Composition, Solutions, and Stoichiometry

This is Unit Three of Chemistry, Part One: the mole and solution concentration. A mole is a counting unit, and that is the whole of what it is. It names a fixed number of entities and no mass at all. Molar mass is the separate fact that one mole of a substance weighs, in grams, the same number as its formula mass in atomic mass units — the same number, in a different unit. Those two facts chain into a conversion that runs from a measured mass all the way to a literal count of atoms, in two steps. The book insists on stopping at moles in the middle rather than jumping straight across, because the mole checkpoint is where the units cancel visibly and errors get caught. Then percent composition, and two procedures that turn measured masses into a formula — first an empirical one, then a molecular one. Watch the rounding warning in the first: a mole ratio of one to one point five gets doubled to two to three, never rounded down. The rest is solutions. Molarity divides by the solution's total volume, not the solvent's, because the solute itself occupies part of that litre. And two words that sound like they mean the same thing do not: strong describes how completely a solute dissociates, concentrated describes how much is there. By the end you will be able to do five things. One: say what a mole counts. Two: carry a mass to a particle count. Three: get a formula from percentages. Four: say what molarity divides by. Five: tell strong from concentrated.

Five entries building the unit's central tool. Two ways of summing a formula's masses, the counting unit, the number behind it, and the bridge that connects a count to a mass you can weigh out.

Summing a molecule.

Chem 0361 Formula Mass for Covalent Compounds

A covalent compound's formula mass is the sum of the average atomic masses of every atom shown in its molecular formula — chloroform sums one carbon, one hydrogen and three chlorines to about one hundred nineteen. Counting chlorine once instead of three times, as its subscript requires, undercounts by two chlorine masses.

Summing a formula unit.

Chem 0364 Formula Mass for Ionic Compounds

An ionic compound's formula mass sums the average atomic masses of every ion in its formula unit, cation and anion together — sodium chloride adds one of each. Ionic compounds form no discrete molecules, so their formula mass is never correctly called a molecular mass.

A counting unit.

Chem 0367 The Mole

The mole is chemistry's counting unit, defined so that one mole of any substance contains one fixed number of entities — it works like a dozen, extending counting in groups down to particles too small to count by hand. A mole counts particles and names no mass by itself, though every mole of a substance has one.

The number.

Chem 0370 Avogadro's Number

Avogadro's number is the count of entities in one mole, fixed by the twenty nineteen redefinition at about six point zero two two times ten to the twenty-third per mole — a mole of carbon atoms and a mole of water molecules hold the same count with different masses. Older sources call it experimentally determined; the redefinition made it exact.

Count to grams.

Chem 0373 Molar Mass

A substance's molar mass is the mass in grams of one mole, numerically equal to its formula mass — carbon-twelve's atomic mass is exactly twelve, so one mole of it weighs twelve grams. Atomic mass and molar mass share a number, not a unit: one is in atomic mass units, the other in grams per mole.

Two procedures, and they connect. The first turns a mass into moles; the second turns moles into a count of particles. Run together they take a laboratory weighing to a literal number of atoms, and the middle step is not optional.

Mass to moles.

Chem 0376 Converting Mass to Moles

Divide the measured mass by the substance's molar mass, letting grams cancel against grams per mole. A four point seven gram sample of potassium, against a molar mass of thirty-nine point one, gives about zero point one two moles — and since four point seven grams is a bit over a tenth of thirty-nine point one, an answer above zero point one zero is expected before the division finishes. Dividing molar mass by sample mass instead inverts the units and gives something that looks plausible and means nothing.

Moles to particles.

Chem 0379 Converting Moles to Number of Entities

Multiply the mole amount by Avogadro's number, letting the mole unit cancel against the constant's per-mole unit. Zero point one two moles of potassium gives roughly seven point two times ten to the twenty-second atoms. Chained with the previous step, a measured mass reaches a literal atom count in two operations, and the chain runs in reverse as well. Skipping straight from mass to particle count hides the unit cancellation that makes the calculation trustworthy.

