The Mastery of Matter

The History, Logic, and Practice of Chemistry

By William P. Green, Ph.D.

The Mastery of Matter

The History, Logic, and Practice of Chemistry

By William P. Green, Ph.D.

© 2010 by William P. Green

This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this

license, visit http://creativecommons.org/licenses/by/3.0/ or send a

letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.

TABLE OF CONTENTS

UNIT 1: The Nature and History of Chemistry

Chapter 1: Beginnings

Section 1: Ancient ChemistsSection 2: Early Ideas About MatterSection 3: The Alchemists

Chapter 2: Modern Chemistry

Section 1: La revolution chimique.Section 2: The Return of the Atom

Chapter 3: The Big Picture

Section 1: What can we learn from the history of chemistry?Section 2: Defining Science and Chemistry

Chapter 4: Measurement

Section 1: The Basics of MeasurementSection 2: The SI System of Measurement

Chapter 5: Uncertainty in Measurement

Section 1: Introduction to UncertaintySection 2: Calculating With UncertaintySection 3: Drawing Reasonable Conclusions from our MeasurementsSection 4: Significant Figures.

Chapter 6: Problem Solving and Unit Conversion

Chapter 7: A Tour of the Elements

Section 1: DiscoverySection 2: Organizing Matter.Section 3: The Element Families

Chapter 8: The Modern Atom

Section 1: Dalton's Atom

Section 2: Dalton's MassesSection 3: Dividing the Indivisible

Chapter 9: The Strange Behavior of the Atom

Section 1: RadioactivitySection 2: Fission and Fusion

Chapter 10: The Stranger Electron

Section 1: IonizationSection 2: The Birth of Quantum MechanicsSection 3: Einstein and the Particles of LightSection 4: Neils Bohr and the Quantum Mechanical AtomSection 5: Electrons in ShellsSection 6: Electron WavesSection 7: The Great Debate

Chapter 11: The Electron Zoo

Section 1: Quantum NumbersSection 2: Building an Atom From the Ground UpSection 3: The Electrical Periodic Table

Chapter 12: The Chemical Bond

Section 1: Chemical AttractionSection 2: Lewis StructuresSection 3: Drawing MoleculesSection 4: The Shapes of MoleculesSection 5: Molecular Geometry, the Easy WaySection 6: Function Follows FormSection 7: The Non-Molecules

Chapter 13: Chemical Reactions

Section 1: Physical Changes (States and Solutions)Section 2: What is a Chemical Reaction?Section 2: Types of chemical reactionsSection 3: Chemical Equations

Chapter 14: Stoichiometry

Section 1: Percent CompositionSection 2: Empirical FormulasSection 3: Mass Relations in Chemical Reactions

Chapter 14: Thermochemistry

Section 1: Energy in Chemical ReactionsSection 2: Energy in Phase ChangesSection 3: Spontanaeity

Chapter 15: Gases

Section 1: Kintetic TheorySection 2: Gas LawsSection 3: Mass Relations in Gaseous Chemical Reactions

Chapter 16: Solutions

Section 1: DissolvingSection 2: ConcentrationsSection 3: Mass Relations in Chemical Reactions in Solution

Chapter 17: Reaction Rates and Chemical Equilibrium

Section 1: RatesSection 2: Equilibrium

Chapter 18: Acids and Bases

Section 1: Definitions and BehaviorSection 2: pHSection 3: Equilibria and Buffers

Chapter 19: Redox

Section 1: Redox ReactionsSection 2: Electrochemistry

Chapter 20: Organic Chemistry

Section 1: NomenclatureSection 2: Reactions

Joseph Wright, The Alchemist in Search of the Philosophers Stone, 1771

Unit 1: The Nature and History of Chemistry

Chapter 1: Beginnings

You have made him a little lower than the angels; You have crowned him with glory and honor, And set him over the works of Your hands.…

-Hebrews 2:7

From ancient times men have sought to manage and control the world around them, whether through chiseling tools of stone and bone, sewing skins with sinews, preserving meat with salt, or igniting a fire with friction or sparks. And through time, they have become more and more adept at the art and science of turning the raw materials of the world into something more useful, more valuable—something new. From the first skills of shaping clay and making fire, to making glass and extracting iron from its ore, to making gunpowder and medicines, to petroleum fuels, chemical fertilizers, pesticides, and plastics, to splitting atoms and splicing DNA, the mastery of men over their environment grew slowly at first until it exploded in the eighteenth century. The story of man’s mastery over matter is a story of lessons learned and obstacles overcome. It is a story of discovery: Men discovered the laws of nature.

