• The mole is chemistry's "counting unit" — it links mass, particles, gas volume, and solution concentration all together.
• Concentration can be measured as mass concentration (g dm⁻³) or molar concentration (mol dm⁻³) — and at very low levels, in parts per million (ppm).
• Reacting mass calculations use the mole ratio from a balanced equation to find unknown masses of reactants or products.
• You can even work backwards — using masses from an experiment to figure out the balanced equation itself.
• Reacting volume calculations apply to gases: at r.t.p. one mole of any gas occupies 24.0 dm³; at s.t.p. it's 22.4 dm³.
• The ideal gas equation PV = nRT handles gases at any temperature and pressure, not just standard conditions.
• Percentage yield compares what you actually got to the maximum theoretically possible.
• Atom economy tells you how much of your reactant mass actually ends up in the product you want (vs. wasted as by-products).

Atoms and molecules are absurdly small and absurdly numerous — you can't count them one by one. So chemists invented the mole: a "chemist's dozen" that lets us talk about huge numbers of particles using ordinary numbers we can calculate with.

Because "amount of substance" is really a blanket term for almost any calculation involving moles, there are several routes into finding n (moles) depending on what information you're given:

"Concentration" just means how much stuff is packed into a given volume of solution — but there are two ways to express "how much stuff":

• Mass concentration — measured in g dm⁻³ (or g cm⁻³, kg m⁻³, mg/ml). This is literally grams of solute per volume of solution — no chemistry needed, just division.
• Molar concentration — measured in mol dm⁻³. This tells you how many moles of solute are packed into the solution, which is far more chemically useful because moles react in fixed ratios, not grams.

Sometimes a concentration is so tiny that grams-per-litre becomes an awkward, fiddly number (like 0.000003 g dm⁻³). Instead, chemists switch to parts per million — perfect for describing pollutants in water or air, where the "stuff" is a whisker of the total.

This is the workhorse skill of the whole chapter. The logic is always a three-step relay race:

• Step 1 — Mass → Moles: convert the mass you're given into moles, using n = mass ÷ molar mass.
• Step 2 — Moles → Moles: use the ratio in the balanced equation to convert moles of the substance you have into moles of the substance you want.
• Step 3 — Moles → Mass: convert those moles back into a mass using mass = moles × Mr.

The balanced equation is the "exchange rate" — it tells you exactly how many moles of one substance correspond to how many moles of another. Get the ratio wrong, and everything downstream is wrong too, so always balance the equation first.

Sometimes an exam flips the whole process on its head: instead of giving you a balanced equation and asking for a mass, it gives you the masses of everything involved and asks you to find the balanced equation itself.

The trick is simple: convert every mass to moles, then divide all the mole values by the smallest one. Whatever whole numbers pop out are your balancing coefficients.

Here's a genuinely beautiful fact about gases: one mole of ANY gas occupies the same volume, at a given temperature and pressure — it doesn't matter if it's helium or carbon dioxide, big molecule or small. This works because gas volume is really about the space between particles (which is huge compared to the particles themselves), not the particles' own size.

The molar gas volume (24.0 or 22.4 dm³) only works at those two specific "standard" conditions. But what if a question gives you some random temperature and pressure — say, 220 kPa and 21°C? That's where the ideal gas equation comes in: a single formula that works at any temperature and pressure.

It's built on the kinetic theory of gases, which assumes:

• Gas molecules move fast and randomly
• Molecules have (almost) no volume of their own
• There's no attraction or repulsion between molecules (no intermolecular forces)
• Collisions are perfectly elastic (no kinetic energy lost)
• Temperature reflects the average kinetic energy of the molecules

Gases that obey this perfectly are called ideal gases. Real gases only approximate this — but they get close enough that the equation works well in practice.

In theory, a reacting mass calculation tells you the maximum possible amount of product you could ever get. In real lab life, you almost never get that much — because of side reactions, incomplete reactions, or product lost during filtering and purification.

Percentage yield measures how close your real-world result got to that theoretical maximum.

Atom economy asks a different question than percentage yield. It doesn't care how efficiently the reaction was carried out in the lab — it asks: of all the atoms that go INTO the reaction, what fraction end up in the product you actually wanted? The rest becomes waste (by-products).

This matters hugely for green chemistry and industrial cost — a reaction can have a perfect 100% yield but a terrible atom economy if most of the reactant mass ends up as unwanted by-product.