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Inorganic Chemistry


This section is a continuation of the previous, Basic Physics, topic and assumes that you have already read the previous section. The following discussion is not meant to be comprehensive or overly technical but strives to explain some basic chemistry topics relevant to understanding water chemistry. There is some generalization and simplification.

Energy Levels / Electron Shells

Electrons in an atom occupy what a physicist would call energy levels and a chemist would describe as electron shells.  These energy levels/electron shells are only found at certain very definite distances from the nucleus of an atom, distances which are unique to a particular element.  The electrons cannot be at any other distances which is because the electrons have both particle and wave-like properties (all matter does but it is only at the very small scale of an electron that the wave-like properties of matter normally become important – quantum physics).  The particular energy level/electron shell that an electron occupies corresponds to a certain amount of energy; the farther away from the nucleus that the energy level is, the greater the amount of energy that the electron in that level has.  

In Physics Basics, you learned that when an electron changes energy levels, it either gains energy (it moves to an energy level farther from the nucleus) or emits (electromagnetic) energy (it moves to a level closer to the nucleus).  In this section, you will learn that a given energy level, or as the chemists would say, an electron shell/subshell can only hold a certain number of electrons.  This is important because an atom can be thought of as trying to do two different things at the same time: balancing electric charge and trying to arrange it so that all of its electron shells and subshells are either empty or full of electrons (Yes, this is anthropomorphising an atom which can’t ‘want’ anything but it makes for a better, more easily understood story). 

The lowest energy level/electron shell (closest to the nucleus) can only hold two electrons.  If an atom at rest has more than two electrons, any additional electrons will occupy higher (more distant) energy levels.  An atom is said to be ‘at rest’ if all of its electrons are at the lowest possible energy level/electron shell.  If one or more of the electrons are not at the lowest possible levels, the atom is said to be excited.  

The second lowest energy level/shell can hold eight electrons in two subshells and so on.  Chemistry gets into considerable detail as to the sequence and capacity of electron shells and subshells but for a cursory understanding, it is only necessary to know whether the lower shells/subshells are filled to capacity with electrons or, if not, what the shortage or overage of electrons is in the highest level/subshell with electrons.  The electrons in that last, unfilled subshell are sometimes known as valence electrons.  

For those of you who want a more detailed explanation, it goes like this:  Shown below is an ideal, simplistic image of an atom with a total of 60 electrons which means, since this is an atom, that it also has 60 protons (element number 60) which makes it an atom of Neodymium.  There is a problem with this image but it illustrates some important points, one of which is that not everything on the internet is correct. 

In this image you can see four shells (different colors) and that within a shell, there are one or more subshells.  The first, lowest energy (closest to the nucleus) shell has only one subshell, the ‘s’ subshell.  As you move outward, each successive shell adds one additional subshell: a ‘p’ subshell, a ‘d’ subshell, and an ‘f’ subshell.  There is a number in each subshell which is the number of electrons that that type of subshell can hold:

Subshell  Number of Electrons
subshell can contain
s 2 s2
p 6 p6
d 10 d10
f 14 f14

The Nomenclature column shows what looks like a letter with an exponent but the number is not an exponent; it simply indicates how many electrons are in that subshell. In the table above, all of the subshells are full. You can indicate which shell that subshell is in by putting the number of the shell in front of the letter for the subshell.

Shells Number of electrons
shell can contain
Number of
1st shell
(lowest energy,
closest to nucleus)
Up to 2 1 1s2
2nd shell Up to 8 2 2s2, and 2p6   
3rd shell Up to 18 3 3s2, 3p6, and 3d10 
4th shell Up to 32 4 4s2, 4p6, 4d10, and 4f14    

If you then list all of the subshells using this nomenclature from the lowest subshell up to the highest subshell that has any electrons in it, you then have what is known as the electronic configuration.  For example, the electronic configuration of oxygen is:  1s2, 2s2, 2p4.  Notice that the second p subshell, although it can hold six electrons, only has four; it is two electrons short of completely filling that subshell. 