In this course we are going to be learning about matter, the laws that govern it, and how we can master it. We are going to study scientists’ current understanding of atoms, molecules, and chemical reactions. But we are also going to learn about history, and about man.

Why study history? First, our current understanding has been shaped by the events of history. Whether we are studying chemistry, philosophy, or economics, it is important that we understand history. Our current understanding of economics, philosophy, or chemistry has been shaped by the events and persons of history, and can’t be fully grasped apart from that.

We can look at what people currently believe, but how do we know they are correct? Of course we can point to evidence, mathematics, and logic, but our current understanding has been shaped by people and events, just like our governmental system. In fact, it is impossible to interpret evidence apart from our unique perspective, and this perspective is the product of our history. Our history and culture have fashioned the glasses through which we view the world.

Science always tries to be as objective as possible, but it is still the product of persons, with their own personalities, world views and biases, likes and dislikes, backgrounds and blind spots. If we can understand the history, we may be better able to understand the real status of our knowledge about the world.

Secondly, we study history in order to better understand how mankind (or science) “works”. By studying how men have lived and worked in the past, we can see the consequences of their world views and ways of living. And we can learn from them. Science has not progressed in a vacuum, but in the fertile field of changing human world view. To divorce science from its history is to cut it off from its life blood.

So, we will not neglect this task. We will begin this course in Chemistry with a survey of the early history of that science, and throughout the course, you will learn the concepts and skills of chemistry in the context of history and culture. We will start by going back 3500 years, to the hills of what is now the country of Turkey.

Joseph Wright, The Iron Forge, 1772

Section 1: Ancient chemists

As for Zillah, she also gave birth to Tubal-Cain, the forger of all implements of bronze and iron…

-Genesis 4:22

A group of ancient Hittites sit around a furnace of fire around 1500 BC. An hour before, they had placed a clay pot full of black iron ore into the inferno. Within the earthen furnace, the carbon in the wood reacts with oxygen in the air to produce carbon monoxide, dioxide, and water vapor. The smoke that stings their eyes consists of these gases, plus other gaseous by-products like sulfur dioxide and nitrogen oxides, mixed with tiny droplets of condensed water vapor and particles of soot. But they are not aware of these details. They know only that they needed wood and a source of heat to get the reaction started. Once started, the reaction itself produces enough energy to start the rest of the wood on fire and smelt the iron ore that they put in the furnace in its clay pot.

Now, with the orange light from the furnace lighting up his sweating face, red with the burning heat, one of them carefully draws out the pot and dumps out a glowing sponge of molten iron. They had put in crushed black rocks of hematite mixed with charcoal, and out came this soft lump of glowing iron.

The iron had been trapped in the black sand, chemically bound to oxygen, and useless. But the carbon monoxide produced by the burning wood and charcoal tore the oxygen from the ore, and the metallic iron was free and pure, and fit for making a hammer or a sword. As the Hittite craftsmen pounded the hot lump with sledges, and glowing sparks sprayed out into the darkness, one man looked at his

old bronze knife in the glow of the fire, and frowned.

The Hittites are believed to be the first to extract iron from its ore, somewhere around 1500 BC. Pieces of iron metal found in Egyptian tombs pre-date this, but they were probably derived from pure metallic meteorites. Iron was an innovation in the field of metallurgy, which had been dominated first by copper, and then by bronze. The easiest metals to use were gold, silver, and copper, which can be found in nature in their pure metallic, or native, form.

Although copper can be found in its native form, larger quantities of it were obtained by smelting copper ore. It is thought that the most important early sources of copper ore were mines of blue-green malachite on the Sinai Peninsula. This mineral could be smelted in much the same way as the Hittites would smelt iron, by heating with charcoal. Lead could be obtained by a similar process from its dense silvery ore.

Bronze is a bit more complicated. It is an alloy (mixture) of copper and tin. Archaeologists speculate that perhaps it was discovered accidentally when some early Sumerians used copper and tin ore rocks around their fire pit. Maybe it was accidental, but maybe it was the product of some ancient genius. Whatever the case, the discovery of new metals and methods for their production revolutionized civilization by making work more efficient.

