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What the symbols, the subscripts and the brackets in a chemical formula actually count.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to read any chemical formula as a count of atoms — including ones with brackets, where the subscript outside multiplies everything inside — and say how many atoms of each element, and how many altogether, one formula unit contains. You will also be able to say what a number written in front of a formula does, which is a different job from a subscript and the thing the next lesson rests on.
You know that matter is made of atoms, that each element has a symbol, and that a compound is made of more than one element joined together. What this lesson adds is how to read the shorthand: a formula is not a name, it is a count, and every number in it is doing a specific job.
| Term | What it means |
|---|---|
| Formula | Which elements a substance contains and how many atoms of each. |
| Formula unit | The smallest group the formula describes. |
| Subscript | The small number after a symbol or a bracket. |
| Coefficient | A full-size number in front of a whole formula. |
| Relative atomic mass | How heavy an atom of an element is compared with the standard scale. |
Read a formula left to right, and take each number as it comes.
So $\mathrm{Mg(OH)_2}$ is one magnesium, two oxygens and two hydrogens: five atoms in a formula unit.
That is the whole rule, and it never changes. Every later lesson in this course is this reading followed by some arithmetic — a molar mass adds the masses up, a percentage composition divides one of them by the total, and balancing an equation compares two of these counts.
Another way: picture
Think of the bracket as a box and the subscript outside it as how many boxes there are. $\mathrm{Ca(NO_3)_2}$ is one calcium plus two identical boxes, and each box holds one nitrogen and three oxygens: two nitrogens and six oxygens in all.
Another way: steps
To count an element in any formula:
Read the symbols left to right. Each capital letter begins a new element; a lowercase letter after it belongs to the same symbol.
Take each symbol's subscript. A bare symbol counts one.
Multiply through brackets. Every count inside a bracket is multiplied by the bracket's subscript.
Multiply through a dot. In a hydrate, the number after the dot multiplies the water that follows it.
Add up an element that appears twice. Oxygen in a hydrate, or hydrogen in ammonium hydroxide, is counted wherever it appears.
Multiply by a coefficient last. A number in front multiplies the whole formula.
Check the work. Is every element in the formula in your list, with no element missing? Did every symbol inside a bracket get multiplied, not just the first? Does the total you add up match the sum of the element counts? And is no count zero for an element the formula names?
Reading a bare symbol as one is allowed because a formula names only elements that are present. If an element is named, at least one atom of it is there, and the convention is to leave the 1 unwritten.
Multiplying through a bracket is allowed because the bracket marks a group of atoms that occurs as a unit, such as the nitrate group in calcium nitrate. The subscript says how many such groups there are, so every atom in the group occurs that many times.
Adding an element that appears in two places is allowed because a count is a count wherever the atoms sit. The oxygens in the salt and the oxygens in the water of a hydrate are all oxygen atoms in the same formula unit.
Multiplying by a coefficient last is allowed because a coefficient counts whole formula units. It cannot change the formula itself, only how many copies of it there are.
Two kinds of number appear in chemistry, and confusing them is the root of more wrong answers than any other single slip.
A subscript is part of the formula. It says what the substance is. $\mathrm{H_2O}$ and $\mathrm{H_2O_2}$ differ by one subscript and are completely different substances: water, which you drink, and hydrogen peroxide, which bleaches hair and would harm you if swallowed. Change a subscript and you have named a new substance.
A coefficient is written in front of a formula. It says how much of the substance there is, counted in formula units. $3\mathrm{H_2O}$ is three water molecules — six hydrogens and three oxygens — and it is still water.
This distinction is the whole of the next lesson. When an equation does not balance, the only numbers you may change are the coefficients, because changing a subscript would change the substances themselves. A learner who has been reading formulas carefully will find that rule obvious; one who has not will try to balance $\mathrm{H_2 + O_2 \to H_2O}$ by writing $\mathrm{H_2O_2}$, and will have made peroxide instead of water. Read every number in a formula by asking which kind it is before using it.
