SCIENCE · INVESTIGATE AND EXPLAIN

Build balanced coefficients—and test whether they are unique

Construct four coefficients, diagnose independent atom budgets and find distinct balanced product-mixture proposals.

Learning outcome: Balance supplied reaction skeletons without changing formulas, reduce common factors and explain why conservation need not identify product proportions.

Starting recap

A coefficient multiplies every atom in a formula. A subscript belongs to the chemical identity. Equal total atom counts do not suffice: each element needs its own budget.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

One CH₄ and one O₂ cannot produce one CO₂ and one H₂O without an element mismatch. Changing coefficients can repair the budgets while preserving every formula.

Open the experiment

Predict

Predict which atom budget fails first, whether doubling a balanced proposal changes its ratio, and whether two carbon oxides can have more than one balanced product ratio.

Your prediction and reason

Experiment

Repair methane combustion, then deliberately double its coefficients and reduce the common factor. Construct the iron-oxide reduction equation. In the carbon-mixture packet, capture two positive primitive balanced proposals with different CO/CO₂ ratios. Try zero coefficients and explain the difference between equal budgets and including every named participant.

Construct coefficients and test independent atom budgets

Learner coefficients · independent atom budgets · Original bounded equation-construction tasks. Species formulas and phases are fixed supplied premises; coefficients are learner proposals. Atom conservation is necessary, not evidence of reaction occurrence, rate, yield or a unique product mixture. All species here are neutral; ionic charge balancing is handled in the linked lesson.

Supplied reaction skeleton: Methane with supplied complete-combustion products packet

Reset keeps your prediction, captures and practice history.

Change amounts while keeping each formula fixed

Carbon dioxide and gaseous water are supplied products. Balancing does not establish ignition, rate, extent or actual product composition.

Build the four coefficientsReactant: CH₄(g)Reactant: O₂(g)Product: CO₂(g)Product: H₂O(g)

Switching skeleton retains the four amounts for its newly labeled species. Reset restores the initial proposal; captures, writing and first practice responses remain.

1 CH₄(g) + 1 O₂(g) → 1 CO₂(g) + 1 H₂O(g)

Element	Reactant contributions	Product contributions	Right minus left
C	1 + 0 = 1	1 + 0 = 1	0 balanced
H	4 + 0 = 4	0 + 2 = 2	-2 mismatch
O	0 + 2 = 2	2 + 1 = 3	1 mismatch

Atom budgets: not equal. Every named participant included: yes.

Sources and limits

OpenStax Chemistry 2e §4.1: writing and balancing equations supports coefficient/formula and conservation conventions. These original exercises and diagrams are not measurements. The 0–4 bound is an interface practice limit, not a bound on chemical coefficients. The carbon-mixture counterexample is an algebraic consequence of the supplied skeleton, not a claim about an experiment.

Repair the element budgets.

Changing coefficients changes amounts, not chemical identities. A zero coefficient omits a named participant. The two-carbon-oxide packet admits more than one primitive positive ratio.

Observation to attach to a capture

Captures retain four proposed coefficients and replay independent element budgets for the supplied skeleton. Balanced proposals are not measured product mixtures or evidence of reaction occurrence.

Understand

Try: change amounts, not identities

Methane is CH₄: each molecule contains one carbon and four hydrogen atoms. Writing 2 CH₄ means two such molecules, with two carbons and eight hydrogens. Changing CH₄ to CH₂ would change the substance, not merely its amount. Keep formulas fixed and edit the four coefficients above.

Predict and repair each budget

For CH₄ + O₂ → CO₂ + H₂O, the initial coefficients 1:1:1:1 give hydrogen counts 4 and 2, and oxygen counts 2 and 3. Repair hydrogen with two waters; then oxygen needs two O₂. The resulting 1:2:1:2 ratio balances carbon, hydrogen and oxygen separately. These are relative molecular or molar amounts, not equal masses.

Double every coefficient to 2:4:2:4. All budgets remain equal, but the represented amount doubles. Dividing the common factor restores the primitive whole-number ratio. Zero equals zero also passes arithmetic; the empty equation represents no reaction. A zero product coefficient removes that product from the proposed skeleton.

Apply: independent construction

Now build Fe₂O₃ + CO → Fe + CO₂. Start with the iron budget, then reconcile carbon and oxygen together. The supplied product identities are premises: these balances do not establish reaction conditions, rate or yield. This is a symbolic exercise, not a practical procedure.

Understand: balance can leave a choice

For a C + b O₂ → c CO + d CO₂, carbon gives a = c + d, and oxygen gives 2b = c + 2d. Each letter is a whole-number coefficient, not an atom label. Find two positive primitive solutions within the controls. Capture them and compare the CO/CO₂ ratio. One solution is 3:2:2:1; a second is 4:3:2:2. Neither is an overall multiple of the other.

The supplied skeleton leaves the product mixture underdetermined. Balancing alone cannot decide which composition is observed; conditions and product evidence are needed. Even a uniquely balanced skeleton does not establish that the reaction occurs. A failed search within coefficients 0–4 would only exhaust this interface range, not prove chemical impossibility.

Transfer and continue

Explain why independently counting every element is stronger than checking the total number of atoms. Test the unfamiliar A₂/B₂ practice, then connect coefficient construction to net ionic cancellation: identical species cancellation is a separate operation, and ionic representations must also conserve charge.

Sources and boundaries

OpenStax Chemistry 2e §4.1 explains fixed formulas, coefficients and element conservation. The displayed diagrams and product-mixture exercise are original symbolic teaching constructions. All listed species are neutral; ionic charge and redox balancing require additional bookkeeping. Notebook prose and captures support later review, not automatic verification of an explanation or independent mastery.

Recognize combustion as electron accounting too

In the stipulated complete methane combustion, carbon changes oxidation number from −4 in CH₄ to +4 in CO₂, while oxygen changes from 0 in O₂ to −2 in the products. Carbon is oxidized and oxygen is reduced. Hydrogen stays +1. Thus the balanced combustion equation is also a redox representation, even though no free electrons appear in the net equation. Complete hydrocarbon combustion yields CO₂ and H₂O; incomplete combustion can have other products and is not described by silently reusing those same coefficients.

Changed formula: Construct complete ethane combustion from C₂H₆, O₂, CO₂ and H₂O. Count carbon and hydrogen first, then oxygen.

Check coefficients and oxidation changes

2 C₂H₆ + 7 O₂ → 4 CO₂ + 6 H₂O. Each carbon's formal assignment in ethane is −3 and becomes +4; four carbon atoms lose 28 electron equivalents in total, matched by fourteen oxygen atoms gaining two each. Coefficients conserve material and formal electron accounting; they do not establish yield, reaction rate or a safe experiment.

Reaction classes and oxidation numbers, checked 31 October 2026.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain coefficient versus subscript, primitive ratio versus represented amount, and why atom conservation alone cannot establish occurrence or select the carbon-oxide mixture. Identify the additional evidence needed.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Plan reaction extent when reagent supplies have bounds Next: Construct a net ionic change without deleting matter

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.