CHM110H5 Chap.2 Writing and Balancing Chemical Equations
Writing and Balancing Chemical Equations
Why balancing comes first in CHM110H5
Writing and balancing chemical equations sits in the background toolkit for Unit 1 Stoichiometry, alongside units, notation and nomenclature, and the course outcomes ask you to classify reactions by type and balance them.
Almost every later calculation in the course, from precipitate masses to gas volumes and heats of reaction, reads its mole ratios straight from a balanced equation. If the coefficients are wrong, every number built on them is wrong too, even when the arithmetic is flawless.
The rule underneath every method
Atoms are rearranged during a reaction, never created or destroyed.
That means that for each element, the coefficient multiplied by the subscript, summed over all reactants, must equal the same sum over all products. You are only allowed to change coefficients. Subscripts are part of a compound's identity: changing H2O to H2O2 does not fix a count, it describes a different chemical. When an ionic equation is written, the total charge on each side must also agree.
The final answer should use the smallest set of whole-number coefficients, so a fraction such as 7/2 in front of O2 is cleared by multiplying every coefficient by 2.
Balancing by inspection
Most equations you meet on quizzes balance quickly by inspection. Start with an element that appears in only one reactant and one product.
In combustion of a hydrocarbon, that means carbon first, then hydrogen, and oxygen last, because O2 is a free element whose coefficient can be set without disturbing anything already fixed. Treat polyatomic ions such as nitrate, sulfate and phosphate as single units when they pass through unchanged; this is especially helpful in neutralisation and double displacement reactions.
Finish with a full tally of every element on both sides rather than trusting the last step you changed.
Quiz items in the course often give a four-species equation with blank coefficients, for example a salt plus a halogen or a hydroxide plus an acid, so practise filling every blank and then writing out the element-by-element check that proves the set is correct and fully reduced.
Classifying reactions by type
Lectures classify reactions in two complementary ways.
The first compares the number of reactant and product species: combination reactions join species together, decomposition reactions break one species apart (by heating or by electrolysis), and substitution reactions swap partners, either as a single displacement or a double displacement.
The second looks at chemical nature: acid-base neutralisation, precipitation of an insoluble product predicted by the solubility guidelines, and redox reactions involving electron transfer, tracked with oxidation states. Naming the type helps you predict the products before you balance, and the solubility guidelines tell you which product leaves solution as a solid.
Once the equation is balanced, its coefficients become the mole ratios you will use to convert between grams of one substance and grams of another.
What this chapter covers
- 01
Conservation of atoms in equations
- 02
Coefficients versus subscripts
- 03
Balancing by inspection
- 04
Clearing fractional coefficients
- 05
Combination, decomposition and displacement
- 06
Neutralisation, precipitation and redox
- 07
Coefficients as mole ratios
Worked example · free
Balancing butane combustion and predicting CO2 mass
- 3Balance by inspection: 4 C gives 4 CO2; 10 H gives 5 H2O; oxygen on the right = 4 x 2 + 5 = 13, so 13/2 O2. Multiply through by 2: 2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O. Tally: C 8 = 8, H 20 = 20, O 26 = 16 + 10.
- 2Molar mass of butane = 4(12.01) + 10(1.008) = 48.04 + 10.08 = 58.12 g/mol, so n = 5.81 g / 58.12 g/mol = 0.1000 mol.
- 1Mole ratio CO2 : C4H10 = 8 : 2 = 4, so n(CO2) = 0.1000 x 4 = 0.4000 mol.
- 2Molar mass of CO2 = 12.01 + 2(16.00) = 44.01 g/mol; mass = 0.4000 mol x 44.01 g/mol = 17.6 g.
Key terms
- Coefficient
- The whole number written in front of a formula in an equation; it multiplies every atom in that formula and gives the mole ratio between substances.
- Subscript
- The small number inside a formula showing how many atoms of an element one unit contains; it fixes the identity of the substance and is never changed to balance.
- Skeleton equation
- An equation showing correct formulas for reactants and products but no coefficients yet, used as the starting point before atoms are tallied and balanced.
- Double displacement
- A substitution reaction in which two ionic compounds exchange partners, often producing an insoluble solid, water or a gas; also called metathesis.
- Precipitation reaction
- A reaction that forms an insoluble product from dissolved ions, predicted using solubility guidelines such as chlorides of silver and most hydroxides being insoluble.
- Mole ratio
- The ratio of coefficients between two substances in a balanced equation, used to convert moles of one reactant or product into moles of another.
Writing and Balancing Chemical Equations FAQ
Why can't I just change H2O to H2O2 when oxygen does not balance?
Because the subscript is part of what the substance is. H2O2 is hydrogen peroxide, a completely different compound from water, so the equation would describe another reaction. Only the coefficient in front of a formula can be adjusted, which multiplies the whole unit.
Is it acceptable to leave 7/2 O2 in my answer?
A fractional coefficient is useful while working, especially for O2 in combustion, but the reported equation should use the smallest whole numbers. Multiply every coefficient by the denominator, so 7/2 becomes 7 and the other coefficients double as well.
How do I decide which element to balance first?
Pick an element that appears in only one reactant and one product, typically carbon in a fuel. Leave free elements such as O2 or a lone metal until the end, since changing their coefficient does not upset any other atom count.
Exam move
Work through the recommended textbook problems for the stoichiometry chapters and balance each equation twice: once by inspection and once by writing a full atom tally table for every element. Time yourself on the practice quiz balancing items until each takes under two minutes. For every equation, also name the reaction type and, for precipitation, state which product is insoluble from the solubility guidelines.
Finally, take three balanced equations and convert a given mass of one reactant into a product mass, so the mole-ratio step becomes automatic.
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