Four entries running from measured masses to a molecular formula. The first defines what percent composition is and warns that it is about mass rather than atom counts — a distinction the next two procedures then have to bridge.

Mass shares.

Chem 0382 Percent Composition

A compound's percent composition states each element's mass as a percentage of the compound's total mass — a ten gram sample holding seven and a half grams of carbon and two and a half of hydrogen is seventy-five percent carbon. Percent composition describes mass ratios, not atom-count ratios; a heavier element's percentage can exceed its share of the atoms.

From measured masses.

Chem 0385 Calculating Percent Composition from Experimental Mass Data

Divide each element's measured mass by the sample's total mass and convert each result to a percentage. A sample holding carbon, hydrogen and nitrogen at seven point three four, one point eight five and two point eight five grams totals twelve point zero four grams, giving about sixty-one, fifteen and twenty-four percent. Checking that the three sum to nearly a hundred confirms no element's mass was left out of the total — which is the error the check exists to catch.

Percentages to a ratio.

Chem 0388 Determining Empirical Formula from Percent Composition

Treat each percentage as grams in a hundred-gram sample, convert each mass to moles, and reduce the mole amounts to a small whole-number ratio. A gas at twenty-seven percent carbon and seventy-three percent oxygen gives about two point two seven and four point five four moles; dividing both by the smaller gives one to two. Rounding a ratio like one to one point five down to one to one instead of doubling both to two to three discards real information the data supports.

Ratio to molecule.

Chem 0391 Determining Molecular Formula from Empirical Formula and Molar Mass

Divide the compound's known molar mass by its empirical formula's mass, then multiply every empirical subscript by that whole number. Nicotine's empirical formula has a mass near eighty-one against a measured molar mass near one hundred sixty-two, so the multiplier is two and every subscript doubles. A division result far from a whole number signals an error upstream, usually in the empirical formula — not a reason to round the multiplier anyway.

Four entries. The vocabulary first, then the standard concentration unit and its calculation in both directions. Molarity's warning is the one worth carrying into the laboratory: the denominator is the solution's volume, not the solvent's.

Three terms.

Chem 0394 Solution, Solute, and Solvent

Within a solution, the solvent is present in the greater amount and each solute is a substance dispersed throughout it — in seawater, water is the solvent and dissolved salts the solutes, spread evenly enough that any scooped sample matches any other. Homogeneous describes uniformity throughout, not equal amounts; solutes are usually the minor component.

Moles per litre.

Chem 0397 Molarity

Molarity is a solution's concentration — the number of moles of solute dissolved in exactly one litre of solution. Zero point one three three moles of sucrose in zero point three five five litres gives about zero point three seven five molar. It divides by the solution's total volume, not the solvent's alone, since the solute itself fills part of that litre.

Mass to molarity.

Chem 0400 Calculating Molarity from Solute Mass and Solution Volume

Convert the solute's mass to moles using molar mass, then divide by the solution's volume in litres. Thirteen point one grams of sodium chloride, molar mass fifty-eight point four four, gives about zero point two two four moles; in zero point seven five litres that is about zero point two nine nine molar. Dividing by the solute's mass in grams rather than converting to moles first produces a number with the wrong units entirely, not merely the wrong value.

Molarity to mass.

Chem 0403 Calculating Solute Mass from Molarity and Volume

Multiply molarity by volume in litres to get moles, then multiply by molar mass to get grams. A five point three molar solution in zero point two five litres holds one point three two five moles of sodium chloride, which at fifty-eight point four four grams per mole is about seventy-seven point four grams — the mass weighed out to prepare it. Rounding the intermediate mole value before the final multiplication, rather than carrying a guard digit, can shift the answer by several tenths of a gram.

Two entries, and they exist to separate two words people use as though they were synonyms. One is about how completely a solute breaks into ions. The other is about how much of it is in the container. Any combination of the two is possible.

How completely.

Chem 0406 Strong and Weak Electrolytes

A strong electrolyte dissociates completely into ions in solution; a weak electrolyte dissociates only partially — dissolved sodium hydroxide exists almost entirely as separate ions, while dissolved ammonia stays mostly intact. Strong describes how completely a solute dissociates, never how much is dissolved.

