LearnChem · Part V — Why that product and not another?
This page follows small molecules becoming big things, by joining, by gathering and by folding, across three benches.
Your hands are greasy after cooking, and plain water leaves the grease where it is. Why does a little soap take it off, when the water is the same water?
Section 4 comes back to this. First the page asks a smaller question. How does a small molecule become a big one?
Module 29 built a peptide bond. Two amino acids were joined, and the link was an amide. Module 28 supplied the attack that makes it. Module 29's bench stopped at three units, and it said so on its own face. A chain of three is not a big molecule. This page owes you the other half. First, the word for doing that one reaction many times over. Second, that a chain of such units takes a shape. The shape is where the interest lies.
A milk bottle is made of one plastic. Its name is polyethylene. It is built from one small molecule, ethene. A chain is a run of units joined one to the next. One ethene joined into that run is a unit. Nothing else goes into a milk bottle's plastic. So how long is one chain? Guess before you read on.
About how many ethene units does one chain in a milk bottle hold? Give your best guess.
Predict first. The rest of the section opens when you answer.
The count is large. One chain holds hundreds to a few thousand ethene units. The readout below builds that from one reference sample of straight-chain polyethylene, held by NIST. The sample has two different average masses, and each average gives its own chain length. So the sample is not one length. It is a spread of lengths, and one figure can only be an average over that spread.
Big means two different things on this page, and they are not the same object. One is a single big molecule. Its parts are joined, and they are no longer separate molecules. The other is a body built from many separate molecules, held in one arrangement, with nothing joined at all. Sections 2 and 3 build the first kind, a chain joined by bonds. Section 4 meets the second kind.
Diamond and silica are big, but they are bonded atoms and not joined small molecules, so they were module 9's.
Picture a chain of paperclips. Each clip is joined to the next in the same way. A longer chain is simply more clips, joined the same way. The image breaks twice, and both breaks matter. First, every paperclip is the same, and any clip will join any other. The units of a protein are not the same, and the order is the whole point. Second, a chain of clips does nothing that one clip cannot do. The point of this page is that an arrangement does something a unit cannot.
— Big can mean one molecule, or many molecules in one arrangement.
A chain is built by joining units one after another. Ethene carries a double bond. That is two bonds between the same two carbon atoms, from module 23. The double bond is what lets one ethene hold the next. Now do the bookkeeping of one joining. Ten ethene molecules go in. What comes out besides the chain?
Ten ethene molecules join through their double bonds. Ignore the chain's two ends. How many atoms are left over?
Predict first. The rest of the section opens when you answer.
Module 28 left you a sentence. The neighbour will take the electrons, and nothing is in the way. Module 29 put that to work once and made a peptide bond. A chain is that same reaction, run again on the next pair, and again on the pair after that. Nothing new happens chemically at the tenth join that did not happen at the first. This page does not re-derive the attack. It counts what the repetition costs.
The first kind of joining has a name. It is called addition. The double bond of ethene opens, and the two carbon atoms each take a new neighbour. Propene joins the same way, through its own double bond. Nothing leaves. That is the answer to the question above. It is why the small molecule ethene is the whole of the unit. LibreTexts states it plainly for addition polymers, that no atoms are lost and the units are only joined.
The second kind of joining has a name too. It is called condensation. At every join a small molecule leaves the two units and goes free. Nylon-6,6 is built from two units, adipic acid and hexamethylenediamine. Each join makes an amide link and lets one water go. That amide is module 29's peptide bond, the same reaction as module 28's attack. PET is built from terephthalic acid and ethylene glycol, and its link is an ester.
PET has two industrial routes, and the small molecule that leaves is not the same in both. By the acid route above, water leaves. By the dimethyl terephthalate route, methanol leaves at the first stage. This page uses the acid route throughout.
