INTRODUCTION TO CHEMISTRY

The Laws of Chemical Change:
1. The Law of the Conservation of Matter (Lavoisier, 1789).
  When a chemical change (reaction) takes place in a closed system, the gain experienced in any one part of the system is exactly counterbalanced by the loss by the rest of the system, or the total quantity of matter within a closed system remains constant no matter what changes occur within the system. That is, when matter undergoes either an ordinary physical or chemical change in a closed system, there is no detectable gain or loss of mass; the total quantity of matter within the system remains constant. In other words, matter cannot be created or destroyed. According to this law, in a chemical reaction there is no change in mass - the mass of the products is equal to the mass of reacting substances. Since weight is directly proportional to mass, this means that the weight of products is equal to the weight of the reactants.
2. The Law of Definite Proportions or Composition (Proust, 1799)
  In a pure compound the several elements are always combined in a definite ratio by weight; that is, the compound has a definite percentage by weight of constituents regardless of origin or method of preparation. Percentage composition is the part divided by the whole times 100. Eamples:
```
                                     percentage composition
hydrogen + oxygen -> water               88.81 % oxygen
1.008 gm    8 gm     1.008 gm            11.19 % hydrogen
           
iron  + sulfur  ->  iron sulfide         63.6 % iron
7 gm    4 gm         11 gm               36.4 % sulfur
           
carbon  +  oxygen  -> carbon monoxide    42.9 % carbon
3 gm       4 gm       7 gm               57.1 % oxygen
           
carbon  +  oxygen  -> carbon dioxide     27.3 % carbon
3 gm       8 gm       11 gm              72.7 % oxygen
```
  Some combination of elements form more than one compound.
  When the French chemist Joseph Louis Proust (1754-1822), then professor at Madrid, formulated this law, the leading French chemist Claude Louis Berthollet (1748-1822) had come to a different conclusion. He thought that when copper or tin were heated in air, a series of "compounds of varying colors and composition" were formed. Berthollet also cited as further examples that solution and alloys lack a constancy in their composition. (For example, sugar may be dissolved in water to any degree of saturation) The controversy went on for eight years. Although Berthollet was a famous chemist, being an honored statesman of the Empire, scientific adviser to Napoleon, and a lifelong friend of Lavoisier, Proust was able to show by experimentation that there were just two compounds of copper and oxygen and that what Berthollet had obseved was a variable mixture of these two compounds. Thus by clarifying the definition of chemical compound, he clearly distinguished between compounds on the one hand and mixtures and solutions on the other.
3. The Law of Multiple Proportions (Dalton, 1808). See below.
4. The Law of combining Volumes (Gay-Lussac, 1808). See below.

The Atomic Theory of Matter.
1. The History of Atomic Theory.
  1. Two views concerning the ultimate nature of matter.
    1. The Continuous View: matter is infinitely subdivisible in principle.
    2. The Discontinuous or Discrete View: matter is not infinitely subdivisible in principle; there is a limit to the divisiblity of matter and one ultimately reaches an indivisible particle of matter, an atom (Greek, atomos - "that which cannot be cut").
  2. The Greek philosophers who held the Discontinuous View:
    1. Leucippus (lived about 440 B.C.) originated the theory.
    2. Democritus (460-370 B.C.) expounded and expanded the theory.
    3. Plato (427-347 B.C.) and Aristotle (384-322 B.C.) both opposed the atomistic view and adopted the continuous view.
    4. Epicurus (c. 341-270 B.C.) expanded the theory further.
    5. Leucretius (98-55 B.C.) popularized the theory in his De Rerum Natura. He formulated the theory to solve a philosophical problem and not a physical problem: the possibility of change. The physical problem was the description and explanation of physical and chemical change.
  3. The 17th and 18th century Revival of Atomism.
    1. Peter Gassendi (1592-1665) in 1649 revived atomism. During the middle ages the atomic view of matter was ignored and/or opposed because of its association with naturalisiic Epicureanism. Gassendi attempted to divest the atomic view of these assocations.
