7. Chemical Reactions

Magnesium burns by combining with oxygen in the air. The product, magnesium oxide, contains both. Weighed alone, the metal has lost nothing: it has gained the weight of the oxygen. This is what Lavoisier showed for burning in general, against the older idea that burning released a substance (phlogiston) and so should make things lighter.

Yes. Joseph Proust argued in the 1790s that a given compound always has the same elements in the same proportion by mass, however it is made. Magnesium oxide from any source is 60.3 % magnesium by mass, and so the ash is always 1.658 times as heavy as the metal.

Equal masses of different elements hold different numbers of atoms, because the atoms have different masses. 24.3 g of magnesium and 16.0 g of oxygen hold the same number of atoms. Dividing a mass by the atomic mass gives a number proportional to the number of atoms, which is what a formula is about.

No: they are simulated. Each result is computed from the atomic masses in the course's table of elements, with a random scatter of about 0.4 %, roughly what a careful student gets on a school balance. The scatter is why the points do not fall exactly on the line.

A mole of water is only 18 g, about a tablespoon, and it holds 6.022 × 10²³ molecules. If a million people counted a million molecules every second, it would still take them about 19,000 years. The number is huge because atoms are tiny, and it is chosen so that the mass of a mole in grams comes out as a number you can handle.

The word comes from the German Mol, short for Molekül, and was introduced around 1900 by Wilhelm Ostwald. The number was first estimated from experiments such as the oil-drop measurement of the electron's charge combined with electrolysis (the charge on a mole of electrons divided by the charge of one): from this section onward, that is the number you use.

By definition, the mole was set up so that one mole of carbon-12 weighs 12 g (now fixed through Avogadro's number). The atomic mass of an element on the periodic table is its average mass in atomic mass units (u), and the same number is its mass in grams per mole.

Add up the atomic masses in the formula. Water, H₂O, is 2 × 1.008 + 15.999 = 18.015 g/mol. A mole of water is 6.022 × 10²³ molecules and weighs 18.015 g. Ethanol, glucose and any other compound work the same way.

A subscript is part of the identity of a substance. H₂O is water; H₂O₂ is hydrogen peroxide, a different compound. Changing a subscript describes a different reaction. A coefficient only says how many of the molecules there are.

Octane gives 25/2 O₂. Multiply every coefficient by 2 to clear it. The result, 2 C₈H₁₈ + 25 O₂ → 16 CO₂ + 18 H₂O, is a perfectly good equation: coefficients count molecules in the recipe, and two molecules of octane burn together.

It appears in several formulas, so changing its coefficient early disturbs the other elements. Balance the elements that appear once on each side first, and oxygen usually comes out right at the end.

Yes. Add the molar masses times the coefficients on each side, as the notebook does after a correct answer, and they match. That is Lavoisier's result, and the fact that makes the mass calculations in the next section possible.

The oxygen in the sample leaves as CO₂ and H₂O together with the oxygen from the furnace, so the products' oxygen cannot be used. But the carbon and hydrogen in the sample are fully accounted for, so whatever mass of the sample is not C or H must be something else, here oxygen. A compound with nitrogen or sulfur needs more measurements.

The method counts atoms in proportion, not in absolute numbers. Ethylene glycol is C₂H₆O₂, whose simplest ratio is CH₃O; acetic acid is C₂H₄O₂, simplest ratio CH₂O, the same as glucose, C₆H₁₂O₆. They differ in molar mass, and that is what separates them.

Real masses are never exact, so the mole ratios come out near whole numbers but not on them: 2.01 and 5.98, not 2 and 6. You round to the nearest whole-number ratio, and if a ratio looks like 1.5 you multiply everything by 2.

Yes: it contains no oxygen, so the oxygen found by difference is close to zero. The method says so, and the formula comes out as C₃H₈ without any oxygen.

The coefficients count molecules (and so moles); they do not count grams. In 2 H₂ + O₂ → 2 H₂O, two moles of hydrogen react with one mole of oxygen, but those are 4.03 g and 32.0 g. The masses are different because the molar masses are different. Converting to moles first puts everything on the same footing.

By the units. Write down the unit you have and the unit you want, and choose the factor with the unit you have on the bottom, so it cancels. If the units do not cancel, the factor is upside down. The bench refuses a factor that does not cancel.

Any balanced equation. The same three steps work whatever the substances are, whether they are solids, liquids or gases, as long as you know their formulas to get molar masses, and the balanced equation for the coefficients.

Then one reactant runs out first, and it limits how much product can form. That is the limiting reagent, the subject of the last experiment of this unit.

Because the coefficient says how many moles of that reactant one run of the equation uses. Dividing moles by it gives how many runs that reactant could supply. The reactant that supplies the fewest runs stops the reaction.

No. In the ammonia example the nitrogen weighs 28 g and the hydrogen only 5 g, yet it is the hydrogen that limits, because it is needed in three times the number of moles and a hydrogen molecule weighs so little. Always convert to moles first.

Several reasons: the reaction may not go to completion (many reach an equilibrium), side reactions use some reactant, product is lost in transfers and filtering, and some is left in the apparatus. The 78 % here is chosen to look like a typical laboratory result.

Not if everything is done correctly. If it is, the product is wet with solvent, contaminated with another substance, or was weighed wrongly. It is a useful warning sign.