Earlier it was mentioned that an atom ‘wants’ to do two things: maintain a balanced electrical charge and have all of its subshells either completely full or completely empty.  Oxygen can accomplish the latter by making bonds (of which more later) with another atom(s) which have a subshell with only one or two electrons.  Water is a great example.  Two hydrogen atoms can donate (they are electron donors) their lone electrons to an oxygen atom (an electron acceptor).  However, there is now a charge imbalance so the two hydrogens must remain closely associated (bonded with) the oxygen atom to balance the electrical charges; three atoms become a compound, a water molecule.  

If, however, an atom on its own already has completely filled or empty subshells, it has no need to form bonds with any other atoms and so, doesn’t.  Such elements are known as the noble (they don’t bond with other atoms) gases and make up the 18th column, farthest to the right, of the Periodic Table of the Elements.  

Electron arrangements of the first 15 elements

Element   Atomic
Number of electrons in shell  
      Shell 1 Shell 2 Shell 3  
Hydrogen H 1 1      
Helium He 2 2     shell 1 filled
Lithium Li 3 2 1    
Beryllium Be 4 2 2    
Boron B 5 2 3    
Carbon C 6 2 4    
Nitrogen N 7 2 5    
Oxygen O 8 2 6    
Fluorine F 9 2 7    
Neon Ne 10 2 8   shell 2 filled
Sodium Na 11 2 8 1  
Magnesium Mg 12 2 8 2  
Aluminum Al 13 2 8 3  
Silicon Si 14 2 8 4  
Phosphorus P 15 2 8 5

Here is where there is a problem with the image of the neodymium atom shown above. The image shows that all of its subshells are either completely filled or completely empty which means that it should be a noble gas in column 18 in the Periodic Table of the Elements. But it is in column 6 and is definitely not a noble gas. According to the image, the electronic configuration of Neodymium should be 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2, 4p6, 4d10, 4f14 but it is actually (1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p6), 3s2, 3s2, 4f4.

In both configurations, the electron total is 60 (it is neodymium) but there are several striking differences. One difference is that the 3d10 and 4s2 subshells (shown in bold) swap positions in the actual configuration. What this means is that the first subshell in the fourth shell has less energy than the last subshell in the third shell. You should be able to spot similar switches and notice that the actual configuration for neodymium includes electrons in a fifth shell.

The consequence of all this is that the last subshell in the actual configuration has only four electrons in it, not fourteen (it is not a misprint); neodymium has a partially filled subshell which is why it isn’t a noble gas.  That part of the real configuration in parentheses is the configuration of Xenon (element 54) which is a noble gas; all of its subshells are either completely full or empty.   The electron shell image of neodymium is now seen to be an oversimplification.  The real world is more complicated (and interesting), leading to the transition elements (not discussed) that make up so much of the periodic table and multiple oxidation numbers (discussed later).  

Electromagnetic Spectrum

Electrons can and do move between energy levels but it requires a change in energy.  In order to move to a higher energy level, the electron must absorb enough energy to do that.  If there should be an opening available at a lower energy level, the electron will drop down to it but will emit energy characteristic of the difference in energy levels.  That absorbed or emitted energy is electromagnetic radiation which includes everything from radio waves, through microwaves, infrared, visible light, ultraviolet, x-rays, to gamma radiation.  

All of the radiation above, carried by photons (do not confuse them with protons), is part of the electromagnetic spectrum; the difference is in the wavelength and energy of the radiation (by the way, all of those radiations move at the speed of light).  Radio waves at the low end of the spectrum have very long wavelengths and little energy.  At the high end, gamma radiation has an extremely short wavelength and carries enormous energy.  If it helps to visualize it, you could think of wavy electromagnetic radiation as being like a spring.  Compress (shorten the wavelength) of a spring and it has more energy (don’t take this analogy too far). 

Electromagnetic Spectrum

An electron can be bounced up to a higher energy level by absorbing select wavelengths of electromagnetic energy which match the difference in energy levels.  When that happens, the atom is said to be excited.  If the absorbed energy is great enough, the electron might be bounced completely free of the atom at which point the atom is no longer an atom (the charges no longer balance) and the atom becomes what is known as an ion.  Any radiation less energetic than visible light cannot ionize an atom (note that that includes microwaves).  Visual light is borderline but not normally described as ionizing radiation.  Plants, however, can set up special conditions that will allow visible light to ionize atoms, which is what photosynthesis is all about; solar panels do something similar (the photoelectric effect).  Ultraviolet light, x-rays, and gamma radiation do have enough energy to ionize atoms and are, therefore, described as being ionizing radiation.  Ionizing an atom in a chemical compound can break bonds.  Break the wrong bond in an organic compound in a cell and it can lead to cancer.  Incidentally, heat and chemical reactions also break bonds.  