    2. The 17th and 18th century scientists, Descartes, Boyle, and Newton, adopted the atomism but their theories were not formulated primarily to solve philosophical problems. Although their theories were formulated to solve physical problems they were not quantitatively formulated and experimentally verified.
2. Dalton's Atomic Theory (1808 and 1810).
  John Dalton (1766-1844) was a Quaker teacher of Manchester, England. He set forth his theory in a work called A New System of Chemical Philosophy, published in two parts in 1808 and 1810. The theory was proposed with the purpose of explaining chemical change.
  1. Postulates of the theory.
    His atomic theory can be summarized by giving its basic assumptions or postulates:
    1. The First Postulate has two parts:
      (1) All matter consists of tiny, indivisible particles called atoms which have the following characteristics: they are simple (no structure), solid, hard, impenetrable.
      (2) Atoms are unchangeable; that is, during a chemical change atoms can not be created or destroyed or changed into one another (no transmutation of matter).
      This postulate was not original with Dalton and has been modified in the light of modern knowledge of the structure of the atom.
    2. The Second Postulate:
      Atoms of the same element are alike in all respects; in particular, alike in weight, size and shape. Atoms of different elements are unlike in weight, size and shape. Dalton's new contribution here is the emphasis on weight as the primary difference between atoms of different elements. Thus his theory differed from his predecessors by his emphasis on this quantitative aspect of weight.
    3. The Third Postulate:
      Atoms of different elements combine chemically in definite, simple (whole numbers) ratios to form particles of a compound. These particles of the compounds were called by Dalton "compound-atoms." We shall use the term "molecule", introduced later by Avogadro.
    4. The Fourth Postulate:
      Atoms of different elements may sometimes combine in more than one ratio to form several different compounds of the same elements.
    5. The Fifth Postulate (simplicity rule):
      When two elements form only one compound, their atoms combine one-to-one; if there are two compounds of the same two elements, then in one compound, the most abundant, the atoms of the elements combine one-to-one and in the other compound two-to-one; similarly, when three compounds are formed of same two elements. This postulate is called the Rule of Greatest Simplicity of the most common stable compounds. Since Dalton had no way of determining in what ratios they combined, he made an educated guess based on the conviction that nature behaves simply.
  2. The Achievements of Dalton's Atomic Theory.
    1. The theory explained and integrated the Law of Conservation of Matter and the Law of Definite Proportions or Composition. Postulates 1 and 2 explain the Law of Conservation of Matter; postulates 2 and 3 explain the Law of Definite Proportions. The theory by explaining the laws integrated them. But this does not constitute a verification of the theory.
    2. Predicted the Law of Multiple Proportions:
      When two elements combine to form more than one compound, the weights of one element in the compounds which unite with identical weights of the other element are in small whole number ratios. For example:
```
     carbon + oxygen -> carbon monoxide
      3 gm     4 gm         7 gm
     carbon + oxygen -> carbon dioxide
      3 gm     8 gm        11 gm
```
      With an identical weight of carbon (3 gm) in each compound, the ratio of the weights of oxygen in the compounds are in 1 to 2 ratio. This law compares the compounds formed from the same two elements not the structure of the compounds themselves. The prediction and discovery of this law was the strongest verification of Dalton's atomic theory. The ability of a theory to predict and lead to the discovery of previously unsuspected laws and facts is the test of the truth of a theory. This the atomic theory was able to do.
    3. Raised the problem of atomic weights.
      The acceptance of the atomic theory upon its successful attempt to explain and predict the laws of chemical change, led to a new problem, the problem of the determination of atomic weights.
      (1) Definition of atomic weights.