Here is the rule, and it is pure counting. Lay the units of a chain out in a row. Every neighbouring pair of units needs exactly one join between them. So the number of joins is the number of units minus one. Ten units in a row therefore need nine joins between them. In an addition chain nothing leaves at any of those nine joins. In a condensation chain one small molecule leaves at each of them. So ten units release nine small molecules in all.
The readout above does that same bookkeeping twice over. For nylon-6,6 it adds the ten unit masses together first. Then it subtracts the mass of the nine waters that left, one water for each of the nine joins. For ethene it adds the twelve unit masses and subtracts nothing at all, because nothing left at any join.
Two condensation chains, of six and eight units, are joined into one. How many more small molecules leave?
Doing one reaction many times over has a name. It is called polymerisation, and the long molecule it makes is a polymer. The small molecules it is built from are called monomers. You have now met joining twice. Once with nothing leaving, and once with a small molecule leaving at every join. The chemistry of the join is module 28's and module 29's. The word for doing it many times is this page's.
— One reaction, done many times, makes a long chain.
Now a harder question about the same molecule. Ethene is the whole material of two very different plastics. One is stiff. It goes into milk bottles, crates, drums and pipes. The other is soft. It goes into cling film and squeeze bottles. Nothing in the small molecule differs. Something about the chains must. A chain can carry short side chains. These are called branches.
A stiff milk bottle and a soft cling film are both nothing but ethene. Which has the more branched chains?
Predict first. The rest of the section opens when you answer.
The cling film is the more branched. Its name is low-density polyethylene, LDPE, and the density in that name is the clue. The milk-bottle plastic is high-density polyethylene, HDPE, and it has very few branches. The bench below grows seven chains for you. A unit is one small molecule in the chain, and a join is one link between neighbours. One slider sets how many units. Every number it prints is worked out from the atomic masses in its own table, to the digits shown.
Now put the two chains side by side on the bench at the same number of units. Set it to a straight chain and read the mass. Then set it to a branched chain and read it again. Compare the two masses before you answer the question below.
The density ranges above come from class-level sources, and they overlap. The sources do not even agree where the line between the two classes sits. So this page asks nothing about it. On branching, the sources agree on the order and disagree on the number. Measured lab samples of LDPE give 8 to 12 branches per thousand carbon atoms. General statements give 15 to 30. For straight-chain material the figures are 0.5 to 3, and the NIST reference resin measures 1.5. Many against few is what the sources agree on. The units are the same. Branches keep chains from lying close, which is why the density is lower.
A straight chain and a branched chain each hold exactly one thousand ethene units. Which of the two weighs more?
Cotton is the other half of the everyday pair, beside the milk bottle. A cotton fibre is about 90 percent cellulose, and cellulose is a chain of glucose units. The joining is condensation, so one water leaves at every join. Here the unit really does repeat, because every unit along the chain is glucose.
An amino-acid chain is joined the same way, by condensation, at module 29's peptide bond. But the units are not the same units. Twenty kinds go into such chains, and the order along the chain is not a repeat. So this page may not draw a protein as identical beads, and the bench does not. Its letters change from one box to the next, which is the point.
The backbone of DNA is a chain made this same way, by joining small units, and it takes a shape.
Vulcanised rubber carries sulfur bridges from one chain across to the next, and section 6 comes back to that idea.
— Same units, different arrangement, different plastic.
This page opened with soap on greasy hands. So look at a soap molecule. One end is a charged head, and a charged head sits well among water molecules, for module 8's reasons. The rest of it is a long oily tail. That tail is a plain chain of carbon and hydrogen. It offers water nothing to grip. Now add soap to plain water, a little at a time, stirring as you go. Predict what happens in the water as the amount climbs.
Soap is added to plain water a little at a time, and stirred. What happens in the water?
Predict first. The rest of the section opens when you answer.
There is a threshold, and the bench below finds it. Its left panel is a drawing of what is in the water, not a photograph. Its right panel is different. Those bars are measured values, read from a published table. They are module 14's two terms, the heat term and the term for the freedom changed. Module 14 wrote the second with a Greek delta. This page writes it T dS, which is the temperature times the entropy change.
