SCIENCE · INVESTIGATE AND EXPLAIN

Carry named entities through mass and mole conversions

Treat the specified entity as part of an amount-of-substance calculation, not an optional label.

Learning outcome: Hold sample mass 4 g while comparing AB2, A2B3, AB3. Then double mass for one formula. Capture amount and count ledgers, and write unit-canceling chains for each.

Starting recap

Use algebra and dimensional consistency; distinguish a measured reading, a model estimate and the evidence needed to accept the model.

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

Try

For 4 g of fictionalAB2 with M=40 g/mol, there are .10 mol formula units, .10 mol A atoms and .20 mol B atoms.

Open the experiment

Predict

Does .10 mol AB2 imply .10 mol total atoms?

Your prediction and reason

Experiment

Hold sample mass 4 g while comparing AB2, A2B3, AB3. Then double mass for one formula. Capture amount and count ledgers, and write unit-canceling chains for each.

Convert mass to defined entities

Worked teaching model · synthetic values · Fictional atomic molar masses A20 and B10 g/mol are exact assigned values. The solid consists of formula units, not necessarily discrete molecules. Avogadro constant 6.02214076×10²³ mol−1 is exact in SI; sample mass is treated as exact only for this model.

Sample mass: 4 g Formula selector:1=AB2, 2=A2B3, 3=AB3: 1 index

Reset keeps your prediction, captures and practice history.

Conditional calculations; not physical measurements
Quantity	Value	Unit
Formula molar mass	40	g/mol formula units
Formula-unit amount	0.1	mol
A atom amount	0.1	mol A atoms
B atom amount	0.2	mol B atoms
Formula-unit count	6.022141e+22	formula units
Total atom count	1.806642e+23	atoms

The entity named after mol is part of the calculation.

Mass divided by molar mass gives formula-unit amount. Multiply by formula subscripts for atom amounts, and only then by Avogadro constant if a count is requested. Subscripts do not multiply the original sample mass.

Predict before changing controls, retain contrasting captures, and explain a changed case. Displayed digits are computational precision, not an uncertainty claim. Flags check stipulated numerical compatibility, not identity, reasoning quality or practical proficiency.

The entity named after mol is part of the calculation.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

A mole must name its entity

Amount of substance is not simply a large number of unspecified objects. One can count atoms, molecules, ions or formula units, and the same sample has different counts for these different entities. A solid formula unit is a compositional accounting unit; calling it a molecule would imply a discrete structural unit that may not exist in an extended ionic solid.

Build the dimensional chain

For the fictional element masses A = 20 g/mol atoms and B = 10 g/mol atoms, AB₂ has molar mass 40 g/mol formula units. A 4 g sample gives 4 g × (1 mol formula units / 40 g) = 0.10 mol formula units. Each unit contains one A and two B atoms, so atom amounts are 0.10 mol A and 0.20 mol B. Total atom amount is 0.30 mol, not 0.10 mol.

Distinguish amount from count

The SI Avogadro constant is exactly 6.02214076 × 10²³ mol⁻¹. Multiplying 0.10 mol formula units by this constant gives 6.02214076 × 10²² formula units in the stipulated exact model. Total atom count is three times larger. The exact definition does not make a balance reading, sample purity or atomic-mass estimate exact. Those are separate inputs.

Change formula without changing sample mass

At the same 4 g mass, A₂B₃ has molar mass 70 g/mol, so formula-unit amount is 4/70 mol. Its atom amount is five times that value. AB₃ instead has molar mass 50 g/mol and four atoms per formula unit. Predict which gives the greater total atom count before inspecting the ledgers; comparing subscripts alone ignores the different formula masses.

Test extensivity

Double sample mass while keeping formula fixed. Formula-unit amount, every atom amount and every count should double. Molar mass and atom-to-formula ratios should remain unchanged. Explain which quantities are extensive and which are conversion relationships. A model that doubles molar mass when sample mass doubles has confused a property of the substance with an amount of material.

Transfer and assumptions

For a new 7 g A₂B₃ sample, compute 0.10 mol formula units, 0.20 mol A atoms and 0.30 mol B atoms. If the sample is only 90% A₂B₃ by mass, the original calculation cannot be used unchanged: the relevant compound mass is 6.3 g, and the impurity composition determines any additional atom counts. State the purity assumption rather than hiding it inside arithmetic.

Source and evidence boundary

These explanations, calculations and diagrams are original. Conceptual references checked 30 October 2026: NIST mole definition, OpenStax dimensional calculations. The linked textbook is a reference, not copied lesson text or imagery. All displayed datasets are synthetic teaching packets. Saved numerical agreement or prose is not a performed practical, independent reasoning review or laboratory certification. No handling, heating or chemical preparation procedure is requested.

Apply

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

Explain what the exact Avogadro constant does not make exact about a measured sample.

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: Separate sample spread from accuracy and common bias Next: Solve a composition balance and reject impossible mixtures

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.