It works the other way too.  When an electron drops down to a lower energy level, it will emit photons of electromagnetic radiation.  The bigger the drop (the greater the difference in energy levels), the shorter the wavelength and the greater the energy of the emitted photon.  The electron does not have to drop from a high energy level to the lowest possible energy level in one big drop but can drop in a series of steps down sub-shells, each step resulting in the emission of photons whose energy and wavelength are directly related to the energy difference between the levels.  The sum of the energy of each individual step should equal the energy of one big drop.  Should an electron be able to drop from a very high level to a very low level in one big drop, it might even emit gamma radiation (which is what happens in beta decay, described in the previous topic, Basic Physics).  UV light (ultraviolet or black light) can be used to excite the atoms of some fluorescent materials.  When the electrons drop back down in several steps, they may emit several photons of visible light (they fluoresce).  Some laboratory water-testing equipment uses these principles to identify what and how much of something is dissolved in water.

Electron Shell Balance

It was earlier mentioned that atoms, by definition, have balanced electric charges; the number of protons = the number of electrons.  There is, however, another important balance.  Since this discussion is not really a strictly technical one, I shall take the liberty of anthropomorphizing the atom for the sake of a better story (atoms don’t ‘want’ anything).  Remember those energy levels/electron shells?  An atom ‘wants’ (is more stable if) its energy levels are either completely filled to capacity with electrons or have no electrons at all.  So, an atom is trying to do two things at once: maintain a balanced electric charge and have completely filled or empty electron shells.  

The first, lowest energy level can hold two electrons.  Helium, element #2, has two electrons and so is completely satisfied both with respect to charge balance and electron shells.  Neon, element #10, has ten electrons, two for the first shell and eight for the second shell; it, too is completely satisfied in both respects.  You might recognize where this is going by looking at the right-most column of the periodic table of the elements, the column of the noble gasses.  These elements are ‘noble’ because they don’t form compounds (yes, there are a few rare exceptions).  These ‘noble’ elements are completely satisfied both with respect to balanced charge and filled/empty electron shells – they don’t need to interact with (form compounds) with anything else to achieve a balance, but all the other elements do.  

Periodic Table of Elements

Periodic Table of Elements

Ions and Compounds

Hydrogen (almost all of it is protium) can achieve a shell balance by either getting rid of its one electron or acquiring a second electron, thereby making its first shell either completely empty or completely full; it usually gets rid of its electron instead of accepting a second electron.  But now the charge is out of balance; what was once an atom or molecule becomes an ion.  If the ion has an excess positive charge, it is a cation.  If it has a negative charge, it is an anion.  The hydrogen ion, with one excess positive charge (the single proton in its nucleus), is a cation although it is usually just referred to as a hydrogen ion with the understanding that it does have a positive charge.  

Oxygen, with a total of eight electrons, is two electrons short of filling its second sub-shell and so tries to acquire two more electrons, throwing its charge out of balance.  Since hydrogen usually gives up its one electron; it is an electron donor.  Oxygen tries to take two extra electrons; it is an electron acceptor.  Triple up an oxygen with two hydrogens and all three can attain a shell balance; each hydrogen donates one electron to the oxygen.  But in doing that, the oxygen now has two excess negative charges (the extra electrons) and the hydrogens one positive charge each (a lack of an electron).  Since opposite charges attract, the hydrogens become bonded to the oxygen (the charges are balanced) and the three atoms form a compound (water, of course).  As a compound, all charges are balanced and all electron shells are either full or empty; the three atoms, now a compound, become a water molecule.  

Compounds, then, are atoms of at least two different elements bonded together. Molecules are two or more atoms bonded together which is not quite the same thing because you could have two atoms of the same element bonded together. Many gaseous elements do this, forming what are known as diatomic (two atoms, same element) molecules such as H2, O2, N2, and Cl2 (chlorine gas).


Bonds form when, in trying to balance electron shells, a charge imbalance is created. In order to balance the charge, an ion will associate (bond with) another ion of opposite charge, creating a compound (the charges are balanced). Water itself is a classic example. H2O consists of two hydrogens (one positive charge each) bonded to an oxygen (a double negative charge). Such an association allows for both an electron shell balance and a charge balance. Note that both atoms and compounds require a charge balance.

