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# Formula Mass

17th Jul 2019 @ 22 min read

Physical Chemistry

The formula mass is often confused with the molar mass or the molecular mass, but it differs from both. As the name suggests, it has some relation with the formula of a molecule. The formula mass is a mass calculated using the formula. It is determined by adding the average atomic masses of the atoms present in a molecule.

## Definition

It is the sum of the average atomic masses of the atoms in the formula of a compound. Let take an example to make it clearer, the formula of anhydrous calcium sulphate is CaSO4. We can calculate the formula mass by adding the average atomic mass of each atom present in the formula of a compound.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) Ca 1 40.08 40.08 S 1 32.06 32.06 O 4 16.00 64.00 Formula Mass of CaSO4 136.14

As you can see from the above table the formula mass of CaSO4 is 136 u. If you have noticed, this is the same way we calculate the molecular mass of a molecule. But there is some difference, which is explained later in this article.

## Units

Since it is calculated from the average atomic mass, it has the same unit of the average atomic mass. It is expressed in the unified mass unit or the dalton or the atomic mass unit. The symbol for the unit is u or amu.

## Relative Formula Mass

The relative formula mass (aka the formula weight) is the sum of the atomic weights (not average atomic masses) of the atoms in the formula of a compound.

It, unlike the formula mass, is a dimensionless quantity. It does not have any unit. Both the quantities have the same numerical value, they only differ in the unit. Thus, the relative formula mass of CaSO4 is 136.14, not 136.14 u.

Note: The relative atomic mass and the atomic weight are synonymous of one another. So, we can use the relative atomic mass instead of the atomic weight in the above definition.

## Difference between Molecular Mass and Formula Mass

The molecular mass is the mass of a molecule. It is estimated by adding the average atomic masses of atoms present in a molecule. The molecular mass is the same as the formula mass in some cases while in others not.

To calculate the molecule mass, we need to have a discrete molecule, which is not always a case. For example, ionic compounds like sodium chloride (NaCl), magnesium oxide (MgO), iron sulphate (FeSO4) exist in large crystal lattices. They do not have any definite molecule form. In ionic compounds, there are positively-charged cations and negatively-charged anions. These ions are arranged to form various crystal structures like monoclinic, tetragonal, orthorhombic, cubic. Thus, the concept of the molecular mass itself falls. This is where the formula mass comes into play. Instead of calculating the molecular mass, which is not possible for such compounds, we calculate the formula mass. Figure 1: Different Crystal Lattices (on the top) and Sodium Chloride Structure (on the bottom)

As we can see from the above figure sodium chloride does not exist as a discrete entity. The chemical formula of sodium chlorine is NaCl, but in the above figure, one sodium ion is surrounded by six chloride ions, which does not represent its formula. Hence, the concept of the molecular formula is out of the picture.

The difference between the molecular mass and the formula mass perishes, in case of covalent compounds. In most covalent compounds, molecules exist as a discrete entity. So, the molecular mass and the formula mass are the same. Examples of covalent compounds are methane (CH4), ethanol (C2H6O), chloroform (CHCl3), glucose (C6H12O6). Figure 2: Examples of Covalent Compounds (Covalent Compounds, unlike ionic compounds, exist as a discrete entity.)

## Examples and Calculations

To calculate the formula mass of any compound, we only require its formula and the average atomic mass of its elements. The average atomic mass of any element can be found from the periodic table. The below mentions some examples.

### Example 1: To Determined Formula Mass of Glucose

Glucose is one of the important monosaccharides and the main source of energy in all organisms. It exists in both a straight-chain as well as a ring form.

The molecular formula of glucose is C6H12O6. Figure 3: Glucose in Straight-Chain (on the left) and in Ring form (on the right)

The formula mass of glucose is calculated in the below table.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) C 6 12.01 72.06 H 12 1.01 12.12 O 6 16.00 96.00 Formula Mass of C6H12H6 180.18

The formula mass of glucose is 180.18 u and its relative formula mass is 180.18.

### Example 2: To Determined Formula Mass of Paracetamol

Paracetamol is also known as acetaminophen. It is widely known as a pain reliever. Other uses of paracetamol are reducing fever, headache, lower back pain, dental pain.

The molecular formula of paracetamol is C8H9NO2.

The formula mass of paracetamol is calculated in the below table.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) C 8 12.01 96.08 H 9 1.01 9.09 N 1 14.01 14.01 O 2 16.00 32.00 Formula Mass of C6H12H6 151.18

The formula mass of paracetamol is 151.18 u and its relative formula mass is 151.18.

### Example 3: To Determined Formula Mass of Sebacic Acid

Sebacic acid is a dicarboxylic acid with the molecular formula C10H18O4. It is used as a monomer in the production of nylon-610, plasticizers, hydraulic fluids etc. Figure 5: Structure of Sebacic Acid with Two Carboxylic Acids at Each End of Carbon Chain

The formula mass of sebacic acid is calculated in the below table.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) (C) 10 12.01 120.1 (H) 18 1.01 18.18 (O) 4 16.00 64.00 Formula Mass of (C10H18O4) 202.3

The formula mass of sebacic acid is 202.3 u and its relative formula mass is 202.3.

### Example 4: To Determined Formula Mass of Sodium Chloride

Sodium chlorine, unlike in the above examples, is an ionic compound. It does not have a discrete molecule. It consists of positively-charged sodium ions surrounded by negatively-charged chloride ions. Its chemical formula is (NaCl).

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) Na 1 22.99 22.99 Cl 1 35.45 35.45 Formula Mass of (NaCl) 58.44

The formula mass of sodium chloride is (58.44 u) and its relative formula mass is 58.44.

### Example 5: To Determined Formula Mass of Aluminium Sulphate

Aluminium sulphate is a water-soluble chemical compound with the chemical formula Al2(SO4)3. It is used as a coagulating agent in the purification of water. Its anhydrous form consists of two aluminium ions and three sulphate groups.

The formula mass of aluminium sulphate is calculated in the below table.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) Al 2 26.98 53.96 S 3 32.07 96.21 O 12 16.00 192.0 Formula Mass of Al2(SO4)3 342.17

The formula mass of aluminium sulphate is 342.17 u and its relative formula mass is 342.17.

### Example 5: To Determined Formula Mass of Copper Sulphate Pentahydrate

Copper sulphate is an ionic salt of copper and sulphuric acid. Its most common form is copper sulphate pentahydrate having chemical formula CuSO4·5H2O. The appearance of copper sulphate hydrates is bright blue in colour.

The formula mass of copper sulphate is calculated in the below table.

 Element Number of Atoms Average Atomic Mass (u) Subtotal (u) Cu 1 63.55 63.55 S 1 32.07 32.07 H 10 1.01 10.1 O 9 16.00 144.0 Formula Mass of CuSO4·5H2O 249.7

The formula mass of copper sulphate is 249.7 u and its relative formula mass is 249.7.

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