Now the central claim of this section, and it is the one most readers get wrong. A micelle is not one molecule. It is a body of soap molecules, heads outward and tails inward. The word micelle names that body. Nothing in it is joined to anything else. Two things the bench will show you say so, and neither is a picture. Slide the amount down past the threshold and the body is gone, back to single molecules in the same water. And while the body is there, its own members leave it and others arrive in their place. A molecule joined by bonds does neither of those. It stays one molecule. The ring on the canvas is only a cartoon slice of a body that holds several dozen separate molecules.
So the arrangement is a condition, met or not met. Below the threshold the same molecules, in the same water, form no body at all. Above it a body appears, and some molecules still stay single. The readout says which side of the line your setting is on. The threshold has a name, the critical concentration. The figure on the bench is a detergent's, not a soap's. It is sodium dodecyl sulfate, about 8 mM at 25 degrees Celsius. A soap has the same kind of oily tail and a different head.
Slide the tail length and watch the threshold move. Each carbon added to the tail lowers the critical concentration by about a half. The figures are Abbott's sulfate column, from eight carbons to sixteen, at 25 degrees Celsius and low salinity. Across the first four of those steps the threshold falls from 130 mM to 8 mM. Divide 130 by 8 and the factor is 16.25. That factor is 2.008 raised to the fourth power. So the step is about twofold per carbon. Seventeen and eighteen carbons are not shown, because there the pattern breaks and the source says nothing about it.
Why does a body form at all? Not because of anything the tails do to each other. The measured heat term for moving a small alkane into a micelle interior is zero, or against the move. Read the mechanism in this order. A water molecule beside an oily tail has fewer ways of holding its four hands. The tail has no hand to hold. When the tails meet, that water goes back into the crowd. The number of ways open to the water then goes up, and module 14's two terms decide the verdict. This is module 13's method and not module 13's argument. Module 13 counted places, which side of a box a bead is on. What is counted here is the pattern of held hands. Extending an arrangement from a place to a pattern is one new idea. Module 8 priced an unheld hand in energy. This page refines that price rather than contradicting it. The hands are re-formed around the tail, but in fewer patterns than before. Module 13 also said, first and plainly, that oil and water lie outside what counting alone can settle. The right panel's bars are for butane, a four-carbon alkane and not a tail tied to a head. Its heat term is about zero, and its T dS term is about plus 21 kJ per mole. So at room temperature the count carries the move for a small oily thing like that one. For a large surface, which of the two pays is argued over, and the next block says so. One more limit. Across those three measured alkanes the gain per added carbon comes from the heat values, not from the counting ones. So it may not be carried up to a twelve-carbon tail.
Keep the amount at 5 mM. Now make the tail two carbons longer, twelve to fourteen. Is a body present?
Be clear about whose number that is. The bench's threshold is sodium dodecyl sulfate's, a synthetic detergent with a twelve-carbon tail. For a real soap the sources disagree by a factor of two. One end gives about 12 mM and the other about 25 mM. So no single figure is printed here. A soap also has a second way to have no body at all. Below its Krafft temperature it forms none. For sodium myristate that temperature is 44.9 degrees Celsius at one weight percent.
One tidy picture is often told with this, and it is disputed in print. The story says water freezes into a rigid ice-like cage around an oily group. Chandler in 2005 called that extreme view clearly incorrect, while allowing remnants of such order near small solutes. Sun in 2020 read Raman results that do not support the iceberg picture. Whether the count or the energy pays for burying a large surface is argued over too. So this page says water beside an oily tail has fewer ways of holding its hands, and stops there. It makes no claim about any ordering of the water. Module 13 set that limit first, and chemists are still arguing inside it.