Metals revolutionized tool making, but their ores often served other purposes as well. The metal ores were often brightly colored, and the blue-green of malachite, or the bright red of weathered hematite (iron ore) served as pigments. Along with brightly colored extracts of plants (like indigo), and even insects (the bright red cochineal dye was from scale insects in the Americas), these pigments were used to color clothing or pottery.

Pottery itself represents an important example of man’s mastery over matter. If clay is heated to a high enough temperature (1200°F, 650°C) the clay particles would partially melt, fusing together so that the clay changed color slightly and became hardened like glass. Of course, primitive men did not understand the process as we do today, but they knew it well enough to do it.

Other, more advanced civilizations learned to make a kind of “pottery” that was as clear as water! The ancient Egyptians were manufacturing clear glass on a large scale as early as 1370 BC. This glass was made by melting pure quartz sand together with sodium carbonate (washing soda). It was colored by adding compounds containing copper (to make the glass green or blue) or other elements. Colorful glazes for clay pottery were made even earlier in much the same way.

Photo by Petr Kratohcvil

Aside 1MANIPULATING MATTERWhat is the difference between shaping a stone tool or making rope from plant fibers and burning wood or extracting iron from its ore? How is the first pair of actions different from the second?

All of these are important examples of ways that ancient man gained mastery over matter, and there are others we have not mentioned. Ancient men and women also used plant extracts as medicines and spices. And speaking of seasonings, I have not mentioned the commonest and possibly the oldest example of all: salt. Sodium chloride (table salt) has probably been used since the beginning, its tiny cube-shaped crystals were used to preserve and season meats and other foods. Obtaining salt from evaporated salt water is a simple but essential demonstration of man’s mastery over matter.

Raphael (1510—1511), The School of Athens

Section 2: Early ideas about matter.

It is the glory of God to conceal a matter,But the glory of kings is to search out a matter.

Proverbs 25:2

Though progress toward the mastery of matter was well underway, it appears that people did not really begin puzzling about the nature of matter until the time of the ancient Greeks. Some of the ancient Greeks thought that all things were made of water (Thales, 640-546 BC), air (Anaximenes, 560-500 BC), or fire (Herakleitos, 536-470 BC). Empedokles (490-430 BC) combined all of these and added one. He thought that there were four “roots” of matter: fire, air, water and earth. These four roots interacted with each other by attraction and repulsion.

But Democritus of Abdera (460-370 BC) had another, completely different idea, which he is believed to have learned from his teacher, Leucippus (450 BC?). He taught that the only things that exist in the universe are atoms and the void (empty space) in which they moved. The word atoms came from the Greek adjective ατομος, meaning uncuttable. These solid, too-small-to-see particles came in different shapes—round, sharply pointed, angular, which determined their properties. Bitter atoms were pointy, while sweet atoms were smooth and round, for example.

By convention sweet and by convention bitter, by convention hot, by convention cold, by convention colour: in reality atoms and void. -Democritus1

These atoms could rearrange themselves and join together with other atoms, but they themselves were never destroyed.2 This idea is beautifully captured by Leucretius, writing about Democritus ideas in a poem called, On the Nature of Things (50 BC):

So primal germs have solid singlenessNor otherwise could they have been conserved

Through eons and infinity of timeFor the replenishment of wasted worlds.3

Unlike Democritus who, as a true philosophical materialist, believed that the physical world of atoms was all that existed, Plato (427-347 BC) believed that the world we observe is not true reality and could not be understood without reference to the world of ideal “forms”. Plato was a philosophical idealist. True reality, he taught, was the world of rational ideas like perfect circles and triangles, and even philosophical ideas like justice and "good”. These were called forms. Plato taught that the four “elements” (στοιχεια, pronounced stoicheia) of matter were composed of tiny particles too small to see. In this respect he was like Democritus. But Plato’s tiny particles were formed of combinations of triangles, which determined the shapes of the tiny particles: fire, a tertrahedron, air, an octahedron, water, an icosahedron (a 20 sided solid), and earth, a cube. Plato taught that these elements could transform into one another by simply rearranging the triangles. For example, you could make an octahedron from two terahedra, and so you could make air from fire. It is not clear what these triangles were made of, and it almost seems as if they are simply made of empty space.

Plato's student, Aristotle (384-322 BC) criticized Plato’s view on the grounds that triangles and other geometrical entities do not have mass. Instead, Aristotle imagined that things consisted of form and matter—that the basic forms of hot and cold, moist and dry could be imposed on primary matter called ύλή (pronounced hule) in various combinations. Hot and dry made fire, hot and moist made air, cold and dry made earth, and cold and moist made water.

