Atomic mass, relative atomic mass and average atomic mass
Atoms are too light to weigh, so we compare them with 1/12 of a carbon-12 atom. Most elements are isotope mixtures, so we use an average atomic mass.
Why we need a reference atom
One hydrogen atom weighs only about 1.67 × 10⁻²⁴ g. No balance can weigh something so light. So scientists compare every atom with one standard atom. Since 1961 the standard is carbon-12 (C-12). One atomic mass unit (amu) is 1/12 of the mass of one C-12 atom. Today it is also called the unified atomic mass unit, with the symbol u.
Relative atomic mass in simple words
- Relative atomic mass (RAM) tells how many times one atom is heavier than 1/12 of a C-12 atom.
- RAM = average mass of one atom of the element ÷ (1/12 × mass of one C-12 atom).
- It is a ratio of two masses, so it has no unit. When we write it with u, we call it the atomic mass.
- Common values: H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24, S = 32, Cl = 35.5, Ca = 40.
- Many values are not whole numbers because natural elements are mixtures of isotopes (atoms of one element with different masses).
Worked example: average atomic mass of chlorine
Chlorine has two isotopes: Cl-35 (abundance 75.77%) and Cl-37 (abundance 24.23%). Find the average atomic mass of chlorine.
- Formula: average atomic mass = (A₁ × p₁ + A₂ × p₂) ÷ 100, where A is the mass of an isotope and p is its percentage.
- Cl-35 part: 35 × 75.77 = 2651.95
- Cl-37 part: 37 × 24.23 = 896.51
- Add: 2651.95 + 896.51 = 3548.46
- Divide by 100: 3548.46 ÷ 100 = 35.48 (rounded to two decimal places)
Average atomic mass of chlorine = 35.48 u. Tables round it to 35.5.
Worked example: average atomic mass of magnesium
Natural magnesium has three isotopes: Mg-24 (79%), Mg-25 (10%) and Mg-26 (11%). Find its average atomic mass.
- Formula: average atomic mass = (A₁ × p₁ + A₂ × p₂ + A₃ × p₃) ÷ 100
- Mg-24 part: 24 × 79 = 1896
- Mg-25 part: 25 × 10 = 250
- Mg-26 part: 26 × 11 = 286
- Add: 1896 + 250 + 286 = 2432
- Divide by 100: 2432 ÷ 100 = 24.32
Average atomic mass of magnesium = 24.32 u. Tables round it to 24.3.
Salt makers in India add potassium iodate (KIO₃) to make iodised salt. They use atomic masses (K = 39, I = 127, O = 16) to work out how much to mix into each tonne of salt.
1 marks: “The reference atom used for atomic masses today is: (a) H-1 (b) O-16 (c) C-12 (d) N-14” (c) C-12. One amu is 1/12 of the mass of one C-12 atom.
2 marks: “What is relative atomic mass? Why is it written without a unit?” RAM = average mass of one atom of the element ÷ (1/12 × mass of one C-12 atom). It is a ratio of two masses, so the units cancel.
4 marks: “Lithium has two isotopes, Li-6 (7.5%) and Li-7 (92.5%). Calculate the average atomic mass of lithium.” Write the formula. (6 × 7.5 + 7 × 92.5) ÷ 100 = (45 + 647.5) ÷ 100 = 692.5 ÷ 100 = 6.925 u.
One-twelfth of carbon-twelve is the ruler for every atom.