A few groups of atoms travel together through so many formulas that it pays to recognize them on sight, because a bracket usually encloses one of them.
| Group | Formula | Where you meet it |
|---|---|---|
| hydroxide | $\mathrm{OH}$ | $\mathrm{Mg(OH)_2}$, an antacid |
| nitrate | $\mathrm{NO_3}$ | $\mathrm{Ca(NO_3)_2}$, a fertilizer |
| sulfate | $\mathrm{SO_4}$ | $\mathrm{Al_2(SO_4)_3}$, used to treat drinking water |
| phosphate | $\mathrm{PO_4}$ | $\mathrm{Ca_3(PO_4)_2}$, in bones and teeth |
| ammonium | $\mathrm{NH_4}$ | $\mathrm{(NH_4)_2SO_4}$, a fertilizer |
When one of these groups appears more than once in a compound, the formula puts it in a bracket with a subscript, rather than writing it out twice. When it appears only once, the bracket is left off: calcium sulfate is $\mathrm{CaSO_4}$, not $\mathrm{Ca(SO_4)}$. So a bracket is a sign that something is about to be multiplied, and the count inside it is going to be needed more than once. Spotting the group first, before counting any atoms, turns a long formula into a short one: aluminum sulfate is two aluminums and three sulfates, and only then twelve oxygens.
You will need these from the second unit onwards, and they are worth meeting now so that a formula and its mass are read off the same page. Each is the relative atomic mass of the element: how heavy one of its atoms is compared with the standard scale. They have no unit, because they are a comparison.
| Element | Symbol | Relative atomic mass |
|---|---|---|
| hydrogen | $\mathrm{H}$ | 1 |
| carbon | $\mathrm{C}$ | 12 |
| nitrogen | $\mathrm{N}$ | 14 |
| oxygen | $\mathrm{O}$ | 16 |
| sodium | $\mathrm{Na}$ | 23 |
| magnesium | $\mathrm{Mg}$ | 24 |
| aluminum | $\mathrm{Al}$ | 27 |
| sulfur | $\mathrm{S}$ | 32 |
| chlorine | $\mathrm{Cl}$ | 35.5 |
| potassium | $\mathrm{K}$ | 39 |
| calcium | $\mathrm{Ca}$ | 40 |
| iron | $\mathrm{Fe}$ | 56 |
| copper | $\mathrm{Cu}$ | 63.5 |
| zinc | $\mathrm{Zn}$ | 65 |
Chlorine's $35.5$ and copper's $63.5$ are not typing errors. Both elements occur as a mixture of isotopes — atoms of the same element with different masses — and the number quoted is the average over that mixture, weighted by how common each one is. Rounding either to a whole number would change the mass of every chloride and every copper salt in this course, so they are kept as they are.
A bag of lawn fertilizer from an Iowa farm store carries three numbers on its front, such as 21-0-0, and a chemical name on its back: ammonium sulfate, $\mathrm{(NH_4)_2SO_4}$. Reading the formula is the first step to understanding what the gardener is paying for.
The bracket says there are two ammonium groups. Each holds one nitrogen and four hydrogens, so one formula unit carries $1 \times 2 = 2$ nitrogens and $4 \times 2 = 8$ hydrogens, plus one sulfur and four oxygens outside the bracket: 15 atoms in all. Nitrogen is the nutrient the grass needs, and the bracket subscript is what doubles it.
The front-of-bag number, 21, is the percentage of the fertilizer's mass that is nitrogen. That figure comes straight from counting atoms and multiplying by their masses — two nitrogens at 14 each, out of a formula unit weighing 132 — which is the arithmetic the second unit of this course teaches. A shopper comparing a bag of ammonium sulfate with a bag of urea, $\mathrm{CO(NH_2)_2}$, which is 46 percent nitrogen, is comparing two formulas read exactly this way.
A bottle of antacid tablets lists calcium carbonate, $\mathrm{CaCO_3}$: one calcium, one carbon and three oxygens, five atoms in a formula unit. The 3 belongs to the oxygen alone, because there is no bracket for it to multiply. Another brand uses magnesium hydroxide, $\mathrm{Mg(OH)_2}$, where the bracket does matter: one magnesium, two oxygens and two hydrogens. Both tablets neutralize stomach acid, and the formulas on the labels are what tell a pharmacist how much of each active ingredient a dose contains.
The bracket gets ignored. $\mathrm{Ca(NO_3)_2}$ read as one nitrogen and three oxygens. The subscript outside the bracket is doing the same job as any other subscript; it just has more to multiply.
The subscripts get added. $\mathrm{Al_2(SO_4)_3}$ read as seven oxygens, from $4 + 3$. The bracket subscript multiplies. There are $4 \times 3 = 12$ oxygens.
A missing subscript is read as zero. There is no such thing as a formula containing no atoms of an element it names. A bare symbol means one.
A coefficient is read as a subscript. $2\mathrm{H_2O}$ is two water molecules, not a new substance with two more hydrogens.
The reading errors go unnoticed. All four are reading errors rather than chemistry errors, and that is exactly why they are dangerous: the arithmetic that follows them is often flawless, so nothing later in the working looks wrong.
