What our models of structure leave out

Why would a chemist keep a model they know is wrong? Plenty of school labs have one: a plastic water molecule, a red ball and two white balls, joined by two grey sticks. The tempting answer is that the model is right, only bigger than the real thing. But a real molecule has no sticks: the bond is a shared pair of electrons. The real atoms overlap instead of sitting apart, and the model is more than a hundred million times too big. What the model does get right is the shape. Water is bent, not straight, and the plastic model shows that at a glance, which is why it stays on the shelf.

Every picture of a structure is a model, a simplified version that gets some things right and leaves others out. Four kinds come up for structures. Dot-and-cross diagrams, ball-and-stick models, two-dimensional drawings and three-dimensional drawings. Here are all four for one substance, sodium chloride. In every one of them, the spheres marked plus and minus are ions: sodium ions and chloride ions. The signs are their charges, not protons and electrons. A dot-and-cross diagram shows where each electron came from. It shows one pair of ions, so it leaves out the lattice that keeps going in every direction. It also leaves out the shape. And every electron is identical: the dots and crosses only record which atom each one came from. A ball-and-stick model shows the arrangement in three dimensions, so you can see each ion's six neighbours. But it shows sticks that are not there, and big gaps where the ions in a crystal are packed close together. A two-dimensional drawing shows the alternating pattern clearly, and it is quick to count. It leaves out the third dimension, and it stops at the edge of the paper when the real pattern keeps going. A three-dimensional drawing shows the arrangement in all three directions. But the ions at the back hide behind the ones at the front, so it is harder to count. Judging models like this is part of both the Foundation and the Higher papers. Three statements about the ball-and-stick model of sodium chloride. The first: it shows the ions in three dimensions. The second: it shows sticks that do not exist. The third: it shows which ions are positive. Which of those three is a limitation of the model? The sticks. A real lattice has no sticks: the attraction between oppositely charged ions acts in every direction. The other two are things the model gets right.

Questions on models ask for something precise: an advantage of one model over another, or a limitation of one. An advantage of model A is something A shows that B does not. Its sentence shape is: the ball-and-stick model shows this, which the dot-and-cross diagram does not. Methane is drawn both ways: a dot-and-cross diagram on paper, and a ball-and-stick model with four hydrogens round a carbon. Keep that sentence frame in mind for this one. What is one advantage of the ball-and-stick model over the dot-and-cross diagram? It shows the three-dimensional shape of the molecule, with the four hydrogens spread out round the carbon instead of flat on paper. Now three answers a student might give instead. It shows the structure. It shows the arrangement of the atoms. It shows the relative sizes of the atoms. All three are true of the model. So why does each one earn nothing? Because a dot-and-cross diagram of methane shows every one of them too, even drawing each hydrogen smaller than the carbon. A feature both models show is not an advantage of either. So run a two-column check before you write. Tick the feature against both models, and if both columns tick, cross it out. One examiner's report on a Higher paper says: "The question asked for an advantage of the ball and stick model; those answers which referred only to a disadvantage of the dot and cross diagram did not gain credit." It goes on: "Answers that did not gain credit included the idea that the ball and stick model shows: the structure, both do." The list continues: "the arrangement of atoms, both do; the relative sizes of the atoms, both do." In plain words, students wrote about the wrong model, or named a feature both models share. The fix is the sentence shape: the model you were asked about shows this, which the other does not.

The same skill works on two models of a lattice. Model A is a flat grid of circles marked plus and minus. Model B is a three-dimensional ball model of sodium chloride. A student writes: A shows the protons and electrons, B shows the atoms in 3D. There are two jobs here, and they are separate ones. Pick one thing each model shows that the other does not, then correct the student. A shows every ion at once in two dimensions, quick to count. B shows the arrangement in three dimensions, with each ion's six neighbours. The correction: A shows positive sodium ions and negative chloride ions, not protons and electrons. B shows the ions in 3D, not atoms. One more feature to check is size. A real chloride ion is almost twice as wide as a sodium ion, so a model with equal circles leaves out the relative sizes. A report on a Higher paper records the same slip: "Many referred to atom, molecule or subatomic particle instead of ion". It adds that some students thought the charges "meant the spheres were protons and electrons." The plus and minus were read as particles instead of charges. The habit to build is to call every sphere in an ionic model an ion, with its charge.

A limitation always names a real feature the model gets wrong. Saying it is only a model earns nothing, because it names no feature. Three claims about a ball-and-stick model of sodium chloride. The sticks are not really there. The ions are held in fixed positions. There is empty space between the balls. One of the three is not like the other two. Which claims are limitations of the model, and which is true of the real substance? The sticks and the empty space are limitations. Real ions are held by attraction in every direction, and they are packed close together. The fixed positions are true. In a solid lattice the ions do stay in place, so the model gets that right. And a molecule drawn flat is flat only because the paper is. Real molecules have a shape in three dimensions. When this is set on a giant ionic structure, sodium chloride is the example to have ready. When it is set on a molecule, the same two-column check works.

Four questions to finish, and the plastic water molecule comes back for the last one. What makes an answer an advantage of model A over model B? It names something A shows that B does not show. Here's a student comparing two drawings of sodium chloride. The 2D drawing is better because it shows the ions. Does that earn credit? No. The 3D drawing shows the ions too. An advantage of the 2D drawing is something only it shows, like every ion visible and quick to count. Now a model of a molecule this video has not judged. What does a dot-and-cross diagram of ammonia leave out about the real molecule? It is flat, so it leaves out the real three-dimensional shape of the molecule. One more, on the shelf where the video began. The plastic water molecule: what does it get right, and what does it get wrong? It gets the bent shape right. It gets the bond wrong, because there are no sticks, only shared pairs, and it is more than a hundred million times too big.

That brings the chapter's drawings back in to be judged, from the dot-and-cross to the lattice. If you fully understood it, one tap on the thumbs up crosses it off for good. If not, save it. Ideas about models often land on a second viewing, once the diagrams themselves feel familiar.

That completes our chapter on Bonding: ionic, covalent and metallic. Next chapter: Structure and the properties of materials. Hopefully that's next in your feed, but if not, search for ScholaFly C H oh five, oh oh.

Every other video is on scholafly.com too, easy to search by video code or by keyword. Whatever you're revising, go there and have a look, or, watch the next video.