Reading Relative Atomic Masses from the Periodic Table

Introduction

Every mole calculation starts by looking up relative atomic masses. It sounds easy, but students regularly lose marks by reading the wrong number from a periodic table box or by rounding too much. This page shows how to find Aᵣ values quickly and how to decide how precise they need to be.

Core explanation

Two numbers in each box. A periodic table box usually shows the element's symbol, its name and two numbers. One is the atomic number, Z, which is always a whole number and increases by one across the table. The other is the relative atomic mass, Aᵣ, which is usually not a whole number and is always the larger of the two (except for hydrogen, where both are about 1). Different tables place these numbers in different positions, so check the key printed on your table rather than relying on "top" or "bottom".

Values used in this unit. Unless a question gives other values, use these rounded Aᵣ values:

Element Aᵣ Element Aᵣ --- --- --- --- H 1.0 S 32.1 C 12.0 Cl 35.5 N 14.0 K 39.1 O 16.0 Ca 40.1 Na 23.0 Fe 55.8 Mg 24.3 Cu 63.5 Al 27.0 Zn 65.4

How precise? Most school calculations use Aᵣ values to one decimal place, which is precise enough for three significant figure answers. Some examination tables give whole numbers for most elements (such as Mg = 24) but keep 35.5 for chlorine and 63.5 for copper, because rounding these would cause noticeable errors. The rule is simple: use the values on the data sheet you are given, exactly as printed.

Never round chlorine to 36. Rounding 35.5 up to 36 changes the Mᵣ of CaCl₂ from 111.1 to 112.1 and the Mᵣ of Cl₂ from 71.0 to 72.0. Errors like this spread through every later step.

Unusual boxes. Some elements, especially radioactive ones such as technetium, have no stable isotopes and no fixed natural composition. Their box shows a whole number in square brackets, such as [98], which is the mass number of one of its longest-lived isotopes, not a true Aᵣ.

Order oddities. The table is arranged by atomic number, not by mass. Argon (Aᵣ = 39.9) comes before potassium (Aᵣ = 39.1), and tellurium (127.6) comes before iodine (126.9). If you see a mass that seems "out of order", you have not misread the table.

Step-by-step reasoning

1. Find the element's symbol in the table. 2. Use the key to identify which number is Aᵣ; it is the larger one and usually has a decimal. 3. Copy it at the precision given on the data sheet. 4. Do not round further unless the question tells you to. 5. Write the values you used in your working so the examiner can follow them.

Visual explanation

Imagine the box for sodium: a large symbol "Na" in the centre, the word "sodium" underneath, the small whole number 11 (the atomic number) in one corner and 23.0 (the relative atomic mass) in another. Highlighting Aᵣ in one colour on your own table can help you pick it out quickly.

Real-world analogy

A price list might show a product code and a price next to each item. If you copy the code into the bill instead of the price, the total will be wrong even though the arithmetic is perfect. Reading the right number from the periodic table is the same kind of care.

Real-world example

Pharmaceutical companies calculate the masses of ingredients in tablets using Aᵣ values given to four or five significant figures, because a small error in every tablet of a large batch would matter. School calculations need less precision, but the principle of using the right values is the same.

Why?

Why are some Aᵣ values given more precisely than others? An element's Aᵣ is only as reliable as the measurements of its isotope abundances. For elements with one stable isotope, such as sodium or aluminium, Aᵣ is known very precisely; for elements whose abundances vary in nature, the value is less certain.

Common misconception

"The bigger number in the box is the number of protons." The number of protons is the atomic number, the smaller whole number. The larger number is the average mass of the atoms, which includes neutrons as well as protons.

Worked example

Question: A data sheet gives Mg = 24, Cl = 35.5. A student uses Mg = 24 and Cl = 36 to find the Mᵣ of MgCl₂. What answer does the student get, and what should it be?

Reasoning: Student: 24 + 2 × 36 = 96. Correct: 24 + 2 × 35.5 = 24 + 71 = 95.

Answer: The student gets 96; the correct value, using the data sheet, is 95.

Quick check

1. Which is the relative atomic mass in a box showing 26 and 55.8? Answer: 55.8; 26 is the atomic number of iron.

Exam focus

Use only the Aᵣ values from the examination data sheet, even if you remember more precise ones. Quote chlorine as 35.5 and copper as 63.5. Show the values in your working, because a wrong Aᵣ with correct method can still earn method marks.

Advanced insight

IUPAC reviews atomic masses every few years as measurements improve. For elements such as boron, lithium and oxygen, the value you see may be an "abridged" or "conventional" value chosen to cover most natural samples. For very accurate work, chemists use the full values with their stated uncertainties.

Summary

Each periodic table box shows the atomic number (a whole number) and the relative atomic mass (usually larger, often with a decimal). Use the Aᵣ values exactly as given on the data sheet, typically to one decimal place, and never round chlorine to 36. The table is ordered by atomic number, so masses are occasionally out of sequence.

Practice questions

1. State the Aᵣ values of oxygen, sodium and chlorine used in this unit. Answer: O = 16.0, Na = 23.0, Cl = 35.5. 2. Explain why argon appears before potassium even though its Aᵣ is larger. Answer: The periodic table is ordered by atomic number. Argon has 18 protons and potassium has 19, so argon comes first despite being heavier on average. 3. A box shows [98] for technetium. What does the square bracket mean? Answer: Technetium has no stable isotopes, so the number is the mass number of a long-lived isotope rather than a weighted average Aᵣ. 4. Using Ca = 40.1 and Cl = 35.5, find the Mᵣ of CaCl₂. What error results from using Cl = 36? Answer: 40.1 + 71.0 = 111.1. Using 36 gives 112.1, which is 1.0 too high.