Appendix: Some Fundamental Principles and Calculations Introduction This appendix provides some very basic principles of chemistry and some informa- tion on calculating concentration of substances in solution. Much more detailed information is available in a general inorganic chemistry textbook. Elements, Atoms, Molecules, and Compounds Elements are the basic substances of which more complex substances are composed. Anything that has mass (or weight) and occupies space is matter made up of chemical elements such as silicon, aluminum, iron, oxygen, sulfur, copper, etc. Substances more complex than atoms of a single element consist of molecules. A molecule is the smallest entity of a substance that has all the properties of that substance. Elements are classified broadly as metals, nonmetals, or metalloids. Metals have a metallic luster, are malleable (but often hard), and can conduct electricity and heat. Some examples are iron, zinc, copper, silver, and gold. Nonmetals lack metallic luster, they are not malleable (but tend to be brittle), some are gases, and they do conduct heat and electricity. Metalloids have one or more properties of both metals and nonmetals. Because metalloids can both insulate and conduct heat and electric- ity, they are known as semiconductors. The best examples of metalloids are boron and silicon, but there are several others. There also are less inclusive groupings of elements than metals, nonmetals, and metalloids. Alkali metals such as sodium and potassium are highly reactive and have an ionic valence of +1. Alkaline earth metals include calcium, magnesium, and other elements that are moderately reactive and have an ionic valence of +2. Halogens illustrated by chlorine and iodine are highly reactive nonmetals, and they have an ionic valence of À1. This group is unique in that its members can exist in solid, liquid, and gaseous form at temperatures and pressures found on the earth’s surface. Because of their toxicity, halogens often are used as disinfectants. Noble gases such as helium, argon, and neon are unreactive except under very special conditions. In all there are 18 groups and subgroups of elements. Most elements are included in the # Springer Nature Switzerland AG 2020 411 C. E. Boyd, Water Quality, https://doi.org/10.1007/978-3-030-23335-8 412 Appendix: Some Fundamental Principles and Calculations groups referred to as alkali metals, alkaline earth metals, transitional metals, halogens, noble gases, and chalcogens (oxygen family). The elements are grouped based on similar properties and reactions. However, in reality, each element has one or more unique properties and reactions. The most fundamental entity in chemistry and the smallest unit of an element is the atom. An atom consists of a nucleus surrounded by at least one electron. Electrons revolve around the nucleus in one or more orbitals or shells (Fig. A.1). The nucleus is made up of one or more protons, and with the sole exception of hydrogen, one or more neutrons. The protons and neutrons do not necessarily occur in the nucleus in equal numbers. For example, the oxygen nucleus has eight protons and neutrons, sodium has 11 protons and 12 neutrons, potassium has 19 protons and 20 neutrons, copper has 29 electrons and 34 neutrons, and silver has 47 electrons and 61 neutrons. Protons are positively charged and assigned a charge value of +1 each, electrons possess a negative charge and are assigned a charge value of À1 each, and neutrons are charge neutral. In their normal state, atoms have equal numbers of protons and electrons resulting in them being charge neutral. Atoms are classified according to the numbers of protons. All atoms with the same number of protons are considered to be the same element. For example, oxygen atoms always have eight protons while chlorine atoms always have 17 protons. The atomic number of an element is the same as the number of protons, e.g., the atomic number of oxygen is 8 while that of chlorine is 17. There are over 100 elements each with an atomic number assigned to it according to the number of protons in its nucleus. Some atoms of the same element may have one to several neutrons more than do other atoms of the particular element, e.g., carbon atoms may have 6, 7, or 8 neutrons but only 6 protons. These different varieties of the same element are known as isotopes. Moreover, all atoms of the same element may not have the same number of electrons. When uncharged atoms come close together, one or more electrons may be lost from one atom and gained by the other. This phenomenon results in an imbalance Fig. A.1 The structure of oxygen, hydrogen, and