SCIENCE · INVESTIGATE AND EXPLAIN

Determine molecular polarity from vector evidence

Combine declared bond vectors and test how asymmetric contributions break cancellation.

Learning outcome: Compare equal and unequal dipoles in linear, trigonal-planar and tetrahedral templates. Then compare equal trigonal-planar and trigonal-pyramidal arrangements, retaining all three components.

Starting recap

Review the electron and formal-charge budget, bond multiplicity, signed interaction energies and the distinction between a model and a measured property.

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

Try

Two equal opposite unit bond dipoles sum to zero; changing the first magnitude to2 leaves a net magnitude1, although their magnitude sum is3.

Open the experiment

Predict

Does a symmetric drawing guarantee cancellation when bond-dipole magnitudes differ?

Your prediction and reason

Experiment

Compare equal and unequal dipoles in linear, trigonal-planar and tetrahedral templates. Then compare equal trigonal-planar and trigonal-pyramidal arrangements, retaining all three components.

Add bond-dipole vectors rather than magnitudes

Worked teaching model · synthetic values · Each bonded direction has outward dipole magnitude 1 except the first selected control. This explicitly stipulated vector model omits other electronic contributions. Chemical dipole-arrow conventions can differ; here all vectors use one declared outward convention. Molecular net is the vector sum, not sum of magnitudes.

Geometry template: 0 choice First bond dipole magnitude: 1 relative units

Reset keeps your prediction, captures and practice history.

Orthographic projection: bonds toward the viewer use thicker lines; dashed outlined sites are lone-pair domains. Overlap in a view does not merge sites. The table retains depth coordinates. Ideal domain directions are not measured bond angles.

View coordinates on a unit sphere; z positive toward the viewer
Site	x	y	z
bond 1	0.8660254	0	-0.5
bond 2	-0.8660254	0	0.5

Actual stipulated dipole components on unrotated model axes, not the camera coordinates above
Contribution	x	y	z
bond 1	1	0	0
bond 2	-1	0	0

The geometry diagram shows unit bond directions, not dipole magnitudes. Use these weighted components and the net ledger to compare cancellation.

Axes rescale. Connected samples represent the supplied continuous parameter relationship; stems denote discrete pairs or steps, not a time trajectory.

Numerical plot coordinates

unordered bonded pair index	ideal angle (degrees)
1	180

Calculated evidence under the declared representation
Quantity	Value	Unit
Total electron domains	2	domains
Bonded atoms	2	atoms
Lone-pair domains	0	domains
Smallest ideal bond angle	180	degrees
Largest ideal bond angle	180	degrees
Net dipole x	0	relative units
Net dipole y	0	relative units
Net dipole z	0	relative units
Net dipole magnitude	0	relative units
Sum of dipole magnitudes	2	relative units

AX2 linear

Components use the unrotated model axes; the diagram camera changes their appearance, not the vector sum. Equal symmetric bond contributions can cancel; unequal magnitudes break that cancellation. Lone-pair electronic contributions are not separately computed, so this is a declared bond-vector model, not an ab initio molecular dipole.

AX2 linear

Observation to attach to a capture

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

Understand

A polar bond does not settle the molecular question

Each bond can contribute a directional dipole, but the net molecular moment is a vector property. Equal opposite contributions cancel; unequal contributions do not. CO2 provides the familiar qualitative cancellation idea, whereas a bent arrangement can retain a resultant even with equal bond magnitudes. Chemical identity, structure and electron distribution all matter.

Declare the convention

This workbench assigns outward unit vectors from the central atom and stipulated magnitudes. It does not infer real bond dipoles from electronegativity. All vector arrows use the same declared convention, avoiding confusion with chemical arrow conventions that may point toward an electron-rich end. Reversing every vector convention reverses the resultant direction but not whether its magnitude is zero.

Add components before magnitudes

For the linear template, vectors of magnitude2 in+x and1 in−x sum to+x with magnitude1. Adding magnitudes would give3 and erase the cancellation. Three equal planar directions at120° also sum to zero. Four equal tetrahedral directions sum to zero because each coordinate appears twice positive and twice negative.

Remove a symmetric contribution

Three of the four equal tetrahedral directions have a sum opposite the missing fourth vector, with unit magnitude. Thus the supplied trigonal-pyramidal model does not cancel. Two tetrahedral directions sum to magnitude2/√3≈1.1547. These are results of the declared ideal vectors, not calculated experimental moments of ammonia or water.

Test an asymmetry

In a trigonal plane with two unit contributions and a first contribution of2, the sum equals one additional copy of the first unit vector. Its magnitude is1. Symmetric nuclear geometry was not enough to cancel unequal contributions. The model also omits a separate lone-pair electronic moment and distortion of the structure by substitution. It is a controlled representation test, not a complete electronic calculation. A transfer explanation should state what is held fixed before using cancellation to infer a chemical property.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Molecular polarity. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.

Apply

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

What electronic contributions or structural changes are omitted by a simple bond-vector sum?

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: Rotate a domain model without changing its molecular shape Next: Audit sigma, pi and hybrid descriptions without literal orbital machinery

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.