Relative formula mass adds up every atom the formula shows
Definition
Relative formula mass
The sum of the relative atomic masses of all the atoms shown in the formula of a substance, given the symbol Mr.
Definition
Relative atomic mass
The weighted mean mass of an element's atoms, taking the abundance of each isotope into account, compared with one-twelfth of the mass of a carbon-12 atom.
- Read the formula and note how many atoms of each element it contains.
- Multiply each element's ArA_rAr by the number of its atoms, then add the results together.
- A symbol with no subscript stands for one atom.
- A number outside a bracket multiplies every atom inside that bracket.
- MrM_rMr carries no unit, because it compares one mass with another.
- Take the ArA_rAr values from the periodic table, decimals included, such as 35.535.535.5 for chlorine.
Example
- H2O\text{H}_2\text{O}H2O: Mr=(2×1)+16=18M_r = (2 \times 1) + 16 = 18Mr=(2×1)+16=18.
- CaCO3\text{CaCO}_3CaCO3: Mr=40+12+(3×16)=100M_r = 40 + 12 + (3 \times 16) = 100Mr=40+12+(3×16)=100.
- Ca(OH)2\text{Ca(OH)}_2Ca(OH)2: Mr=40+2×(16+1)=74M_r = 40 + 2 \times (16 + 1) = 74Mr=40+2×(16+1)=74.
Percentage by mass compares one element with the whole compound
- The percentage by mass of an element is the share of a compound's total mass that the element contributes.
- Find the total ArA_rAr of that element in the formula, which is its ArA_rAr multiplied by its number of atoms.
- Divide that by the MrM_rMr of the whole compound, then multiply by 100100100: percentage by mass=total Ar of the elementMr of the compound×100\text{percentage by mass} = \frac{\text{total } A_r \text{ of the element}}{M_r \text{ of the compound}} \times 100percentage by mass=Mr of the compoundtotal Ar of the element×100
- Repeating the calculation for another element changes only the numerator.
- The percentages of every element in a compound add to 100100100, apart from small rounding differences.
Common Mistake
- The denominator is the whole compound's MrM_rMr, never the ArA_rAr of the named element.
- Every atom counts, so the 333 in CO3\text{CO}_3CO3 multiplies oxygen's ArA_rAr before anything else happens.
A worked percentage: oxygen in calcium carbonate
- The formula is CaCO3\text{CaCO}_3CaCO3, with ArA_rAr values of 404040 for calcium, 121212 for carbon and 161616 for oxygen.
- First find the relative formula mass of the compound: Mr=40+12+(3×16)=100M_r = 40 + 12 + (3 \times 16) = 100Mr=40+12+(3×16)=100
- Then find the total contribution of oxygen in the formula: 3×16=483 \times 16 = 483×16=48
- Divide by the MrM_rMr and multiply by 100100100 to reach the percentage: 48100×100=48%\frac{48}{100} \times 100 = 48\%10048×100=48%
- Oxygen makes up 48%48\%48% of the mass of calcium carbonate.
Note
- A percentage lands between 000 and 100100100, and one above 100100100 means the denominator is wrong.
- Rounding happens once, at the end, so extra figures are carried through the working.
Where these calculations usually go wrong
- Using the atomic number instead of the relative atomic mass changes every figure in the answer.
- Ignoring a bracket subscript undercounts the atoms inside it.
- Leaving a unit on MrM_rMr is wrong, and so is leaving the %\%% sign off a percentage.
- Checking that the formula matches the compound named catches an error before the arithmetic starts.
- Adding the percentages of all the elements gives a final check close to 100100100.
Self review
- What does the relative formula mass of a compound count?
- What is the MrM_rMr of Ca(OH)2\text{Ca(OH)}_2Ca(OH)2?
- Which value goes on the bottom of a percentage by mass calculation?
- Why does MrM_rMr carry no unit?
- What is the percentage by mass of oxygen in H2O\text{H}_2\text{O}H2O?