sodium atoms. Appendix: Some Fundamental Principles and Calculations 413 between electrons and protons in each of the two interacting atoms that imposes a negative charge on the one that gained the electron(s) and a positive charge on the one that lost the electron(s). The charge on the atom is equal to the number of electrons gained or lost (À1 or + 1 charge per electron). Charged atoms are called ions, but the normal atom is uncharged. In the periodic table of chemical elements, an element is assumed uncharged and to have equal numbers of protons and electrons. The mass of atoms results almost entirely from their neutrons and protons. The masses of the two entities are almost identical; 1.6726 Â 10À24 g for one proton and 1.6749 Â 10À24 g for one neutron. Thus, their atomic masses usually are considered unity in determining relative atomic masses of elements. An electron has a mass of 9.1 Â 10À28 g—nearly 2000 times less than the masses of protons and neutrons. The mass of electrons is omitted in atomic mass calculations for elements. The atomic mass of elements increases as the atomic number increases, because the number of protons and neutrons in the nucleus increases with greater atomic number. The atomic mass of a given element differs among its isotopes because some isotopes have more neutrons than others, while all isotopes of an element have the same number of protons. The loss or gain of electrons by atoms forming ions is not considered to affect atomic mass. Because of the different natural isotopes of atoms of a particular element, the atomic mass typically listed in the periodic table for elements does not equal to the sum of the masses of the protons and neutrons contained in atoms of these elements. This results because the atomic masses typically reported for elements represent the average atomic masses of their isotopes. For example, copper typically has 29 protons and 34 neutrons, and the atomic mass of the most common isotope would be 63 based on addition of neutrons and protons. However, the atomic mass reported in the periodic table of copper is 63.546. The additional mass results from the effects of averaging the atomic masses of the copper isotopes. Atomic masses of some common elements are provided (Table A.1). The atomic mass is very important in stoichiometric relationships in reactions of atoms and molecules. The relative molecular mass (or weight) of a molecule is the sum of the atomic masses of the atoms contained in the molecule. Thus, when sodium atoms (relative atomic mass of 22.99) react with chlorine atoms (relative atomic mass of 35.45) to form sodium chloride, the reaction will always be in the proportion of 22.99 sodium to 35.45 chlorine, and the molecular mass of sodium will be the sum of the atomic masses of sodium and chloride or 58.44. Atomic and molecular masses may be reported in any unit of mass (or weight), but the most common is the gram. The mass or weight of atoms (Table A.1) often is referred to as the gram atomic mass (or weight) and the molecular mass of molecules usually is referred to as the gram molecular weight. Each element is assigned a symbol, e.g., H for hydrogen, O for oxygen, N for nitrogen, S for sulfur, C for carbon, and Ca for calcium. But, because of the large number of elements, it was not possible to have symbols suggestive of the English name for all elements. For example, sodium is Na, tin is Sn, iron is Fe, and gold is Au. The symbols must be memorized or found in reference material. The periodic 414 Appendix: Some Fundamental Principles and Calculations Table A.1 Selected atomic weights Element Symbol Atomic weight Element Symbol Atomic weight Aluminum Al 26.9815 Magnesium Mg 24.305 Antimony Sb 121.76 Manganese Mn 54.905 Arsenic As 74.9216 Mercury Hg 200.59 Barium Ba 137.327 Molybdenum Mo 95.94 Beryllium Be 9.0122 Nickel Ni 58.6934 Bismuth Bi 208.9804 Nitrogen N 14.0067 Boron B 10.811 Oxygen O 15.9994 Bromine Br 79.904 Phosphorus P 30.9738 Cadmium Cd 112.411 Platinum Pt 195.078 Calcium Ca 40.078 Potassium K 39.0983 Carbon C 12.0107 Selenium Se 78.96 Chlorine Cl 35.453 Silicon Si 28.0855 Chromium Cr 51.996 Silver Ag 107.8682 Cobalt Co 58.9332 Sodium Na 22.9897 Copper Cu 63.546 Strontium Sr 87.62 Fluorine F 18.9984 Sulfur S 32.065 Gold Au 196.9665 Thallium Tl 204.3833 Helium He 4.0026 Tin Sn 118.71 Hydrogen H 1.0079 Tungsten W 183.84 Iodine I 126.9045 Uranium U 238.0289 Iron Fe 55.845 Vanadium V 50.9415 Lead Pb 207.19 Zinc Zn 65.39 Lithium Li 6.941 table of the elements is a convenient listing of the elements in a way that elements with similar chemical properties are grouped together.