Worked examples
Three examples. All three use the same formula — only what you are given changes.
Example 1 — two masses given
Problem
The mass of an atom of potassium (K) is 6.476 × 10-23 g, and the mass of a 12C atom is 1.99 × 10-23 g. Find the relative atomic mass of potassium.
Solution
Ar = mass of one potassium atom ÷ (1/12 × mass of one 12C atom)
= (6.476 × 10-23 g) ÷ (1/12 × 1.99 × 10-23 g)
= 39
Example 2 — a ratio given, not a mass
Problem
The mass of an atom of an element A is eight times the mass of an atom of the 12C isotope. Find the relative atomic mass of A.
Solution
mass of one atom of A = mass of one 12C atom × 8
∴ Ar = (mass of one 12C atom × 8) ÷ (1/12 × mass of one 12C atom)
= 8 × 12
= 96
The mass of the 12C atom is on the top and the bottom, so it cancels. That is why an answer comes out without any value in grams being given — no real masses are needed here at all.
Example 3 — the unit given directly
Problem
The mass of an atom of sodium is 3.819 × 10-23 g. The value of the atomic mass unit is 1.67 × 10-24 g. Find the relative atomic mass of sodium.
Solution
Ar = mass of one sodium atom ÷ atomic mass unit
= (3.819 × 10-23 g) ÷ (1.67 × 10-24 g)
= 23
There was no need to divide by twelve here — the value of the unit was given already. Reading what you have been given and picking the matching form of the formula saves time.
Remember the method
What goes on the bottom is a twelfth of the mass of one atom. Dividing by the whole mass of a 12C atom is the common slip, and it makes the answer a twelfth of what it should be.