But Leucippus’ real opponent was the so-called Elatic school, whose best-

1 http://www.stanford.edu/~jsabol/sophia/democritus.html2 http://people.wku.edu/jan.garrett/democ.htm3 http://classics.mit.edu/Carus/nature_things.html

Antoine Coypel, Democritus, 1992

Aside 2ANCIENT GENIUSHow do you think Democritus (or his teacher Leucippus) figured out that everything was made of atoms?

known master had been Zeno (b. 489 BC). Zeno believed that the universe was one consistent whole. Matter is continuous and so there can be no motion, because there is no empty space, or void. Zeno devised a number of paradoxes to demonstrate the impossibility of motion. Aristotle describes one of Zeno’s famous paradoxes:

Zeno's arguments about motion, which cause so much disquietude to those who try to solve the problems that they present, are four in number. The first asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal. 4

That is, it can never reach its goal because it is always cutting the distance to the goal in half. We can always ask when it is at the half way point, the ¾ point, the 7/8 point, and so on. Aristotle answered the problem by pointing out that an object “passes over a less magnitude in less time; for the divisions of time and of magnitude will be the same” and so the time required decreases with the distance.

These ideas may seem strange to us, but we must admit that they make some sense. And it was Aristotle’s ideas, and not those of Democritus, that prevailed among the competing theories of the day and held sway for centuries. Which was actually closer to the truth? This is a question we will have to revisit later.

4 http://www.kennydominican.joyeurs.com/GreekClassics/AristotlePhysics.htm

David Teniers the younger (1610—1690), The Alchemist.

Section 3: The Alchemists.

…If by fire Of sooty coal th' empiric alchymist Can turn, or holds it possible to turn, Metals of drossiest ore to perfect gold as from the mine.

- John Milton

Throughout the time of the ancient Greeks and Romans, men continued to experiment with manipulations of matter. They learned how to “gild” objects with mixtures (called amalgams) of gold and mercury, how to manufacture various chemical compounds, such as white lead (used as a white pigment in paint) and how to produce silvery liquid mercury (quicksilver) from the red mineral mercurius calcinatus.

During this period, the Egyptians became particularly skilled with the manipulation of matter. They had historically been adept at glassmaking and at smelting and working metals. Now they had become skilled enough to change the appearance of metals and make them look as if they were gold or silver. A recipe in one manuscript, called the Leyden Papyrus (dated 300 AD, but probably written much earlier), explains how to coat a copper ring with a mixture of powdered lead and gold. Heating the powdered ring caused the ring to “take the color”. The

author frankly explains, “It is difficult to detect the fraud, since the touchstone gives the mark of true gold.”

Fraud was apparently a common practice among these early, practical chemists, but a change soon took place in the art of the mastery of matter in Alexandria, Egypt. Founded by Alexander the Great in 331 BC, Alexandria was a cosmopolitan city of Egyptians, Greeks, Syrians, and Jews. There, the Egyptian mastery of matter mixed with the philosophical ideas of Aristotle and Plato and elements of Eastern mysticism. The new “science” that resulted was called chemeia, which simply meant “the Egyptian art”. We call it by its later name—alchemy, which is derived from the ancient name combined with the Arabic definite article “al”.

Early alchemists appear to have believed that metals like lead could really be turned into gold or silver by changing the color. For example, copper was given a silver color by treating with arsenic, and the resultant piece of metal was considered a kind of silver. The agent of this change was referred to as the “elixir” or, later in Europe, the philosopher’s stone. Manuscripts from this period, such as those written by Zosimos are filled with cryptic descriptions, such as the preparation of the “bile of the serpent” or “divine water” by boiling sulfur in lime water. They also contain references to astrology—various metals were associated with the gods and planets. Silver was associated with the moon, and copper with Venus, for example. Though much of this ancient work was secretive and mystical, these early manuscripts also included important developments, drawings and descriptions of equipment and techniques, like distillation.

Alchemy seems to have been restricted to Egypt until the Arab conquest of Egypt by the Arabs in 640 AD, and the Arabs spread the art throughout the Muslim world. During the Arabic period of alchemy that followed their conquest of Egypt, the art seems to have evolved such that alchemists no longer believed that changing the color of the metal was the same as changing the metal. An Arabic writer named Avicenna believed that the transmutation of the elements was impossible, and that alchemy could produce only imitation of the precious metals.