Picture a ball of soap molecules with every tail turned inward and every head facing out. The drawing shows it. The image breaks three times. First, nothing joins those molecules. The drawing has no line between any two of them, and the ball is not a molecule. Second, the ball is a condition and not something the molecules carry about. Below the threshold the same molecules in the same water form none. Third, the ring drawn is a cartoon slice of a body holding several dozen. Its own members leave it and others arrive in their place. No rate for that is sourced, so none is given.
So why does soap shift the grease? Three things happen, and only one of them is the micelle. A tail that meets grease ends up in the grease, for the reason this section just gave. The charged heads are left facing the water. So the water meets a surface of heads, not one of grease. That coated droplet then goes down the drain in the rinse. Above the threshold, grease can also sit inside the tails of a micelle. Wikipedia's detergent and micelle articles carry this account. A micelle here is an arrangement, not a new molecule.
Every reading on this bench can be run the other way. Instead of an oily thing leaving water, take an oily thing going into water. Section 7 sets that as an exercise, with measured rows for alcohols. Before you compute it, predict which way the T dS term points.
— A micelle is not a molecule.
A protein is a chain of amino acids, joined as in section 3, and here it is already made. The bench below folds a toy version of one. The toy is a chain of twelve beads on a square grid. Its path never crosses itself. Six beads are non-polar, which is the oily kind. Six are polar, which is the kind water grips. A bead that touches an empty grid point stands for a unit touching water. The bench counts those touches. That score is the bench's own choice of what to count. Two toy chains can hold the same six non-polar and six polar beads in different orders. In the alternating order the two kinds take turns. In the mixed order they have no pattern.
One chain has the beads alternating, one mixed. At its best shape, which has fewer non-polar beads touching water?
Predict first. The rest of the section opens when you answer.
The same beads in two orders give different best results. The mixed order gets down to four non-polar beads touching water. The alternating order never gets below seven. The bench did not guess that. It counted all 30,073 shapes of a twelve-bead chain and took the smallest. Three orders are on offer, alternating, clustered and mixed. Notice what is not happening here. Nothing is being built. The chain is already joined, and folding is what happens to it afterwards.
Keep the toy in its place. The score counts non-polar beads touching water. That score is the bench's own assumption about a good shape. It was put in by construction, not found. The shape drawn is whichever one the view control asks for. What the bench does show honestly is how fast the count of shapes climbs. On this grid each added bead multiplies the count by something near 2.7. That is steep enough to make listing every shape hopeless very fast. A real chain has vastly more shapes than this. Note also that the factor had not settled at thirteen beads. Over the last three steps it went 2.71, then 2.73, then 2.70. So the page does not call that growth settled, and it quotes no limit.
There is a tidy rule often attached to this bench, and it is not true. The rule says non-polar in, polar out. Miller and co-workers in 1987 measured both surfaces of real proteins. About 58 percent of the buried surface is non-polar, and about 57 percent of the exposed surface is non-polar. Those are near enough the same. Folding does bury most of the surface. That is 55 percent for a small chain and 77 percent for a large one. What it buries is still 39 percent polar. So take the counting away from this bench, and leave the tidy rule behind.
One experiment stands behind the claim that a made chain finds a working shape. Module 16 said what an enzyme is. It is a large folded molecule, and the folded shape is what speeds the reaction. Anfinsen took one small enzyme in a test tube, its chain already made. He undid its shape with two chemicals. Urea makes a folded chain come apart. The second one cuts sulfur-to-sulfur links. The enzyme then stopped speeding its reaction. He took both chemicals away again. The chain took its shape back, and the speeding came back with it. Same chain, same order of units, and the job returns only with the shape. This page prints no recovery figure, because the reported figures disagree. A 2022 re-examination found that the sulfur links must re-form correctly for the shape to assemble. That reverses the order most textbooks give. Levinthal differed on another point, holding that the final shape need not be the lowest in free energy.
Levinthal put a number on the size of the problem in 1969. Take a chain of 150 residues, with the bond angles resolved to about a tenth of a radian. He counted 10 to the power of 300 shapes. That is his own figure under his own conditions. This page quotes no other, because the retellings assume different things and disagree. No chain gets through a list that long. So folding cannot be one shape after another until the right one turns up. Levinthal's own reading is that local contacts form fast and set what the rest of the chain can do. His paper gives no time for folding, and neither does this page.
