Relative formula mass

AQA·Chemistry (Combined Science)·5.3.1.2·Trilogy — Foundation

Relative formula mass in balanced equations

A balanced chemical equation shows the same number of each type of atom on both sides. Since atoms are rearranged rather than created or destroyed, the total mass of the reactants equals the total mass of the products.

This can be checked using relative formula masses. The relative formula mass, $$M_r$$, of a substance is the sum of the relative atomic masses of all the atoms in its formula. To find the total relative mass represented on one side of an equation, multiply each substance’s $$M_r$$ by its coefficient—the number in front of its formula—then add the results. If there is no coefficient, it is 1.

Comparing relative masses in an equation

Consider the balanced equation for the formation of water:

2 HX2+OX2→2 HX2O\ce{2H2 + O2 -> 2H2O}

Using relative atomic masses of 1 for hydrogen and 16 for oxygen, the $$M_r$$ values are 2 for $$\ce{H2}$$, 32 for $$\ce{O2}$$ and 18 for $$\ce{H2O}$$. The coefficients show that the relative masses of two units of $$\ce{H2}$$ and two units of $$\ce{H2O}$$ must be included.

For the reactants, the total is:

(2×2)+(1×32)=36(2 \times 2) + (1 \times 32) = 36

For the product, the total is:

2×18=362 \times 18 = 36

The totals match because each side contains four hydrogen atoms and two oxygen atoms. The equation therefore expresses conservation of mass using relative masses and the quantities shown by its coefficients.

Percentage by mass in a compound

The percentage by mass of an element tells us what percentage of a compound’s mass comes from that element. It compares the element’s total contribution to the compound’s relative formula mass with the relative formula mass of the whole compound.

To find the element’s contribution, multiply its relative atomic mass, $$A_r$$, by the number of its atoms in the formula. The compound’s relative formula mass, $$M_r$$, is the sum of the relative atomic masses of all the atoms in its formula.

Percentage by mass of element=Number of atoms of element×Ar of elementMr of compound×100\text{Percentage by mass of element} = \frac{\text{Number of atoms of element} \times A_r\text{ of element}}{M_r\text{ of compound}} \times 100

Percentage by mass in water

Water has the formula $$\ce{H2O}$$. Using $$A_r = 1$$ for hydrogen and $$A_r = 16$$ for oxygen, its relative formula mass is $$M_r = (2 \times 1) + 16 = 18$$.

There are two hydrogen atoms in the formula, so hydrogen contributes $$2 \times 1 = 2$$ to the total relative formula mass. Its percentage by mass is:

218×100=11.1% (to one decimal place)\frac{2}{18} \times 100 = 11.1\%\text{ (to one decimal place)}

Hydrogen therefore makes up approximately 11.1% of the mass of water. The two hydrogen atoms must both be counted; using the relative atomic mass of only one would underestimate hydrogen’s contribution.

Relative formula mass

A chemical formula shows which elements are present in a compound and how many atoms of each element are in one formula unit. The relative formula mass, written $$M_r$$, is the total of the relative atomic masses of all those atoms.

To calculate $$M_r$$, identify each element in the formula and find its relative atomic mass, $$A_r$$. Multiply each $$A_r$$ by the number of atoms of that element, then add the contributions together. A small number after an element symbol shows how many atoms of that element are present; if there is no number, there is one atom.

Relative formula mass of water

The formula $$\ce{H2O}$$ contains two hydrogen atoms and one oxygen atom. Using $$A_r = 1$$ for hydrogen and $$A_r = 16$$ for oxygen:

Mr(HX2O)=(2×1)+(1×16)=18M_r(\ce{H2O}) = (2 \times 1) + (1 \times 16) = 18

The $$M_r$$ of water is therefore 18. This is a relative value, not a mass in grams: it compares the mass of one formula unit with the atomic mass scale, based on one-twelfth of the mass of a carbon-12 atom.