      The atomic weight of an element is the relative weight of an atom of that element compared with the weight of oxygen atom taken as 16. Distinguish between the absolute weight and the relative weight of an atom: the absolute weight of an atom is the weight of an atom measured in terms of an ordinary unit like the gram. (Although the gram is a unit of mass, the chemist often uses the gram to measure weight. Since weight is directly proportional to mass, the gram may be used in such a way as an indirect measure of weight.) The absolute weight of the lightest atom, for example, hydrogen is 1.67 × 10^-24 grams. This is many times smaller than the smallest weight that can be weighed on the most sensitive balance which is about 10^-5 grams. The relative weight of an atom is the weight of an atom compared with the weight of a standard atom, which is usually the oxygen atom. As such it has no units being just a ratio of weights. The relative weight of the lightest atom hydrogen is 1.008, that is, 1.008 to 16 of the weight of the oxygen atom. Since the chemist works with bulk quantities of atoms rather than individual atoms, the relative weight is much more convenient than the absolute weight of the atoms. Hence the atomic weight of an element is the the relative weight of an atom of that element. Oxygen has been chosen as the present standard (Dalton used hydrogen with an atomic weight of 1.00 as the standard) because oxygen is the most abundant element and combines more easily with most elements. The atomic weight of oxygen has been taken as 16.0000 because that allows the atomic weights of other elements to come out closer to whole numbers, especially hydrogen to come out nearly equal to one.
      (2) Method of determination of atomic weights.
      The atomic weight of an element can be determined by use of the following formula:
```
weight of sample of element A   Number of atoms of A   wt of an atom of A
----------------------------- = -------------------- × ------------------
weight of sample of element B   Number of atoms of B   wt of an atom of B
```
      The ratio on the left may be determined experimentally by chemical analysis. The second ratio on right, the ratio of the weight of atoms of A and B, may be replaced by the ratio of the atomic weights of element A and B, since the ratio of the absolute weights equals the ratio of the relative weights. Thus the formula becomes
```
weight of sample of element A   Number of atoms of A   Atomic weight of A
----------------------------- = -------------------- × ------------------
weight of sample of element B   Number of atoms of B   Atomic weight of B
```
      If the element chosen for element B is oxygen or another element whose atomic weight has been previously determined, then the atomic element A alone has to be found. The first ratio on the right, the ratio of the number of atoms of A and of B in the sample, is equal to the whole number ratio that the atoms of A and B combine with each other in the compound of A and B. Dalton used his Rule of Simplicity (Postulate 5 above) to determine this ratio. But since there was much uncertainty concerning the accuracy of the rule, the atomic weights determined by its use were also uncertain. Thus the problem of the determination of the atomic weights of the elements reduces to the problem of how to determine for certain the ratio that the atoms of element A and B combine with each other. It was with this problem in mind that Avogadro proposed his modification of Dalton's atomic theory. But in order to understand Avogadro's hypothesis, we must look at the discovery of the Law of Combining Volumes, which led to his hypothesis.
3. Gay-Lussac's Law of Combining Volumes (1808).
  In the same year that Dalton published his atomic theory, the noted French experimentalist, Joseph Gay-Lussac (1778-1850), discovered an important regularity in the way two gaseous substances combine. When two gases combine, there is a whole-number ratio between their volumes, and between the volumes of either one of them and that of the product, if it is also a gas, and provided the volumes of all the gases are measured at the same temperature and pressure.
  1. Examples:
```
     hydrogen + oxygen -> water vapor
       2 vol.     1 vol.    2 vol.
     hydrogen + nitrogen -> ammonia
       3 vol.     1 vol.      2 vol.
     nitrogen + oxygen  ->  nitric oxide
       1 vol.     1 vol.      2 vol.
     hydrogen + chlorine -> hydrogen chloride
       1 vol.     1 vol.      2 vol.
