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Bright Minds. Chemistry Chemistry course pack
Instructor toolkit · Draft for review

The concept dependency graph.

Which concepts depend on which — so a guide knows what must be mastered before a student moves on, and where a gap will cascade.

Draft for review

This is a working draft for Leslie's review. The dependency edges below are a first pass — the diagram and the prerequisite table are the parts to check hardest, since they drive hold-vs-advance decisions.

The course map shows the eight units as a spine — atoms first, electrochemistry last. But the real prerequisite structure isn't a straight line: it's a directed graph. Chemistry is more strictly cumulative than most subjects — bonding needs atomic structure, stoichiometry needs bonding, equilibrium needs both energy and the mole. A weak concept early doesn't just lower one grade, it cascades into everything downstream that needs it. This page is the map a guide uses to find the concept that's actually blocking a stuck student.

The dependency graph

An arrow means “must be mastered first.” Units 05, 06, and 08 each pull from two upstream units — those are the cascade points where one soft prerequisite quietly breaks several later units.

The chemistry concept dependency graph A directed graph of the eight units. Atomic Structure feeds Chemical Bonding, which feeds both Stoichiometry and States of Matter; Stoichiometry and States of Matter feed Thermochemistry; Stoichiometry and Thermochemistry feed Kinetics & Equilibrium; Thermochemistry feeds Acids & Bases; Kinetics & Equilibrium and Acids & Bases feed Electrochemistry. 01Atomic Str. 02Bonding 03Stoichiom. 04States/Gas 05Thermochem. 06Kinetics/Eq. 07Acids/Bases 08Electrochem.
When a student stalls, read the arrows backward — the visible symptom is usually downstream of the concept that’s really broken.

Prerequisite gating

A unit unlocks when its prerequisites are mastered — demonstrated, not merely seen. "Covered in class" is not the gate; a cleared rubric is. The difference matters most at the cascade points, where a soft prerequisite quietly breaks two or three later units.

UnitMust have mastered first
01 Atomic Structure— (entry point)
02 Chemical Bonding01 (electron configuration, periodic trends)
03 Stoichiometry02 (formulas & balanced equations depend on bonding)
04 States of Matter & Gas Laws02 (intermolecular forces depend on bonding)
05 Thermochemistry03 (mole/energy bookkeeping) + 04 (kinetic-molecular energy)
06 Kinetics & Equilibrium03 (mole ratios) + 05 (energy & spontaneity)
07 Acids & Bases06 (equilibrium — Ka/Kb are equilibria)
08 Electrochemistry06 (equilibrium, Nernst) + 07 (redox & proton transfer)

Gap-cascade diagnosis

When a student stalls late, the visible symptom is rarely the real problem — the broken concept is usually upstream. Trace the arrows backward. Common cascades:

Late symptomUpstream concept to check first
pH and buffer problems fall apart (Unit 07)Equilibrium from Unit 06 — an acid constant is an equilibrium constant.
Equilibrium expressions don't balance (Unit 06)Mole ratios and balanced equations from Unit 03 — not the equilibrium itself.
Cell potentials and Nernst stall (Unit 08)Free energy / spontaneity from Unit 05 thermochemistry.
Enthalpy bookkeeping goes wrong (Unit 05)Where the moles come from — Unit 03 stoichiometry.

Using the graph to plan a re-attempt

The graph turns a "not yet" into a targeted re-attempt instead of a whole-unit re-teach. When a student fails a downstream demonstration:

  1. Trace backward to the upstream node the symptom points to.
  2. Re-attempt the upstream concept first — close the gap at its source, not where it surfaced.
  3. Then re-run the downstream demonstration. Often it passes without any re-teaching of the downstream unit at all, because the cascade is resolved.

This is also where the integration guide matters: some chemistry concepts depend on an applied-math idea — logarithms for pH, proportional reasoning for the mole — from another spoke. When the upstream chemistry node looks solid but the student still stalls, check the cross-disciplinary dependency before re-teaching the chemistry.