Not all bonds are equal. Consider fluorine (element #9) and sodium (element #11). Fluorine, lacking just one electron to fill its second sub-shell, really really wants an electron to balance the charge imbalance. Sodium, with one extra electron in its third shell, really really wants to get rid of that extra electron. Put those two together and they will certainly form a bond but that electron is going to be much much closer to the fluoride (when fluorine, the element, is part of a compound, it is referred to as fluoride). Such an unequal bond is an ionic bond, ionic because, although it is a compound (NaF), the bond is so unequal, it is almost Na+F.

Now consider carbon, element #6. Carbon has two electrons in its first subshell and four in its second subshell; the second subshell is half full (or half empty). Carbon could balance its second shell by either getting rid of four electrons or gaining four electrons which means that, although carbon is eager to share electrons to balance its shell, it doesn’t particularly care whether it accepts or donates electrons. In either case, carbon will share its four electrons by making four bonds. Since carbon can be either an electron donor or an electron acceptor, it can combine with a huge variety of both electron donors and electron acceptors, even with a mix of both on the same carbon atom, creating what are known as covalent bonds. Three simple examples are: CH4 (methane), CH2Cl2 (dichloromethane), and CCl4 (carbon tetrachloride). Note that in methane, the carbon atom is bonded to four electron donors (the hydrogens), in carbon tetrachloride to four electron acceptors (the chlorides), and in dichloromethane to a mix of both. Most importantly, carbon can form multiple bonds with other carbon atoms, creating a huge array of many different compounds collectively known as organic compounds (of which more in the next topic, Basic Organic Chemistry).


Once again, atoms have, by definition, a balanced charge.  So, too, do molecules but the charges do not have to be equally distributed over the entire molecule, they just have to be balanced as a whole.  Molecules that have areas with a slight excess (usually referred to as ‘partial’ charges) of a negative charge and other areas with a slight excess of a positive charge are said to be polar.  Water is an excellent example of a polar molecule.   The angle between the two hydrogen bonds to the oxygen is about 106°; the front end near the hydrogens has a slight positive charge as opposed to the back end of the oxygen which has a slight negative charge.  This means that the front end of one water molecule is weakly attracted to the back end of another water molecule, forming what are known as hydrogen bonds which are much weaker than ionic or covalent bonds.  Nevertheless, these hydrogen bonds are why water is a liquid at temperatures and pressures other similar molecules are gasses.  

Water molecule showing partial charges

Hydrogen bonds

Weak links form between the oppositely charged polar ends of a polar covalent molecule.

This explains why the boiling and freezing points of water are so high for the small size of the molecule.

Water has sometimes been called a universal solvent which is a bit overstated but water does dissolve a huge number of at least partly polar compounds. Consider ordinary table salt (NaCl) which has ionic bonds. NaCl, like NaF, is almost Na+Cl which means if the salt is placed in water, the sodium can easily separate from the chloride by shifting over to the negatively-charged end of a water molecule while the chloride is attracted to the positively-charged end of a water molecule. The salt is now dissolved in water; the sodium is a sodium cation (Na+) and the chloride is a chloride anion (Cl). Remember: if an ion has a positive charge, it is a cation; if it has a negative charge, it is an anion.

All the bonds of ethane (C2H6) are covalent and it is completely non-polar; it is almost insoluble in water. Ethyl alcohol (C2H5OH) has mostly covalent bonds but the –OH part is polar, enough to make it much more soluble in water. The formula for one common form of ordinary soap is C17H35COONa which has a polar end (–COONa) and a nonpolar end (C17H35–). Oil and grease will not dissolve in water but will associate with the nonpolar end of the soap. The polar end of the soap will dissolve in water, taking the non-polar end and anything associated with it into solution, which is how soap and detergents work.

Oxidation Numbers/States

The atoms of an element, uncombined with anything else (not part of a compound), have a balanced charge. Another way of saying that is to say that the element has an oxidation state of zero (no excess or lack of electrons). Such elements are sometimes described as ‘native’ as in native iron. Electron donors, like iron, can move to higher oxidation states if they can find electron acceptors.