```
  2. Observations:
    1. The Law is confined to the gaseous state of the substances.
    2. The volumes must be measured at the same temperature and pressure.
    3. Unrelated to the weights of combining substances: volumetic and not gravimetric.
    4. This is the fourth law of chemical change.
  3. Dalton's opposition to Gay-Lussac's Law.
    Dalton expressed his opposition to Gay-Lussac's Law of Combining Volumes of reacting gases in the second part of his A New System of Chemical Philosophy, which was published in 1810. He rejected it completely and remained opposed to it the rest of his life. His opposition centers on the hypothesis which the Law strongly suggests that equal volumes of different gases at the same temperature and pressure contain the same number of particles - atoms in gaseous elements and molecules in gaseous compounds. The following are Dalton's reasons:
    1. There are a number of chemical reactions in which the volume of the gaseous product exceeds the volumes of at least one of the reacting gases; for example: one volume of nitrogen reacting with one volume of oxygen to form two volumes of nitric oxide. This does not agree with the "equal volumes - equal numbers" hypothesis. For on this hypothesis the number of molecules of the product compound should equal the number of atoms in the volume of one of the reacting gases and this is not so. Since one atom of nitrogen combines with one atom of oxygen forming one molecule of nitric oxide and if equal volumes contains equal number of particles, then how could one volume of nitrogen react with one volume of oxygen produce two volumes of nitric oxide? Obviously the "equal volumes - equal numbers" hypothesis is wrong.
    2. The densities (mass divided by volume) of the gaseous products are less than that of the heaviest gaseous element. For example, when hydrogen and oxygen react to form water vapor, the density of the water vapor is less than the density of the oxygen. If the mass of hydrogen atoms is added to the mass of the oxygen atoms forming a product that contains less mass per unit volume than the density of oxygen itself, how could these equal volumes contain equal number of particles? This contradicts the "equal volume - equal numbers" hypothesis. For on this hypotheis when atoms of the elements combine they should produce molecules that weigh more rather than less. Thus the densities of the products should be more not less than the density of oxygen.
    3. Dalton held a static view of gases in which the particles of the gas are at rest and in physical contact through the "spheres of caloric" which surround the particles of the gas. This implied that differences in gas volumes were due to differences in the size of the particles of the gas. Thus equal volumes of gases at the same temperature and pressure would contain different number of particles. This static view of gases remained the main cause for the rejection of the Law of Combining Volumes.
    4. Dalton asserted that the experimental data did not support the Gay-Lussac Law because the numbers of the data had been rounded off more or less arbitrarily before the data and the law could be brought into agreement. Gay-Lussac replied that this rounding off was a legitimate process in view of the substantial experimental error in data used. Dalton, on the other hand, believed that this was a gross oversimplificaton which covered up significant data. Dalton, whose experiments were generally very crude, often quoted his own poor data in refutation of those of Gay-Lussac, who was an acknowledged skilled experimentalist.
  4. The Problem raised by Gay-Lussac's Law.
    Gay-Lussac's Law raised immediately the following explanatory problem: how are we to interpret and explain the ratio between the volumes of the combining gases and their gaseous products? The answere to the problem was provided by the Italian Physicist Amadeo Avogadro (1776-1856) in 1811.
4. Avogadro's Hypothesis (1811).
  Avogadro introduced the postulates of his hypothesis to explain the Gay-Lussac Law of Combining Volumes by modifying Dalton's atomic theory. He replaced the Fifth Postulate (The Rule of Simplicity) of Daltons' atomic theory with three additional postulates. The first four postulates of Dalton's atomic theory and the three postulates of Avogadro's hypothesis are called the Dalton-Avogadro Atomic-Molecular theory.
  1. The Postulates of Avogadro's Hypothesis:
    1. Equal volumes of all gases (elements or compounds) under the same conditions of temperature and pressure contain equal number of particles.
    2. The particles of a gaseous element are not necessarily individual atoms but may be groups of atoms containing two, three, or more atoms. These groups of atoms are called molecules. Avogadro introduced the term "molecule" which is from the Latin for "small mass". Thus the term "molecule" not only applies to groups of atoms of differents elements (forming compounds) but also to groups of atoms of the same element. If a molecule contains one atom, it is called monoatomic, two atoms - diatomic, three atoms - triatomic, and many or indefinite number of atoms - polyatomic.
    3. Avogadro's Rule of Simplicity: if more than one assumed process is in harmony with both experimental results and the other postulates of the Dalton-Avogadro atomic-molecular theory, then choose as correct the process that is the simplest. This rule of simpicity is different from Dalton's. Dalton's Rule of Simplicity was used to formulate molecular formulas whereas Avogadro's Rule of Simplicity was used to choose between alternate molecular formulas and self-consistent schemes of explanation of various chemical reactions (see below).
  2. The Explanation of experimental results.
    We shall use the atomic-molecular theory to explain various chemical reactions.