But this does not seem to have been the case in Europe. The Arabs spread alchemy into Europe through Spain, which they conquered in the 700’s, and European alchemy seems to have been a mixture of fraud, sincere searching for the philosophers stone (and the elixir of life, which would bring immortality), and genuine chemical explorations.

Photo by Petr Kratohcvil

Aside 3EASTERN CHEMISTRYGunpowder appears to have been invented as early as 1150 AD in China. China and India had been developing their own mastery of matter, including an atomic theory, and then a kind of alchemy, parallel to the western cultures. But their science largely stopped there, while the Europeans went on to develop modern science sin the 16th century. Why do you think that is?

Albertus Magnus (1193-1280), the great Dominican scholar who is credited with the discovery of the toxic element arsenic, did not believe that the transmutation of base metals into gold was possible, but his student, Thomas Aquinas, was more sympathetic with the art. The Franciscan Roger Bacon (1214-1292) was interested in alchemy, even performing his own experiments, and the first formula for gunpowder is found in his writings.

William Blake (1757—1827), Chaucer’s Canterbury Pilgrims

Early receptions of Alchemy in Europe seemed to have varied widely, but by 1400, it seems the practice of alchemy was commonly held in suspicion. This passage from the Yeoman Canon’s Tale in Chaucer’s Canterbury Tales (~1400) is telling:

Come forth, if it's a fool you'd like to be,And learn about the art of alchemy; If you have money, then step forward, sir,And you too can become philosopher.

The story teller continued, telling the tale of his crooked boss, a canon (a cathedral priest) who was also an alchemist, and how he deceived a local parish priest. The canon offered to show the priest (for a fee) how to turn mercury into silver:

There are but few to whom I'd offer, sir, To show my science to such a degree;Here by your own experience you'll see How this quicksilver I'll transmogrifyRight here before your eyes, without a lie,And turn it into silver, just as fineAnd good as any in your purse or mine…

Bade by this canon reprehensible,The priest set on the fire this crucible,

Then busily into the fire he blew.Into the crucible this canon threwA powder--I don't know what it contained,If made of chalk or glass, but though obtainedWhatever way it wasn't worth a fly…

This canon--may the devil come and fetchHim!--from his coat an imitation coal Took, made of beech, in which was drilled a hole;Some silver filings in this hole were packed,An ounce of them, and to conceal the factWere tightly sealed with wax. Now be awareThat this device was not made then and there… This canon took his coal--such a disgrace!--And centered it on top so that it sat Above the crucible; he blew, with that,Until the coals burned at a rapid rate…

And when this canon's imitation coalHad burnt, all of the filings from the holeFell right into the crucible below--They naturally could not help doing soSince they were placed so evenly above it. But still, alas! this priest knew nothing of it,

But we should not condemn all of alchemy as useless fraud. Many important techniques and considerable basic knowledge of substances was gained by the alchemists. As Francis Bacon said in The Advancement of Learning (1605):

…and yet surely to alchemy this right is due, that it may be compared to the husbandman whereof Aesop makes the fable; that, when he died, told his sons that he had left unto them gold buried under ground in his vineyard; and they digged over all the ground, and gold they found none; but by reason of their stirring and digging the mould about the roots of their vines, they had a great vintage the year following: so assuredly the search and stir to make gold hath brought to light a great number of good and fruitful inventions and experiments, as well

Aside 4THE CANONS FRAUDDraw a picture of the Canon’s fraudulent device.

for the disclosing of nature as for the use of man's life.

During this period, the use of chemicals in medicine was becoming increasingly popular. The famous physician Paracelsus was known for his metallic remedies, using mercury and antimony for the treatment of diseases, and for his successful use of opium for medical purposes. He was an influential alchemist, and taught that the four elements appeared in metals as three principles: salt (a broader term than sodium chloride), sulfur, and mercury. Antimony was a popular laxative. It was toxic, and an irritant to the gastrointestinal tract, so swallowing a small antimony pill would stimulate and flush the intestines. Such pills were apparently expensive, since people would often retrieve them from their excrement after use, and even pass them down from generation to generation.