Iron exposed to the wet, oxygen-rich (oxygen is a powerful electron acceptor) environment of the Earth’s surface, will quickly begin to rust (to oxidize). Iron, being an electron donor, will readily team up with oxygen, an eager electron acceptor. If the supply of oxygen is somewhat limited, native iron (Fe0, oxidation number of zero) will give away two electrons and become ferrous iron (Fe++) with an oxidation number of +2. If there is abundant oxygen, the iron will give away three electrons and oxidize to ferric iron (Fe+++) with an oxidation number of +3. Iron has three oxidation states: 0, +2, and +3 which could also be written Fe(0), Fe(II), and Fe(III), respectively. The positive oxidation states indicate that iron is an electron donor (it becomes positively charged). Note that if the oxidation number is not zero, the element becomes an ion. Iron can do this because it dissolves in water and the positive charge of the iron ion can be balanced by associating with the negative partial charge on the backend (oxygen part) of the water molecule.

Other elements have negative oxidation numbers, indicating that they are electron acceptors (if you accept a negatively-charged electron, you become negative). Some elements, depending on conditions, can have either negative or positive oxidation numbers (like sulfur and carbon). Here are three sulfur anions: SO4= (sulfate), SO3= (sulfite), and S= (sulfide). The oxidation states of the sulfur in the anions are: +6, +4, and –2, respectively. So, what are the conditions that would cause an element to be in a particular oxidation state?

An element would be in its highest oxidation state in an environment rich in strong oxidizers (electron acceptors) such as oxygen (O2), chlorine gas (Cl2), and ozone (O3). Oxic (oxygen-rich) environments oxidize (take electrons from) other elements. The opposite of an oxidizing environment is a reducing environment which has a preponderance of electron donors. It is called ‘reducing’ because it reduces (lowers) the oxidation number of elements by forcing them to accept electrons.

Figuring Out What the Oxidation Number of an Element is in a Compound

Any element, by itself and not in a compound, has an oxidation number of 0. The element in molecules of the same element would also have an oxidation number of 0; this would include, for example, the oxygens in O2 and O3 (ozone), N2 and Cl2. There are bonds between the same element in those molecules but, because they are the same element, the electron is shared absolutely equally. Put another way, any bond between two atoms of the same element does not change the oxidation number of either atom.

Some elements in compounds will reliably always have the same oxidation number. Hydrogen in a compound almost always has an oxidation number of +1 (the rare exception is in compounds called hydrides in which the hydrogen has an oxidation number of – 1). Sodium (Na) in a compound will always have an oxidation number of +1 as will the sodium ion (Na+); note that the sodium ion shows what the oxidation number is by giving the ionic charge. Calcium (Ca) in a compound or as an ion (Ca++) always has an oxidation number of +2. Fluorine (F) in a compound or as an ion (F) always has an oxidation number of –1. Chlorine can be trickier but is usually –1.

Oxygen, like chlorine, can be tricky but is usually –2. An example of where it isn’t is in hydrogen peroxide (H2O2) which is also an example of how to figure out the oxidation number of an element in a compound if you know the oxidation numbers of the other elements in the compound. In a compound, the sum of the oxidation numbers of all of its parts must equal 0. The two hydrogens are each at +1 for a total of +2. Since the oxygens must balance that out to zero, the oxidation number of each of the oxygens must be –1 for a total of –2; (+2) + (–2) = 0. How is it possible that the oxygens have an oxidation state of only –1 when each oxygen has two bonds? The answer is that the oxygens share one bond between them and when the bond is between two of the same element, it doesn’t change the oxidation number. But in most cases, you can reasonably assume that the oxygen in a compound, and certainly, as an ion, is at –2.

Here are two more examples, this time with sulfur compounds: H2S (hydrogen sulfide gas) and H2SO4 (sulfuric acid). The hydrogens are at +1 and the oxygens at –2. In H2S, then, the sulfur must have an oxidation number of –2 which is what you would expect in something called a sulfide. In sulfuric acid, the sulfur has an oxidation number of +6. In underground mine pools, very common in coal mine areas, the environment is reducing (lots of electron donors) with the result that the mine water contains quite a bit the more reduced form of ferrous iron (Fe++) and, in some case, H2S gas (usually promoting by microbial action), both of which are stable in such reducing conditions. Bring that mine water to the surface with all that oxygen in the air (oxidizing environment) and the sulfur compounds, like sulfides from pyrite (FeS2; note that in this compound, the iron is +2 and the sulfur at –1 because there is a shared bond between the sulfurs), will tend to become sulfuric acid (the ‘acid’ in acid mine drainage) and the iron will oxidize (donate electrons to oxygen) to the less soluble ferric ion (Fe+++).