    1. The hydrogen and oxygen reaction to form water.
      (1) If hydrogen and oxygen are monatomic, the equal volumes - equal numbers postulate contradicts the postulate that atoms are unchanged and indivisible. That is, this scheme of explanation is not self-consistent and is self-contradictory.
      (2) If hydrogen is monatomic and oxygen is diatomic (Avogadro's second postulate), then the equal volumes - equals number postulate is consistent with the other postulates of the atomic-molecular theory; that is, this is a self-consistent scheme. The scheme fits the facts. But this is not the only self-consistent scheme that explains this reaction.
      (3) If hydrogen as well as oxygen are diatomic, then the equal volumes - equal numbers postulate is also consistent with the other postulates of the atomic-molecular theory. This scheme also fits the facts.
      (4) If hydrogen is quadatomic and oxygen is diatomic (Avogadro's second postulate), then the equal volumes - equals number postulate is consistent with the other postulates of the atomic-molecular theory; that is, this is a self-consistent scheme. The scheme fits the facts.
      Reactions (3) and (4) above are self-consistent schemes and fit the facts. There are also many more complex self-consistent schemes that are also in harmony with the experimental results. But not all these schemes will explain other reactions.
    2. Hydrogen and nitrogen reaction to form ammonia:
      (1) If hydrogen is monatomic and nitrogen is diatomic, the equal volumes - equal numbers postulate contradicts the postulate of atomic-molecular that atoms are unchangeable and indivisible - that is, it is not a self-consistent scheme.
      (2) If hydrogen is diatomic and nitrogen is diatomic (Avogadro's second postulate), then the equal volumes - equals number postulate is consistent with the other postulates of the atomic-molecular theory; that is, this is a self-consistent scheme. The scheme fits the facts. But this is not the only self-consistent scheme that explains this reaction.
      (3) If hydrogen is quadatomic and nitrogen is diatomic (Avogadro's second postulate), then the equal volumes - equals number postulate is also consistent with the other postulates of the atomic-molecular theory; that is, this is self-consistent scheme. The scheme fits the facts.
      Reactions (2) and (3) above are self-consistent schemes and fit the facts. There are also many more complex self-consistent schemes that are also in harmony of the experimental results. Which of these self-consistent schemes are we to choose? Avogadro's Rule of Simplicity provides the necessary criterion: choose the simplest scheme that is in harmony with all the experimental results and the postulates of the atomic-molecular theory; that is, it explains the facts and is self-consistent. Using this criterion, the Reaction (3) of the hydrogen-oxygen reaction and Reaction (2) of hydrogen-nitrogen are the simplest. The schemes in which hydrogen, oxygen and nitrogen are diatomic are not only self-consistent and fit the facts, but they are also the simplist schemes for explaining the reactions containing these elements.
  3. The Answers to Dalton's opposition to Gay-Lussac's Law of Combining Volumes. These answers are provided by Avogadro's hypothesis.
    1. Dalton interpreted the equal volume - equal number hypothesis to mean equal number of atoms for gaseous elements and equal number of molecules for gaseous compounds. He did not recognize that gaseous elements may be made up of physical groups of atoms, that is, molecules as well as individual atoms. This failure resulted in his inabliity to explain how the volume of the product could be greater than the volume of at least one of the reactants. By assuming that the particles of a gaseous element may be more than one atom, the equal volume - equal numbers hypothesis may be brought into agreement with the experimental results. For example, in the reaction of nitrogen and oxygen to produce nitric oxide in which one volume of each of the reactants produces two volumes of product, if the reactants are assumed to be diatomic molecules, then it can be understood how the reaction will produce two molecules of nitric oxide. Thus the two volumes of nitrogen and oxygen can produce two volumes of nitric oxide.
