Write and balance chemical equations to express conservation of matter, and classify reactions as exothermic or endothermic

Learning goal: Identify reactants and products in a chemical equation; write and balance simple equations from formulas or from a word description so that atoms of every element are conserved; explain why the formula of a product such as NaBr is fixed by ionic charges and not by the equation; and describe exothermic and endothermic reactions as transfers of thermal energy between a system and its surroundings, including why some temperature changes cannot be detected.

What an equation says. A chemical reaction rearranges atoms: the bonds in the starting substances are broken and new bonds form, producing different substances. The starting substances are the reactants, written on the left; the substances formed are the products, on the right; the arrow means "react to form". In middle school the law of conservation of matter was extended to chemical reactions: the number and type of atoms, and therefore the total mass, are the same before and after. In this course that law is expressed by writing a balanced equation, one in which every element has the same number of atoms on each side.

Coefficients and subscripts. A subscript inside a formula tells how many atoms of that element are in one unit of the substance; H₂O has two hydrogen atoms and one oxygen atom. A coefficient in front of a formula tells how many units take part; 2H₂O means two water molecules, four hydrogen atoms and two oxygen atoms in all. Balancing is done only with coefficients. Changing a subscript changes the substance: H₂O₂ is hydrogen peroxide, not "two waters", and writing it to make the counts work describes a different reaction. An equation is balanced when, for every element, the count on the left equals the count on the right, and the coefficients are the smallest whole numbers that do it.

A method that works. Write the correct formulas first. Count atoms of each element on each side. Balance elements that appear in only one substance on each side first, saving any element that appears in several places, often oxygen or hydrogen, for last. Adjust coefficients, recount and repeat. Worked model, methane burning in oxygen: CH₄ + O₂ → CO₂ + H₂O. Counts: left C 1, H 4, O 2; right C 1, H 2, O 3. Carbon is balanced. Hydrogen: put 2 in front of H₂O, giving H 4 on the right and O now 2 + 2 = 4 on the right. Oxygen: put 2 in front of O₂, giving O 4 on the left. Final: CH₄ + 2O₂ → CO₂ + 2H₂O, with C 1 = 1, H 4 = 4, O 4 = 4. Reading it: one methane molecule and two oxygen molecules react to form one carbon dioxide molecule and two water molecules, and nine atoms go in and nine come out. Relationships beyond these coefficients, and sorting reactions into named types, are chemistry topics; here the skill is to write, balance and read.

Formulas come first and do not bend. Students often ask why sodium reacting with bromine gives NaBr rather than NaBr₂, since bromine comes as Br₂ molecules. The formula of the product is fixed by the ions: sodium in group 1 forms Na⁺ and bromine in group 17 forms Br⁻, and the charges cancel one to one, so the compound is NaBr. Balancing then handles the Br₂ with a coefficient: 2Na + Br₂ → 2NaBr. Two sodium atoms each give one electron to one of the two bromine atoms, making two Na⁺ and two Br⁻. NaBr₂ would need a sodium ion with a 2+ charge, which sodium does not form. The general lesson is that the identity and formula of each substance is decided by the chemistry of the elements, and only the coefficients are adjustable.

Word descriptions to equations. "Magnesium metal burns in oxygen to form magnesium oxide": magnesium is Mg, oxygen gas is O₂, and the ionic product from Mg²⁺ and O²⁻ is MgO, so Mg + O₂ → MgO, balanced as 2Mg + O₂ → 2MgO. "Hydrogen gas and chlorine gas form hydrogen chloride": H₂ + Cl₂ → 2HCl. Elements that exist as two-atom molecules (the gases hydrogen, nitrogen, oxygen, fluorine and chlorine, plus liquid bromine and solid iodine) are written with the subscript 2 as reactants; metals and most other solids are written as single symbols.

Energy in reactions. Every reaction involves energy as well as atoms. Breaking bonds requires energy and forming bonds releases it, and the net result is a transfer of thermal energy between the reacting system and its surroundings. If the system releases thermal energy to the surroundings, the reaction is exothermic and the surroundings warm: a burning match, a chemical hand warmer, the reaction that sets concrete. If the system absorbs thermal energy from the surroundings, it is endothermic and the surroundings cool: an instant cold pack, or baking soda reacting with vinegar, whose mixture cools by a few degrees. Whether the change can be noticed depends on how much energy moves and how large the surroundings are. A hand warmer is warm to the touch, with no instrument. The baking soda and vinegar reaction cools only a few degrees, observable with a thermometer but not by hand. A nail rusting releases thermal energy too, but so slowly and into such large surroundings that the temperature change is too small to detect with a classroom thermometer; the energy is real but undetectable with that equipment. Saying a reaction "has no energy change" because nothing felt warm is the misconception to avoid.