This exchange of electrons is known as a redox (reduction/oxidation) reaction; something is reduced (accepts electrons) and something is oxidized (donates electrons). In this case, oxygen is an oxidizing agent or electron acceptor which oxidizes (takes electrons from) the sulfur and iron, in the process, becoming reduced itself. Oxygen goes from O2 (oxidation number of 0) to oxygen in a compound (oxidation number of –2) such as H2SO4 and Fe(OH)3 (ferric hydroxide, which then precipitates out of solution). The opposite happens with the sulfur and iron to balance the exchange of electrons. These changes happen because sulfides and ferrous iron (Fe++) are not stable in an oxidizing environment.

In methane (CH4) it should be clear that the oxidation state of the carbon has to be –4 because there are four hydrogens at +1 each. It should also be clear that methane should not be stable in an oxidizing environment such as in the atmosphere. This is true, methane is not stable in the air but it does not immediately oxidize. How fast such changes happen is a branch of chemistry called kinetics. Methane in air has a half-life of about nine years. Admittedly, while most of that methane is removed from the atmosphere by oxidizing it to carbon dioxide, there are other processes that can remove it so its duration in the air is not controlled just by the rate of oxidation. The point, however, is that just because a particular compound is unstable in a particular environment, it doesn’t mean that it will immediately convert to a more stable form.

Carbon dioxide is the most stable form of a simple carbon compound in air but it too has a half-life, of over a century. It is not removed by oxidation into something else because it is already as oxidized as it can get (oxidation number of +4) but is removed by other processes such as dissolving in water; carbon dioxide is stable in an oxidizing atmosphere. Note that carbon dioxide can have an oxidation number of anything from –4 to +4, depending on with what it is bonded. Consider glucose sugar (a carbohydrate; contains C, H, and O and nothing else) which, in addition to six carbons, has hydrogens always at +1 and oxygens always at –2:

Glucose Sugar

The oxidation state of carbon 1 in glucose is + 1, carbon 6 is – 1, and all of the other carbons are at 0.  To see how the oxidation state of the carbons is determined, consider C1 (carbon 1).  It has four bonds, one with C2, another with –OH, with –H, and one with –O–.  All of the carbon bonds are covalent bonds which means that, while the carbon will share electrons, it will not completely let go of them or completely accept them; its partners remain tightly linked to the carbon atom.  

The bond between C1 and C2  is perfectly equal in that an electron is equally shared between the carbon atoms so this bond contributes 0 to the oxidation number of those two carbon atoms.  In the –OH bond, the oxygen ‘wants’ the shared electron more than C1 does so, although C1 will not ‘let go’ of the electron, that electron will associate more closer with the oxygen atom.  This contributes a minus charge to the oxygen and a plus charge to C1.  The link with –H is the opposite; the hydrogen ‘pushes’ an electron closer to the carbon atom, giving C1 a negative charge and the hydrogen a positive charge.   The link with –O– adds a positive charge to C1 and a negative charge to that oxygen.  

The total charge or oxidation number of C1 then, is the sum of the charges from the  individual bonds or 0 + (–1) + (+1) + (+1) = +1.  All of the oxygens are at –2 and the hydrogens have an oxidation number of +1.  The sum of the oxidation numbers of all of the elements in a compound must equal 0 which, as you can see in the glucose molecule, they do even though individual carbons have different oxidation numbers.  

In an oxygen-rich environment, the glucose molecule can break down and all of the carbon ends up as CO2 in which the oxidation state of the carbon is +4 to balance the –4 total charge from the two oxygen atoms. The oxidation of the glucose releases energy (sugar will burn). The body gets energy by oxidizing glucose in a very controlled, multi-step process.