Egg white holds a real, small, named protein. It is lysozyme, and its chain is 129 units long. Those 129 units are drawn from twenty kinds, in thoroughly unequal numbers. That is the plainest proof that the order along a chain is not a repeat. Four sulfur-to-sulfur links hold parts of the folded chain to other parts. The first sixteen letters of that chain are what the bench in section 3 shows you.
A folded chain is also held by hydrogen bonds, and you met those in module 8. One is a giving hand held in a taking hand, and a folded chain makes many of them at once. Which ones get made is decided by the arrangement. A hand can only be held by a hand that is near it. The shape and the grips arrive together.
Egg white in a pan is the everyday case. One conference paper followed two of its proteins as the heat went up. The heat-sensitive one begins to change at 59 degrees Celsius. The heat-resistant one gathers from about 74 degrees. Now ask what the cooked white can no longer do. It cannot dissolve, and it cannot be clear. Held at 89 degrees for twenty minutes, under a quarter of the protein was still dissolved. Cooling it puts none of that back.
Egg white is heated in a pan until it sets. What is different from raw egg white?
The backbone of DNA is likewise a chain made by joining small units, and the whole molecule takes a shape.
None of this says how life began. NASA's own answer, in July 2023, is that we do not know. Making a chain in a flask is not evidence either way, and neither is folding.
— Folding happens to a chain that is already made.
One more idea, and it is the last. A chain that is already made can be tied to another chain. A rubber band is many long chains lying against one another. A bridge means a link from one chain to the next. In rubber those bridges are made of sulfur. Nothing yet about what they do.
More and more sulfur bridges are made from one rubber chain to the next. What happens to the rubber?
Predict first. The rest of the section opens when you answer.
More bridges give a harder, less stretchy rubber. Very many give a hard and brittle solid. A bridge is not a join in a chain. It makes no chain longer. It ties one chain to the next.
This is vulcanised rubber, and it is a clean second example of bonds holding an arrangement. The sulfur bridges run chain to chain, and adding them adds no units to any chain. Put in too many and you get ebonite, a hard solid that will not melt and will not dissolve. Notice what this does to the word hold. A network like this is held together, and held firmly. But no direction through it is a simple line of units. It is joined repeatedly and sideways. The units are the same units they were. The arrangement is what the bridges fix in place.
After a permanent wave the order of amino acids in the hair is the same. What was cut and re-made?
A permanent wave in hair is exactly that idea. Hair is held in shape by sulfur-to-sulfur links between its chains. A reducing agent cuts a share of them. The hair is then set on rollers in a new shape. An oxidising agent makes the links again in their new places. Wortmann and co-workers reported in 2021 on those two steps. About 20 to 40 percent of the links are cut, and about 70 to 80 percent are made again. They also found the curl is not quite permanent. Some of the old shape comes back when the hair is heated in water. The order of the amino acids is untouched throughout. Anfinsen's enzyme had four such links, and the same ones were cut and re-made there.
Gelatin setting is one more case of the same molecules in two states, warm and liquid or cool and set.
Three ways, then, for something small to become something big. Joining, where bonds hold the units. That is addition, with nothing leaving, or condensation, with a small molecule leaving at each join. Gathering, as in a micelle, where nothing is joined at all and the water around it holds the arrangement. Folding, where one chain that is already made takes a shape, and only in that shape does its job. Bridging is not a fourth way, because it makes nothing bigger. It ties chains that are already long, and it fixes the arrangement they are in. Joining and folding give you one big molecule. Gathering gives you a body of many separate molecules. That is why the sentence at the foot says bonds are one way, and not the only way.
This page carries no line about plastics and the environment. No source was found that it could check to its own standard, so it says nothing. One question is left over instead. How does anyone know the shape of a molecule this size? The next page asks it.