How much.

Chem 0407 Concentrated and Dilute

Concentrated and dilute describe how much solute is dissolved relative to solvent, separate from whether it dissociates — a dilute solution of a strong electrolyte still dissociates completely, and a concentrated weak electrolyte still dissociates only partly. Calling a dilute strong-acid solution weak confuses two independent properties.

Two entries. What stays constant when solvent is added, and a procedure whose real trap is not the arithmetic but what you do at the bench afterward.

Moles conserved.

Chem 0410 Dilution of Solutions

Dilution lowers a solution's concentration by adding solvent while the moles of dissolved solute stay unchanged — and because those moles are conserved, the initial molarity times volume equals the diluted molarity times volume. The common error treats the added solvent's volume as the final volume, rather than the diluted solution's total.

Working it out.

Chem 0413 Performing a Dilution Calculation

Set the stock's molarity times volume equal to the diluted solution's molarity times volume and solve for the unknown. Making five hundred millilitres of zero point four molar glucose from a three molar stock needs about sixty-seven millilitres of stock — which is then measured into a flask and brought up to five hundred millilitres total by adding water. Adding five hundred millilitres of water to the sixty-seven gives a final volume and concentration that are both wrong.

Four entries. Three percentages that differ in what goes on top and what goes underneath, and two scales for concentrations too small for a percentage. Each warning is about mixing one formula's numerator with another's denominator.

Mass over mass.

Chem 0416 Mass Percentage

A solution's mass percentage is the mass of one component divided by the solution's total mass, as a percentage — bleach labelled seven point four percent by mass holds that many grams of solute per hundred grams of solution. The numerator and denominator must share identical mass units before dividing, or the result is not a true dimensionless ratio.

Volume over volume.

Chem 0418 Volume Percentage

A solution's volume percentage is a liquid solute's volume divided by the solution's total volume, as a percentage — washer fluid sold as thirty percent by volume holds thirty millilitres of methanol per hundred millilitres of solution. It divides by solution volume, not solvent volume alone; the solute's own volume is part of that total.

Mass over volume.

Chem 0419 Mass-Volume Percentage

A solution's mass-volume percentage is a solute's mass divided by the solution's total volume, as a percentage — physiological saline at zero point nine percent means zero point nine grams of dissolved salt per hundred millilitres. It mixes a mass numerator with a volume denominator, so substituting volume percentage's formula partway through gives the wrong unit pair.

Very small amounts.

Chem 0420 Parts per Million and Parts per Billion

Parts per million and parts per billion extend mass percentage to very low concentrations, scaled by a million or a billion — four parts per million of fluoride means four grams per million grams of water, too small to express as a percentage. Reading parts per billion as parts per million overstates the concentration a thousandfold; the two are never interchangeable.

Five things to carry out of Part One. A mole counts particles and nothing else — one fixed number of entities, Avogadro's number, exact since the twenty nineteen redefinition rather than measured. Molar mass is what connects that count to something weighable: one mole of a substance weighs, in grams, the same number as its formula mass in atomic mass units. Same number, different unit. To carry a mass to a particle count, divide by molar mass to get moles, then multiply by Avogadro's number. Stopping at moles in the middle is what makes the units cancel visibly, and it is where an error shows up before it reaches the answer. To get a formula from percent composition, treat each percentage as grams in a hundred-gram sample, convert to moles, and reduce to a small whole-number ratio. A ratio like one to one point five is doubled to two to three, never rounded. Then divide a measured molar mass by the empirical formula's mass and multiply every subscript by that whole number. Molarity divides by the solution's total volume, not the solvent's. The solute occupies part of that litre, so preparing a solution means bringing it up to volume rather than adding a measured volume of solvent to it. The same applies to dilutions. And strong is not concentrated. Strong and weak describe how completely a solute dissociates into ions. Concentrated and dilute describe how much of it is dissolved. The two vary independently, so a dilute strong acid and a concentrated weak one are both ordinary things. Part Two turns to chemical equations, and to the reactions they describe.