A summary of general rules, oxidation states, and more examples follows:

General Principles of Oxidation States
An atom uncombined with anything else has an oxidation state of 0
In compounds, the oxidation state is the sum of the oxidation state of each of its bonds
An atom combined with another atom of the same element has an oxidation state of 0 
examples of diatomic compounds:  O2, Cl2, N2
The bonds of atoms linked to other atoms of the same element within a larger compound contribute 0 to the total oxidation state, such as the bonds between two carbons in a compound

Oxidation states of some common elements:
Hydrogen 0, +1 rarely -1 (as a hydride like NaH)
Oxygen 0, -2 rarely -1 (as a peroxide like H2O2)
Nitrogen -3, 0 +5 rarely as others in NOx compounds like N2O (nitrogen is +1)
Sulfur -2, 0 +6 occasionally -1, there are others
Sodium 1 Sodium is so active that it will either be in a compound or be an ion.  
Potassium 1  
Calcium 2  
Chlorine   0, -1 rarely others
Magnesium 2  
Phosphorus 5 rarely others
Iron 0, +2, +3  
Carbon from -4 to +4

Examples of Oxidation States of Elements in More Compounds

The sulfur in sulfuric acid has an oxidation state of +6. The nitrogen in nitric acid and the phosphorus in phosphoric acid are +5. The carbon in carbonic acid is at +4. (The sections outlined in red are what make these molecules acids) All of the mentioned atoms happen to be in their highest oxidation states. The sulfur in H2S (hydrogen sulphide gas) has an oxidation state of –2 which means that H2S is not stable in an aerobic environment; it will eventually oxidize, first to SO2 (S is +4) and then to SO3 (S is +6) which will react with water to form sulfuric acid.

Previously you saw the carbon can have different oxidation states in the same compound and while it is rare, this can happen with other elements too. The mineral, magnetite, has a simple chemical formula of Fe3O4 which would suggest that the iron (Fe) has an oxidation number of + 16/3 to balance the –16 from the four oxygens. 16/3 !? No. The magnetite formula could be better written as FeO•Fe2O3 which clearly shows that one of the irons is at +2 and the other two are at +3. In an oxygen-rich environment, the Fe++) will oxidize to Fe+++), react with water, and become (in a temperate climate) Fe2O3•2H2O (limonite). Magnetite will rust.

Sulfur plays a trick in another common iron mineral, FeS2 (pyrite). What are the oxidation numbers of the iron and sulfur in pyrite? Pyrite is considered to be a sulfide which means that the sulfur should be at –2 but that would make the iron +4 which it can’t be. The iron is actually at +2 which means that the sulfur must be at +1 but how is that possible? The answer is that the two sulfurs share one bond with each other which doesn’t count toward the sulfur oxidation number. This leaves one bond each with the iron, giving the sulfur an oxidation number of +1.

Pyrite is often associated with coal; both are stable in reducing environments. The organic matter, which eventually became the coal, was originally deposited in a reducing environment (little or no oxygen, like in a swamp). Any iron present would have a lower oxidation number (Fe++) in such an environment and typically combines with sulfur to form pyrite. When the coal is mined, the crushed pyrite ends up in coal waste piles (locally known as culm banks) exposed to the air and water from rain. The pyrite oxidizes, releasing oxidized iron in the form of ferrous hydroxide (Fe(OH)3 – locally known as yellow boy from its color) and oxidized sulfur combines with water to form sulfuric acid, the ‘acid’ in acid mine drainage.

Burning the coal oxidizes any sulfur that might be in the coal. In our area of NE Pennsylvania (Luzerne County), the sulfur content of the coal (anthracite) is about 0.7% by weight. The oxidized sulfur again ends up as sulfuric acid, this time in the air, producing the acid in acid rain. Acid rain and acid mine drainage definitely affect water quality.

Why are oxidation numbers/states important? The oxidation state of an element in a compound can determine how stable the compound is in a particular environment as well as its solubility and toxicity in water. If a particular compound is not stable, it could be oxidized or reduced into something less desirable as in something more toxic.

The same is true of the oxidation states of ions. Ferrous iron (Fe++) is considerably more soluble in water than ferric iron (Fe+++). Uranium is just the opposite; U (IV) is more soluble in water than U (VI) is. Note that the oxidation number can be given in several different ways, one of which is to use Roman numerals. Uranium can have a very high oxidation number such as +6. Instead of writing U++++++, it is simpler to use U (VI). Cr (VI) is much more toxic than Cr (III).

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