Investigation: conservation of mass and energy transfer. Materials: a clean, empty 500 mL plastic bottle made for carbonated drinks, with its screw cap; about 1 g of baking soda folded into a small square of tissue; about 20 mL of vinegar; a small funnel; a balance reading to 0.1 g; a small open cup; a thermometer or probe; goggles. Part A, mass: pour the vinegar into the bottle through the funnel, put the capped bottle and the tissue packet on the balance together and record the total mass; drop the packet into the bottle and screw the cap on at once; swirl gently until the fizzing stops and record the mass of the capped bottle; then loosen the cap slowly, pointing the bottle away from faces, let the gas escape, retighten and record the mass again. Part B, energy: in the open cup, stir about 1 g of baking soda into 20 mL of vinegar with the thermometer in the liquid and record the starting and lowest temperatures. Record: mass before, mass after while capped, mass after opening, starting and lowest temperature. A result that supports the claims: the capped mass is the same before and after within the balance's precision, showing the atoms were conserved even though a gas formed; the mass falls after opening because carbon dioxide escaped, not because matter was destroyed; the temperature in the cup falls by a few degrees, showing the reaction is endothermic. A rigid bottle is used on purpose rather than a zip-seal bag: a bag that swells by about a liter is pushed up by the extra air it displaces, which can make a sealed bag read about 1 g lighter on a balance even though no matter has left it. Safety: goggles; use only a plastic bottle designed for carbonated drinks, never glass, and no more than the stated amounts, which build only a modest pressure; open the cap slowly. What the model cannot show: the bottle demonstrates conservation for one reaction but cannot show the individual atoms rearranging, and the thermometer measures only the mixture, so it cannot say how much energy moved, only that the reacting system took thermal energy from its surroundings.

Worked example 1 — balance from formulas. Aluminum reacts with chlorine: Al + Cl₂ → AlCl₃. Counts: left Al 1, Cl 2; right Al 1, Cl 3. Chlorine is 2 on the left and 3 on the right, so find a common count of 6: 3Cl₂ on the left and 2AlCl₃ on the right. Now Al is 2 on the right, so 2Al on the left. Final: 2Al + 3Cl₂ → 2AlCl₃; check Al 2 = 2, Cl 6 = 6. The formula AlCl₃ was given and was never changed.

Worked example 2 — balance a combustion. Propane burns: C₃H₈ + O₂ → CO₂ + H₂O. Carbon: 3 on the left, so 3CO₂. Hydrogen: 8 on the left, so 4H₂O. Oxygen on the right is now 3 × 2 + 4 × 1 = 10, so 5O₂ on the left. Final: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O; check C 3 = 3, H 8 = 8, O 10 = 10. Oxygen was left until last because it appears in two products.

Worked example 3 — from a word description. "Hydrogen gas reacts with oxygen gas to form water." Formulas: H₂, O₂, H₂O. Unbalanced: H₂ + O₂ → H₂O has O 2 on the left and 1 on the right. Put 2 in front of H₂O: O balanced at 2, but H is now 4 on the right, so 2H₂ on the left. Final: 2H₂ + O₂ → 2H₂O. The counts are H 4 = 4 and O 2 = 2, and the coefficients 2, 1, 2 cannot be reduced. This is a representation on paper; the real reaction is explosive and is never done by students.

Worked example 4 — classify by energy transfer and by detectability. A camping stove burning is exothermic, and the transfer is obvious without an instrument. Baking soda with vinegar is endothermic; a thermometer shows a drop of a few degrees that a hand would miss. Iron slowly rusting in a garage is exothermic, but the energy leaks into such large surroundings over months that no thermometer detects a change; the direction of transfer is known from faster versions of the same reaction (the iron in a hand warmer rusting quickly gets hot). The classification is about direction of energy transfer between system and surroundings, not about whether it is easy to notice.

Representation task: an atom inventory. For the equation 2Mg + O₂ → 2MgO, draw the reactants and products as labeled circles (Mg and O), then complete a two-column table counting Mg and O atoms on each side. Repeat for CH₄ + 2O₂ → CO₂ + 2H₂O with three rows (C, H, O). Under each table write one sentence stating what the equal counts show and one sentence saying what a coefficient means that a subscript does not.

Independent performance: write, balance and report on a reaction. Choose one safe reaction you can observe, for which the teacher supplies the formulas of the reactants and products: baking soda with vinegar (NaHCO₃ + CH₃COOH → NaCH₃COO + H₂O + CO₂), steel wool rusting in a hand warmer (Fe + O₂ → Fe₂O₃, to be balanced), or a teacher-provided alternative. Success criteria: the balanced equation is written with correct formulas and a table showing each element's count on both sides; the ionic products' formulas are justified from the group charges where the elements come from groups 1, 2, 17, hydrogen or oxygen; the reaction is classified as exothermic or endothermic from a recorded temperature measurement with the starting and ending readings stated; the report names one example of a reaction whose temperature change is too small to detect with a classroom thermometer and explains why in terms of the size of the surroundings; and one paragraph explains what a sealed-container mass measurement would show and why an open container gives a different result.