    2. Dalton assumed that when the atoms of a gaseous elements react, the atoms add together to form the molecule of the gaseous compound. For example, he assumed that an atom of hydrogen combines with an atom of oxygen to form a molecule of water vapor. Thus the water molecule would weigh more that an atom of oxygen. Now since density is defined as the weight per unit volume, the density of the water vapor ought to be more than the density of the oxygen if we assume that equal volumes contain equal number of particles. Since this does not agree with the experimental fact, Dalton concluded that the "equal volume = equal numbers" hypothesis was wrong. But in reality the error was not in this hypothesis but rather in the assumption that the atoms of hydrogen and oxygen were simply added. A study of the reactions given above show that they are not addition reactions but substitution reactions. For example, in the formation of of the molecule of water vapor, two hydrogen atoms have been substituted for one of the oxygen atoms in the molecule of oxygen gas. Since two hydrogen atoms together weigh less than one oxygen atom, one water molecule should weigh less than one oxygen molecule. And since density is defined as the weight per unit volume and equal volumes contains equal number of particles, the density of water vapor should be less than the density of oxygen, which is the case. Thus Avogadro's hypotheis as a modification of Dalton's atomic theory provides the correct interpretation of chemical change as substitution rather than addition of atoms.
    3. Dalton assumed a static view of gases which led him to reject the equal volumes - equal numbers hypothesis and thus also Gay-Lussac's Law. Avogadro abandoned the static view of gases with its contiguous particles for the dynamic view of gases in which the particles of the gases are not in contact and are quite small compared with the distance between them; indeed, they are so small that they occupy only a negligible fraction of the volume of any gas sample. This completes the return to the "atoms and void" view of matter of ancient times. With the adoption of this model of the gases, the connection between the size of the atoms and gas volume must be abandoned. The size of the atoms tells us nothing about the volumes of the gases. The volume of a gas is mostly empty space; only a samll fraction of the volume of the gas is taken up by the gas particles. In the study of gases, therefore, the size of particles gives no information about the volume of the gas and is relatively unimportant. On such a view of gases there is no difficulty in accepting the hypothesis that equal volumes contain the same number of particles.
    4. In conclusion, Dalton rejected the experimental basis that Gay-Lussac had provided for his law for reasons that were motivated by the wrong view of gases and faulty experimental data. Avogadro's hypothesis added no new experimental confirmation but only provided a clearer explanation of experimental data.
  4. Importance of Avogadro's Hypothesis:
    1. Modified Dalton's atomic view in order to explain Gay-Lussac's Law of Combining Volumes and other experimental data involving the volumes of gases.
    2. Determined the formulas of compounds and the ratios in which the atoms of several elements combine.
    3. Provided the basis for determination of atomic weights by giving the ratios in which the atoms of several elements combine.
  5. The Reason Avogadro's Hypothesis was not accepted until 1859:
    1. Most chemists at that time accepted the static view of gases which was not compatible with the equal volumes - equal numbers hypothesis. This static view of gases was widely held until developments in the study of heat led to the development of Kinetic-Molecular Theory of Gases. A truly comprehensive version of this theory was published in 1857 by the German physicist Rudolph Clausius (1822-1888). Only then did the static view die.
    2. Widespread reluctance to believe that two like atoms of an element could form a stable union with each other. The development of the atomic theory in the period from 1811 to 1826 was dominated by the Swedish chemist Jons Jacob Berzelius (1779-1848). Berzelius could not accept Avogadro's hypothesis because he held to the Dualistic Theory of atoms. In order to explain how atoms of different elements could combine together to form compounds he assumed that the atoms had a net electrical charge. In particular the oxygen atoms were assumed to have a net negative charge and the hydrogen atoms had a net positive charge. Thus the hydrogen and oxygen atoms would electrically attract each other to form a water molecule. Since like charges repel each other, two or more atoms of the same element could not form molecules of that element. Thus equal volumes of a gaseous element could not contain diatomic or polyatomic molecules. This explanation was widely accepted until later in the 19th century discoveries in organic chemistry made the Dualistic Theory of electrically charged atoms untenable. The theory was abandoned about 1840 and thus this objection to Avogadro's hypothesis was removed.
    3. Avogadro's Hypothesis did not lead to any new discoveries either of facts or laws; it was an explanation that made no new predictions.
    4. Avogadro's poor presentation of his hypothesis in obscure writing and inconsistent use of terms made understanding of his hypothesis difficult.