Chemistry 1.43 - Formula mass and composition

From a formula to relative formula mass

A chemical formula is a counting statement. In $\ce{CaCl2}$, the formula ratio is one calcium ion for every two chloride ions. Formula-mass calculations add the relative atomic masses for those element counts. A small subscript applies only to the symbol or bracket immediately before it; if there is no written subscript, the count is one.

Brackets matter. In $\ce{Ca(NO3)2}$, the outside $2$ multiplies everything inside the brackets, so the formula contains:

• 1 calcium atom;
• 2 nitrogen atoms;
• 6 oxygen atoms.

The relative atomic mass, $A_r$, compares the average mass of an atom of an element with a fixed reference. The relative formula mass, $M_r$, combines those relative masses for every atom shown in one formula.

Because $A_r$ and $M_r$ are relative ratios, they have no unit. A value such as $M_r = 164$ is not $164 \,\mathrm{g}$. The term relative formula mass works for both ionic and covalent substances. For a molecule, the same calculation may be called its relative molecular mass.

Worked example: calcium nitrate

Calculate the $M_r$ of $\ce{Ca(NO3)2}$ using $A_r(\ce{Ca}) = 40$, $A_r(\ce{N}) = 14$ and $A_r(\ce{O}) = 16$.

1. Expand the atom counts: 1 Ca, 2 N and 6 O.
2. Multiply each count by its $A_r$:
   • calcium: $1 \times 40 = 40$
   • nitrogen: $2 \times 14 = 28$
   • oxygen: $6 \times 16 = 96$
3. Add all contributions:

$M_r = 40 + 28 + 96 = 164$

The final answer is $164$, with no unit.

Sense-check: the six oxygen atoms alone contribute 96, so a total below 96 would be impossible. The bracket multiplier has affected both N and O; it has not multiplied Ca.

A large number written in front of a formula, such as the $2$ in $\ce{2H2O}$, counts two whole molecules or formula units. It does not change the $M_r$ of water itself. Only the atom counts inside $\ce{H2O}$ are used for the $M_r$ of water.