Water Should Be a Gas

Molecules that are not stuck to one another do not make a liquid. What holds hydrogen sulfide together as a liquid, down at −60 °C, is a faint, flickering attraction that every molecule has for every other: the electrons on one side of a molecule momentarily bunch up, the electrons on its neighbour lean away, and for an instant the two are pulled together. Bigger molecules with more electrons feel more of it, which is why the heaviest cousin, hydrogen telluride, stays liquid up to −4 °C while the lighter ones boil away colder.

Water is the lightest of the four, with the fewest electrons, so it should have the least of that attraction and boil coldest of all. The three cousins point in a straight enough line, and the line reaches water at about −80 °C. Whichever way you draw it, the answer is a gas at any temperature you have ever stood in. The measured answer is 100 °C, and FIG 1 shows the gap. This page is about what fills it.

Look at the cousins first, because they are the simple case. Hydrogen sulfide, selenide and telluride are all bent, and bent at almost exactly a right angle: 92°, 91°, 90°. That number is not an accident of chemistry. It is a fact about the shape of the electron waves the central atom bonds with. The waves an atom uses to hold its neighbours come in two shapes: a round one, and a dumbbell with a direction. Dumbbells come in threes at right angles to one another, and a big, lazy atom like sulfur bonds with two of them as they are. Two dumbbells at right angles: two bonds at right angles.

Oxygen is small, and in a small atom the round wave and the dumbbells lie close enough in energy to mix. Mix a little of the round wave into each dumbbell and the two bonds lean apart, opening from 90° towards the corners of a pyramid, and they stop at 104.5°. The four electrons oxygen keeps for itself are pushed to the far side by the same mixing, into two lobes behind the oxygen. Those lobes are negative, because they are electrons; the hydrogens, whose one electron each has been pulled toward the greedy oxygen, are left slightly positive. FIG 2 lets you do the mixing yourself. Water’s angle is the readout.

Now bring a second molecule in. Its hydrogen is tiny, positive, and has nothing to shield it: it is very nearly a bare proton, because its one electron has been pulled toward its own oxygen. So it can get closer to the negative lobe on a neighbour than any other atom could, and the two pull on each other. That pull is the extra attraction, and it is worth about a fifth of an electron volt.

Price it against two things you can picture. The bond holding the hydrogen to its own oxygen is twenty times stronger, so molecules do not fall apart when the pull breaks. The shove of heat at room temperature is eight times weaker, so the pull does not break by accident either, although it breaks and re-forms constantly all the same. Chemists call it a hydrogen bond, and the name is worth using only once you have seen the prices, because the word bond suggests something twenty times sturdier than this is. FIG 3 puts the three energies on one axis.

The cousins have hardly any of it. Sulfur is bigger and less greedy, so its hydrogens are less positive and its spare electrons more diffuse; hydrogen sulfide makes only feeble versions of the pull, and boils at −60.

One molecule can hold four neighbours: two by its hydrogens, and two by its lobes. In the liquid those holds break and re-form about a hundred billion times a second, but at any moment nearly all four are made, and the whole liquid is one flickering network. To boil, a molecule has to leave the network, which means breaking the holds it owns. Each hold is shared between two molecules, so each molecule owns two, and the energy it takes to boil a molecule of water is, near enough, the energy of two hydrogen bonds. That is the hundred and eighty degrees.

Cool the liquid instead. Every hold gets made at once, and four holds pointing to the corners of a pyramid make a scaffold with rooms in it, open hexagonal rings stacked up with channels running through them. A scaffold with rooms in it takes up more space than the crowd it was built from: the same mass of ice fills nine per cent more room than the liquid, so ice is lighter than water and floats. Lakes freeze from the top down, and everything living underneath is insulated by its own roof.

A ball-and-stick model of water is two sticks at 104.5° because somebody measured 104.5° and set the sticks. It has to be told the angle. It has to be told there are two lobes behind the oxygen, and where they point. It has no reason the cousins should differ from water at all. The wave picture has to be told nothing: dumbbells sit at right angles, so the cousins are bent at right angles; oxygen’s round wave mixes in, so its bonds open to 104.5° and its spare electrons are pushed behind; the lobes are negative and the hydrogens positive, so a neighbour’s hydrogen has something to hold; four holds at the corners of a pyramid, so the solid is a scaffold and floats. Every fact on this page is downstream of the shape of a standing wave.

And there is one more wave in the story that this page has left alone. The hydrogen in that pull is a wave too, and a wave cannot sit still; it jiggles even at absolute zero, exactly as the electron in the ground state cannot fall to the bottom of its well. Make that hydrogen twice as heavy, changing not one of the forces, and water freezes four degrees warmer. That is the next page.