Build phase cartoons while conserving intact molecules

Start with a conserved sample

The sample contains four identical AB molecules. Each molecule has one A atom and one B atom joined by a bond. Every requested drawing must retain four molecules and eight atoms. Moving molecules apart does not create new molecules; changing the phase name does not break the A–B bonds.

Use the site checkboxes to build your own arrangement. The site menu is a bounded scaffold, not a physical lattice imposed on every phase. The axes use the same arbitrary distance units in every target. Drawings represent separate samples under appropriate phase conditions; no common temperature or pressure is specified.

Construct three spatial patterns

For the crystalline-solid cartoon, find four nearby sites that form a square. The independent count check should pass, and the geometric ledger should show four equal side distances and two diagonals √2 times a side. This is one small regular motif, not evidence of a whole three-dimensional crystal.

Next keep four molecules but replace one square corner with the displaced nearby site. The count should still pass, while the exact-square check fails. The liquid target requests this kind of compact disordered cartoon. A liquid can have local order; the task rule simply asks you not to repeat the exact square motif.

Finally move the same four molecules to widely separated sites. The gas target requires every pair at least four diagram units apart. This is an illustrative spacing rule, not a threshold that classifies real gases. Real gas molecules can temporarily approach closely during collisions, and a real diagram would need many more molecules and a much larger spacing-to-size ratio.

Inspect the arithmetic instead of trusting appearance

For four molecules there are 4×3/2 = six distinct center pairs. The ledger lists every one. Compact means the largest pair separation is at most two diagram units in this task; dispersed means the smallest is at least four. These checks are independent of the molecule count.

A small pair of occupied sites may be compact but still fail the four-molecule budget. Conversely, selecting every site preserves the fact that each symbol is an AB molecule but doubles the supplied molecular inventory. Repair the wrong count before calling a spatial pattern a representation of the given sample.

One possible set of constructions

Sites 1, 2, 3, 4 form the compact square. Sites 1, 2, 3, 5 form a compact disordered alternative. Sites 1, 6, 7, 8 form a dispersed arrangement. These examples expose task solutions; subsequent use is practice. Other compact disordered subsets can also satisfy the drawing constraints.

Challenge a picture that seems conclusive

Keep your compact disordered drawing unchanged and select the amorphous-solid target. The same geometry can satisfy both liquid and amorphous-solid cartoons. An amorphous solid lacks extended periodic order but does not undergo the liquid’s continual neighbor rearrangement. Geometry alone cannot decide between them.

For a crystalline solid, explain vibration about relatively fixed molecular sites. A static picture does not imply motion stops. For a liquid, explain translation and changing neighbors while molecules stay close. For a gas, explain motion between collisions through the available volume. These are required written explanations, not velocities computed from your selected positions.

The task does not establish that solid and liquid densities are identical, that every solid is denser than its liquid, or that a gas always has the highest temperature. No physical density, phase boundary, time scale or speed is supplied. The automated checker evaluates only declared count and geometric constraints; it does not grade your motion explanation or award mastery.

Compare occupied volume and motion without assuming equality

For a fixed amount of a substance, solid and liquid molar volumes are often similar because particles remain close in both phases. Similar does not mean equal: packing changes can even make a particular solid less dense than its liquid. Gas spacing is much larger under ordinary dilute conditions. At fixed particle number and temperature, decreasing available gas volume increases number density and generally raises the frequency of wall encounters; at fixed volume, higher temperature increases typical speeds. Collisions and free motion allow a gas to occupy its container rather than preserve a fixed shape or volume.

Changed claim: A drawing shows the same six intact molecules in two close-packed arrangements. Does that establish equal densities? If the gas drawing is compressed while molecule count stays six, has molecule size or number necessarily changed?

Check what the drawing omits

Equal count and qualitative close packing do not determine an exact physical volume, so equal density is not established. Compression changes the available sample volume and spacing, not necessarily the size or number of molecules. A physical scale, phase conditions and motion model would be needed for quantitative density or collision-rate claims.

Transfer beyond the site menu

On paper, draw six intact AB molecules in a compact disordered arrangement. State how many A atoms, B atoms and distinct molecule pairs there are, then sketch two successive frames to distinguish liquid neighbor exchange from bounded motion in an amorphous solid. Explain why the frames need a time scale before they could establish a real material’s mobility.

Check the inventory transfer

There are six A atoms, six B atoms and six molecules. Distinct pairs total 6×5/2=15. The arrangement and motion explanation need separate review; these counts alone cannot establish a phase.

Return to the finite vapor-inventory model for a different question: how a supplied saturation condition partitions a finite inventory. The present construction does not calculate that equilibrium.

Sources: College Board CED, topic 3.3 and OpenStax particulate descriptions of condensed phases and gases. The eight sites, thresholds, diagram and checks are original teaching design, not measured molecular coordinates.