Formula Mass of Ionic Compounds

Introduction

Sodium chloride, common salt, is not made of molecules. It is a giant lattice of sodium ions and chloride ions, with no separate little groups of atoms. So it makes no sense to talk about the mass of "a salt molecule". Chemists still need a relative mass for such substances, and they get it from the formula. This page introduces relative formula mass and calculates it for sodium chloride and calcium carbonate.

Core explanation

No molecules in ionic compounds. You have already seen that some substances, including ionic compounds such as sodium chloride, do not contain discrete molecules. A grain of salt is one enormous, regular array of Na⁺ and Cl⁻ ions in a 1 : 1 ratio.

The formula unit. The formula NaCl describes the ratio of ions, not a molecule. The smallest group matching the formula — one Na⁺ and one Cl⁻ — is called a formula unit . We calculate the relative mass of this formula unit.

Relative formula mass. The relative formula mass , also given the symbol Mr , is the sum of the relative atomic masses of all the atoms shown in the formula. It is calculated in exactly the same way as relative molecular mass. In fact, many courses use "relative formula mass" for every substance, whether molecular or ionic. Like Ar, it has no units.

Example 1: sodium chloride, NaCl. (Ar: Na 23, Cl 35.5)

Element Number Ar Total --- --- --- --- Na 1 23 23 Cl 1 35.5 35.5 Mr 58.5

Example 2: calcium carbonate, CaCO₃. (Ar: Ca 40, C 12, O 16) Calcium carbonate contains Ca²⁺ ions and carbonate ions, CO₃²⁻. The carbonate ion is a group of one carbon and three oxygen atoms carrying a charge.

Element Number Ar Total --- --- --- --- Ca 1 40 40 C 1 12 12 O 3 16 48 Mr 100

What about the electrons? Ions form when atoms gain or lose electrons. An electron's mass is only about 1/1840 of the atomic mass unit, so the mass change is far too small to matter. We simply use the Ar values of the atoms.

Other examples. Magnesium oxide, MgO: 24 + 16 = 40. Calcium chloride, CaCl₂: 40 + (2 × 35.5) = 111.

Step-by-step reasoning

To calculate the relative formula mass of an ionic compound:

1. Write the formula, keeping any polyatomic ions such as CO₃ together. 2. Count every atom of each element, including those inside the polyatomic ion. 3. Multiply each Ar by the number of atoms. 4. Add the totals. Ignore the charges and the electrons.

Visual explanation

Picture a chessboard-like pattern of large green chloride ions and smaller purple sodium ions extending in every direction. Draw a loop around any one sodium ion and one neighbouring chloride ion: that pair is one formula unit, worth 23 + 35.5 = 58.5 on the relative mass scale.

Real-world analogy

A tiled floor has no individual "floor units", but the tiler orders tiles by the repeating pattern: one white and one black tile per pattern. The formula unit is the repeating pattern of an ionic lattice.

Real-world example

Limestone, chalk and marble are mainly calcium carbonate, Mr 100. Its round-number formula mass makes it a favourite for calculations in the cement and lime industries, where limestone is heated to make quicklime, CaO (Mr 56), releasing carbon dioxide (Mr 44). Note that 56 + 44 = 100.

Why?

Why can we use the same symbol, Mr, for ionic and molecular substances? In both cases the number is found by adding Ar values for the atoms in the formula, and in both it compares a mass with one-twelfth of a carbon-12 atom. Only the physical meaning of "one formula" differs.

Common misconception

"NaCl has a molecular mass because it has a formula." A formula does not imply molecules. For ionic compounds, NaCl shows only the ratio of ions, so the correct term is relative formula mass.

Worked example

Question: Calculate the relative formula mass of potassium carbonate, K₂CO₃. (Ar: K 39, C 12, O 16)

Reasoning: K: 2 × 39 = 78. C: 1 × 12 = 12. O: 3 × 16 = 48. Total = 78 + 12 + 48 = 138.

Answer: Mr(K₂CO₃) = 138.

Quick check

1. Calculate the relative formula mass of magnesium oxide, MgO. (Ar: Mg 24, O 16) Answer: 24 + 16 = 40.

Exam focus

Use "relative formula mass" for ionic compounds. Remember to count all the atoms inside polyatomic ions such as CO₃²⁻ and to use Cl = 35.5 from the data sheet, giving NaCl = 58.5, not 58 or 59.

Advanced insight

Because electrons are so light, the mass of Na⁺ differs from that of a sodium atom by only about 0.002%. This is why tables list atomic masses but not ionic masses: for all chemical calculations the difference is negligible.

Summary

Ionic compounds form giant lattices, not molecules, so their formula shows a ratio of ions called a formula unit. The relative formula mass, Mr, is the sum of the Ar values of all atoms in the formula, with no units. NaCl has Mr 58.5 and CaCO₃ has Mr 100. The mass of electrons gained or lost is negligible.

Practice questions

1. Why is "relative molecular mass" not the correct term for sodium chloride? Answer: Sodium chloride is a giant ionic lattice with no discrete molecules; its formula shows only the ratio of ions. 2. Calculate the relative formula mass of calcium chloride, CaCl₂. (Ar: Ca 40, Cl 35.5) Answer: 40 + (2 × 35.5) = 40 + 71 = 111. 3. Calculate the relative formula mass of sodium carbonate, Na₂CO₃. (Ar: Na 23, C 12, O 16) Answer: (2 × 23) + 12 + (3 × 16) = 46 + 12 + 48 = 106. 4. Explain why we ignore electrons when calculating the formula mass of an ionic compound. Answer: An electron's mass is tiny, about 1/1840 of an atomic mass unit, so gaining or losing electrons makes a negligible difference.