— Joining, gathering and folding: three ways a small thing becomes a big one.
Modules 8, 13 and 20 meet here, on one measured row. The row is Tanford's, for moving a small alkane, {SOLUTE}, out of water and into the interior of a micelle. Its heat change, written dH, is {DH} kcal per mole. Its entropy change, written dS, is {DS} cal per kelvin per mole. The temperature is {T} K, where K is the kelvin of modules 13 and 20. The table itself states no temperature, and this is the value its own columns need. Take one of module 8's hands as {HAND} kJ per mole, given here and not looked up. T dS means the temperature times the entropy change, and dG, the free energy change, is module 14's referee. R is the gas constant, 8.3145 joules per kelvin per mole, which is module 13's letter. Three things to hold on to before you start. The ways being counted are the ways of the whole transfer, and not of the water alone. The row is for a small free alkane, not for a tail tied to a head. And the trend per carbon across the three rows may not be carried up to a twelve-carbon tail. That gain comes from the heat column falling, not from the entropy column growing. One calorie is 4.184 joules.
1. Multiply the entropy change by the temperature. Then convert the result to kJ per mole, which means times 4.184 and divide by 1,000. Give T dS.
2. Now set T dS against the heat change, both in kJ per mole. Work out the heat term minus T dS, and say what sign it has.
3. Module 13's method next. The entropy change per mole is R times the natural log of the ratio of ways per molecule. So the ratio is exp of the entropy change in joules per kelvin per mole, divided by R. Give that ratio to two significant figures.
4. How many of module 8's hands is the T dS term worth? Take one hand as the figure given above. One decimal place.
5. No box for this one. A water molecule has two giving hands and two taking hands. Beside an oily tail, which kind is left unheld? And why does module 8 say an unheld hand costs energy?
Notice which of the two terms won here, and by how much. The T dS term outweighs the heat term, so the difference between them comes out negative. At room temperature it is therefore the count that makes this move go, not the heat. That is module 13's method, run through module 14's two terms, in module 20's own units. And the ratio of ways is not a near thing at all. It is large.
A chain of {N} units of {CASE} is made by condensation, from the unit masses listed below it. Work out how much water has left the units, and what the finished chain weighs.
6. How many water molecules have left in all? A whole number.
7. What does the whole chain weigh, in grams per mole? Use the unit masses listed above and the mass of water.
The rule you used here was one water leaving at each join of the chain. A chain of a given number of units has one fewer join than it has units. So the count of waters that left is that number of units minus one, every time.
The same reading, run the other way. This row is measured for dissolving the alcohol {NAME}, taken from its pure liquid into water at 25 degrees Celsius. Its free energy change, dG, is {DG} cal per mole. Its heat change, dH, is {DH} cal per mole. Its entropy change, dS, is {DS} cal per kelvin per mole. The temperature is {T} K. The direction matters here. It runs from pure liquid into water, which is the reverse of the alkane row above. It comes from the same author as that alkane table, so this is one source and not two. Predict the sign of the heat term before you compute anything. One warning about the arithmetic. These rows reproduce their own printed free energy to within a few calories, and not exactly. So compare the two values rather than expect a match. Where an oily part goes into water, the water beside it has fewer ways of holding its hands.
8. From the sign of the heat term, does this dissolving give out heat or take it in?
9. Compute T dS in calories per mole, from the entropy change times T.
10. Compute the heat term minus T dS. Then compare your answer with the free energy printed in the row.
11. From the sign of the free energy, is this dissolving uphill or downhill?
12. No box for this one. Which of the two terms makes it uphill? And what does that tell you about the water beside the alcohol's oily part?
The recomputed free energy and the printed one are not the same. The line above prints what is left over rather than claiming they close. The rule you built on butane leaving water predicts this mirror case correctly. The T dS term is the one carrying the sign.
Bonds are one way to hold small molecules together; their arrangement decides what the big thing does.