Structure 1.4.2—Masses of atoms are compared on a scale relative to 12C and are expressed as

relative atomic mass Ar and relative formula mass Mr.

**What You’ll Learn:**

- Determine relative formula masses Mr from relative atomic masses Ar.
- Relative atomic mass and relative formula mass have no units.
- The values of relative atomic masses given to two decimal places in the data booklet should be used in calculations.

**Keywords**

IBDP chemistry, mole, mol, amount of substance, elementary entities, atoms, molecules, ions, electrons, carbon-12, Avogadro’s constant, N_A, 6.022 x 10^23 mol^-1, amount of substance, n, number of entities, formula, oxygen atoms, water molecules, data booklet, units

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**Syllabus Links**

Structure 3.1—Atoms increase in mass as their position descends in the periodic table. What properties might be related to this trend?

The main objectives of this section are to understand the concepts of relative atomic mass (A_{r}) and relative formula mass (M_{r}), and to be able to perform calculations using these values.

## Relative atomic mass (A_{r})

Atomic mass, also known as atomic weight or standard atomic weight, is a term used to describe the average mass of atoms of a specific element. It is typically measured in atomic mass units (amu) or unified atomic mass units (u), where 1 atomic mass unit is defined as one twelfth (1/12) of the mass of a carbon-12 (¹²C) isotope.

Atomic mass is derived from a weighted average of the isotopes of a particular element, taking into account their natural abundance. Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons, resulting in different atomic masses.

Here’s how atomic mass is calculated:

- Identify the isotopes of the element and their respective atomic masses. The atomic mass of an isotope is approximately equal to the sum of its protons and neutrons.
- Determine the natural abundance of each isotope. Natural abundance is the percentage or fraction of each isotope found in nature.
- Multiply the atomic mass of each isotope by its natural abundance (expressed as a decimal).
- Sum the products obtained in step 3 to get the atomic mass of the element.

For example, let’s calculate the atomic mass of chlorine (Cl). Chlorine has two main isotopes: chlorine-35 (³⁵Cl) and chlorine-37 (³⁷Cl).

- The atomic masses of the isotopes are:
- ³⁵Cl: 34.97 u
- ³⁷Cl: 36.97 u

- The natural abundances of the isotopes are:
- ³⁵Cl: 75.78% (0.7578 as a decimal)
- ³⁷Cl: 24.22% (0.2422 as a decimal)

- Multiply the atomic mass of each isotope by its natural abundance:
- ³⁵Cl: 34.97 u × 0.7578 = 26.50 u
- ³⁷Cl: 36.97 u × 0.2422 = 8.96 u

- Sum the products to get the atomic mass of chlorine:
- Atomic mass of Cl = 26.50 u + 8.96 u = 35.46 u

So, the atomic mass of chlorine is approximately 35.46 u.

## Relative formula mass (Mr)

Relative formula mass (Mr) is a similar concept but is used for compounds. It is the sum of the relative atomic masses of all the atoms in a chemical formula. Like relative atomic mass, relative formula mass is a dimensionless quantity and has no units.

To determine the relative formula mass (M_{r}) of a compound, you need to add up the relative atomic masses (A_{r}) of all the elements present in the compound. This requires you to be familiar with the periodic table and the relative atomic masses of elements.

When performing calculations involving relative atomic masses and relative formula masses, use the values provided in the IBDP Chemistry data booklet, which are given to two decimal places. This ensures consistency in calculations and answers.

For example, consider the molecule H_{2}O (water). To calculate the relative formula mass (M_{r}) of water, you would use the relative atomic masses (A_{r}) of hydrogen (H) and oxygen (O) from the data booklet:

- Hydrogen (H) has a relative atomic mass of 1.01.
- Oxygen (O) has a relative atomic mass of 16.00.

The formula for water is H_{2}O, so there are two hydrogen atoms and one oxygen atom:

M_{r} (H_{2}O) = (2 × A_{r} of H) + (1 × A_{r} of O) = (2 × 1.01) + (1 × 16.00) = 18.02

Thus, the relative formula mass of water is 18.02.

Questions

- What is the difference between relative atomic mass (A
_{r}) and relative formula mass (M_{r})? - How is atomic mass defined in terms of atomic mass units (amu)?
- What is the significance of carbon-12 (¹²C) in defining atomic mass units?
- How does the natural abundance of isotopes affect the calculation of atomic mass?
- What are isotopes and how do they contribute to the atomic mass of an element?
- Describe the steps to calculate the atomic mass of an element.
- Explain the concept of relative formula mass and its importance in chemistry.
- How do you calculate the relative formula mass (M
_{r}) of a compound? - When performing calculations involving relative atomic masses and relative formula masses, why should you use the values provided in the IBDP Chemistry data booklet?
- Calculate the relative formula mass (M
_{r}) of ammonia (NH₃) using the relative atomic masses of nitrogen (N) and hydrogen (H) from the data booklet.