Read the formula.
$\mathrm{Ca(NO_3)_2}$
One symbol outside, a bracket with a subscript.
Count the calcium.
$1$
A bare symbol means one.
Count the nitrogen.
$1 \times 2 = 2$
Inside the bracket, times its subscript.
Count the oxygen.
$3 \times 2 = 6$
The bracket subscript reaches every atom inside.
Add the counts together.
$1 + 2 + 6 = 9$
Atoms in one formula unit.
Read the formula.
$\mathrm{Al_2(SO_4)_3}$
A subscript outside and a bracketed group.
Count the aluminum.
$2$
The subscript belongs to the symbol before it.
Count the sulfur.
$1 \times 3 = 3$
Inside the bracket, times three.
Count the oxygen.
$4 \times 3 = 12$
Multiplied, not added.
Add the counts together.
$2 + 3 + 12 = 17$
Atoms in one formula unit.
Check the common slip.
$4 + 3 = 7 \text{ oxygens is wrong}$
Adding the subscripts loses five oxygens.
Read the formula.
$\mathrm{CuSO_4 \cdot 5H_2O}$
A salt and its built-in water.
Count the salt's atoms.
$1 + 1 + 4 = 6$
Copper, sulfur, four oxygens.
Count the water's hydrogens.
$5 \times 2 = 10$
The 5 multiplies the water.
Count the water's oxygens.
$5 \times 1 = 5$
One in each water molecule.
Count all the oxygens.
$4 + 5 = 9$
Oxygen appears on both sides of the dot.
Count all the atoms.
$6 + 10 + 5 = 21$
Every atom in one formula unit.
Count three formula units.
$3 \times 21 = 63$
A coefficient multiplies the whole formula.
Count the calcium.
$\mathrm{Ca_3(PO_4)_2}: 3$
Start where there is no bracket.
Count inside the bracket.
$\text{P: } 1 \times 2 = 2; \ \text{O: } 4 \times 2 = 8$
The bracket subscript multiplies both.
Add the counts together.
How many atoms of sulfur are there in one formula unit of iron(III) sulfate, $\mathrm{Fe_2(SO_4)_3}$?
Complete the worked solution: a compound has the formula $\mathrm{M_{1}(XO_{4})_{3}}$, where M and X stand for two elements. Find the oxygen atoms in one formula unit, all the atoms in one formula unit, and all the atoms in two formula units.
Find the oxygen atoms.
$(\text{inside subscript}) \times (\text{bracket subscript}) =$ o
The bracket subscript multiplies everything inside.
Find all the atoms in one unit.
$(\text{M}) + (\text{X}) + (\text{oxygen}) =$ t
X is also multiplied by the bracket subscript.
Find the atoms in two units.
$\text{two} \times (\text{one unit}) =$ d
A coefficient multiplies the whole formula.
Complete the sentence about nitric acid.
In one formula unit of $\mathrm{HNO_3}$, the count for $\mathrm{O}$ is a, and the count for every element together is b.
How many atoms are there in $6$ formula units of ammonium chloride, $\mathrm{NH_4Cl}$?
Answer:
The label on the treatment tanks of Chicago's water works lists aluminum sulfate, $\mathrm{Al_2(SO_4)_3}$. How many atoms are in one formula unit of it?
The answer: a.
A jar in a stockroom is labeled gypsum, $\mathrm{CaSO_4 \cdot 2H_2O}$. The dot means the crystal has whole water molecules built into it — $2$ of them for every formula unit of the salt. Count the atoms in the whole formula.
| atoms of oxygen | atoms of hydrogen | atoms altogether | |
|---|---|---|---|
| $\mathrm{CaSO_4 \cdot 2H_2O}$ |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
One formula unit of nitric acid is written $\mathrm{HNO_3}$. Fill in how many atoms of each element it contains, and how many atoms it contains altogether.
| atoms in one formula unit | |
|---|---|
| $\mathrm{H}$ | |
| $\mathrm{N}$ | |
| $\mathrm{O}$ | |
| Atoms altogether |
You can read a formula as a count of atoms, and you know what a bracket subscript multiplies. Say out loud how many oxygen atoms are in one unit of calcium nitrate, and why it is not three. Next: why an equation is balanced with numbers in front and never by changing a subscript.
16. Your turn: how many atoms in one unit of calcium phosphate, written as calcium with two phosphate boxes?, step 3
$3 + 2 + 8 = 13$
Atoms in one formula unit.