Molecular Mass and Formula Mass

In the previous topic, you learned how to express the mass of a single atom using the unified mass unit. But most substances around you are not lone atoms. Water is made of two hydrogen atoms bonded to one oxygen atom, methane has a carbon atom surrounded by four hydrogens, and glucose is built from six carbons, twelve hydrogens, and six oxygens. So how do you find the mass of an entire molecule? That is where molecular mass comes in.

Adding Up the Atoms: What Molecular Mass Means

The idea is simple: take every atom in a molecule, look up its atomic mass, and add them all together. The result is the molecular mass (the total mass of one molecule, expressed in unified mass units, u).

More precisely, you multiply the atomic mass of each element by the number of its atoms in the molecular formula, and then sum all the products.

$\text{Molecular mass} = \sum (\text{atomic mass of element} \times \text{number of its atoms})$

Let us see this in action with two familiar molecules.

Methane ($CH_4$)

Methane has one carbon atom and four hydrogen atoms. Using atomic masses from the periodic table:

Step 1: Carbon’s contribution = $1 \times 12.011 \text{ u} = 12.011 \text{ u}$

Step 2: Hydrogen’s contribution = $4 \times 1.008 \text{ u} = 4.032 \text{ u}$

Step 3: Add them up:

$\text{Molecular mass of } CH_4 = 12.011 \text{ u} + 4.032 \text{ u} = 16.043 \text{ u}$

Water ($H_2O$)

Water has two hydrogen atoms and one oxygen atom:

Step 1: Hydrogen’s contribution = $2 \times 1.008 \text{ u} = 2.016 \text{ u}$

Step 2: Oxygen’s contribution = $1 \times 16.00 \text{ u} = 16.00 \text{ u}$

Step 3: Add them up:

$\text{Molecular mass of } H_2O = 2.016 \text{ u} + 16.00 \text{ u} = 18.02 \text{ u}$

The process is the same regardless of how large or complex the molecule is. Count the atoms, multiply by their atomic masses, and sum.

When There Are No Molecules: The Concept of Formula Mass

Not every substance is made of molecules. Consider sodium chloride (common table salt). In the solid state, sodium chloride does not contain separate $NaCl$ “molecules” floating around. Instead, positively charged sodium ions ($Na^+$) and negatively charged chloride ions ($Cl^-$) are packed together in a repeating three-dimensional pattern called a crystal lattice (an orderly, repeating arrangement of ions or atoms in three dimensions).

Fig 1.10: Packing of $Na^+$ and $Cl^-$ ions in sodium chloride

In this lattice, every $Na^+$ ion is surrounded by six $Cl^-$ ions, and every $Cl^-$ ion is surrounded by six $Na^+$ ions. There is no point where you can draw a boundary around one sodium and one chlorine and call that pair “a molecule.” The entire crystal is one continuous structure.

Because there is no discrete molecule, the term “molecular mass” does not quite fit. Instead, chemists use formula mass: the sum of atomic masses of all atoms appearing in one formula unit (the simplest ratio of ions in the compound, as written in its chemical formula).

The calculation itself works exactly the same way as molecular mass. For sodium chloride:

$\text{Formula mass of } NaCl = \text{atomic mass of Na} + \text{atomic mass of Cl}$

$= 23.0 \text{ u} + 35.5 \text{ u} = 58.5 \text{ u}$

When to Use Which Term

The distinction is about the type of substance, not the calculation method:

Type of substance	Term used	Examples
Covalent compounds that exist as discrete molecules	Molecular mass	$H_2O$, $CH_4$, $CO_2$, $C_6H_{12}O_6$
Ionic compounds arranged as extended lattices	Formula mass	$NaCl$, $CaCl_2$, $MgO$, $K_2SO_4$

Both are computed the same way: sum up the atomic masses for all atoms in the formula. The naming just reflects whether the formula represents an actual molecule or merely the simplest ion ratio.

Worked Example: Molecular Mass of Glucose ($C_6H_{12}O_6$)

Glucose is a larger molecule, so the calculation involves more terms. The approach stays identical.

Problem: Calculate the molecular mass of glucose ($C_6H_{12}O_6$).

Step 1: Identify the atoms and their counts from the formula:

• Carbon (C): 6 atoms
• Hydrogen (H): 12 atoms
• Oxygen (O): 6 atoms

Step 2: Look up each element’s atomic mass:

• Carbon: 12.011 u
• Hydrogen: 1.008 u
• Oxygen: 16.00 u

Step 3: Multiply and sum:

$\text{Carbon's contribution} = 6 \times 12.011 \text{ u} = 72.066 \text{ u}$

$\text{Hydrogen's contribution} = 12 \times 1.008 \text{ u} = 12.096 \text{ u}$

$\text{Oxygen's contribution} = 6 \times 16.00 \text{ u} = 96.00 \text{ u}$

Step 4: Add all contributions:

$\text{Molecular mass of } C_6H_{12}O_6 = 72.066 + 12.096 + 96.00 = 180.162 \text{ u}$

So one molecule of glucose has a mass of 180.162 u. Notice that oxygen contributes the largest share (96.00 u out of 180.162 u), even though carbon is the heavier individual atom, simply because there are six oxygens each weighing 16 u.