The famous early chemist Van Helmont (1579-1644) also believed in Alchemy, and even gives an account of his own transmutation of mercury into gold. And yet he marks a transition to a more quantitative and systematic period. He engaged in careful experiments, used a balance, and documented many legitimate chemical preparations, including the preparation of nitric, sulfuric, and hydrochloric acids. Trained in theology and medicine, he once wrote “God has given me a pious and noble wife. I retired with her to Vilvorde and there for seven years I dedicated myself to pyrotechny [i.e. chemistry] and to the relief of the poor.”

He invented the idea of a gas, and distinguished this from air (still considered an element), and identified different gases, such as the suffocating gas that accumulates in mines (carbon dioxide) and nitric oxide, although he did not use the modern names, of course. He believed that gases were composed of atoms that could condense into droplets if cooled. He believed that fire was not an element at all, but only burning smoke, which was a gas. Van Helmont rejected the 4 elements of Aristotle, though he only exchanged them for a similar theory—he believed that the only two elements were air and water.

Van Helmont conducted a famous experiment to prove that plants are formed only out of water:

I took an earthen vessel, in which I put 200 pounds of earth that had been dried in a furnace, which moistened with rain-water, and I implanted therin the trunk or stem of a willow tree, weighing five pounds; and at length, five years being finished, the tree sprung from thence, did weigh 169 pounds and about three ounces: But I moistened the earthen vessel

Carl Ludwig Frommel, Tree, 1800

Aside 5VAN HELMONT’S TREEHow could Van Helmont have improved his experiment?

with rain-water, or distilled water (always when there was need) and it was large and implanted into the earth, and least the dust that flew about should be comingled with the earth, I covered the lip or mouth of the vessel, with an iron plate covered with tin, and easily passable with many holes. I computed not the weight of the leaves that fell in the four Autumns. At length, I dried again the earth and there were found the same 200 pounds, wanting about two ounces, therefore, 164 pounds of wood , barks, and roots arose out of water only.

It is ironic that the man credited with the discovery of gases in general and carbon dioxide in particular would miss the possibility that part of the mass in the tree might come from the air.

Van Helmont had a great influence on Robert Boyle (1627-1691). Boyle also believed in alchemy, but took the experimental approach to chemistry to yet higher levels, being especially fond of experiments with gases using an air pump. Boyle was also an atomist (like Democritus), though the theory in Boyle’s time was called corpuscularianism, and he explained his famous law of gas pressure by relating pressure to the motion of the corpuscles. He refuted the idea of the four elements of Aristotle, showing from experiment that these things could not be extracted from metals. In his famous book, the Sceptical Chymist, he provided what appeared to be a very modern definition of elements:

I mean by Elements, as those Chymists that speak plainest do by their Principles, certain Primitive and Simple, or perfectly unmingled bodies; which not being made of any other bodies, or of one another, are the ingredients of which all those called perfectly mixt bodies are immediately compounded, and into which they are ultimately resolved. And yet it is not clear what he meant by unmingled bodies. Being an early

atomist, it is possible he believed that there was only one type of matter, the “atoms” of which could be different shapes and move or combine in various ways so as to exhibit different properties.

He did experiments in which he attempted to burn things like sulfur and phosphorus in a vacuum, and came to believe that air was required for combustion. Gunpowder was a strange exception, but though the gunpowder did burn in the absence of air, it flashed when air was let into the jar.

Combustion was a favorite topic for early chemists, and many of their procedures involved heat and flame. In 1723, G. E. Stahl introduced the theory of phlogiston (though it was based on earlier work), which became a framework for (incorrectly) understanding a wide range of chemical phenomena. Phlogiston was an element, a kind of greasy earth (think of soot and tar) which was released from substances with a rapid whirling motion when they burned. (Despite the advances of Van Helmont and Boyle, the old alchemical and Aristotelian theories proved to have great staying power.)

According to the phlogiston theory, candles went out when placed in a closed container because the air became saturated with phlogiston. Phlogiston was

also released from metals when they were burned, reducing the metal to a powder, called a calx. The metal could be restored by heating the calx with charcoal because charcoal was almost pure phlogiston. (Recall how the Hittites extracted iron from its ore.)

But the theory was not without its problems. Perhaps the greatest was this: metals do not lose mass when they burn—they gain mass. The ad hoc theories that proliferated to explain this problem demonstrate the lengths to which men will go to justify their preconceived notions. Some suggested phlogiston could have negative mass, and others imagined that it changed the density of objects. But the theory had become a paradigm, a way of viewing the matter, and it would take a paradigm shift to overcome it.