\text{O}\)) or giant structures (like \(\text{Si}\text{O}_2\)) which do not form discrete molecules.

Calculation Example for Sodium Chloride (\text{NaCl}):
\(A_r(\text{Na}) = 23.0\), \(A_r(\text{Cl}) = 35.5\).
\(F_r(\text{NaCl}) = 23.0 + 35.5 = 58.5\)

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Key Takeaway Summary (2.1)

• Standard: All relative masses are based on the mass of Carbon-12 being exactly 12 u.
• \(A_r\) (Relative Atomic Mass): The weighted average mass of a naturally occurring element. Use the Periodic Table value.
• Relative Isotopic Mass: The mass of a specific isotope (usually equal to its mass number).
• \(M_r\) (Relative Molecular Mass): Sum of \(A_r\) for a discrete molecule (covalent).
• \(F_r\) (Relative Formula Mass): Sum of \(A_r\) for a formula unit (ionic/giant structures).