Thus far in the math/science subjects:
- Math/Science Overview
- Basic Types of Numbers
- The Atom and Quantum Physics
- The Periodic Table
- Molecules and Ions
1. There are two basic kinds of changes that substances can undergo. Physical changes do not change the chemical structure of something. Molecules remain the same molecules. Ionic compounds remain the same ionic compounds. But a chemical might change its physical state without changing its chemical structure. A gas might condense into a liquid or a liquid might evaporate into a gas. A liquid might freeze into a solid or a solid might melt into a liquid. These are examples of physical changes.
Chemical reactions, on the other hand, actually involve a change in the chemical structure of the elements or compounds that are reacting. The law of conservation of matter means that no element can be destroyed.  Accordingly, if there are a certain number of atoms of certain types before the reaction, there must be the same number of atoms of the same types after the reaction. The elements just get arranged in different ways.
2. So two very simple kinds of reaction are a "composition" reaction and a "decomposition" reaction. In the first kind of reaction (composition), two different elements or compounds come together to form a single compound. In the second (decomposition), one compound breaks down into two or more elements or compounds.
Take the following reaction:
H2 + O2 → H2O
This is a composition or "synthesis" reaction because a hydrogen and an oxygen molecule combine to form a water molecule. It is also, by the way, a combustion reaction because this process normally takes place by burning hydrogen. Sometimes a little Δ (delta) is put above the arrow to indicate the addition of heat.
3. The equation above is "imbalanced" because there are two oxygens (O) on the left side of the reaction (the "before" side) but there is only one oxygen on the right side (the "after" side). "Balancing" an equation is when you make sure there are the same number of each type of atom on both sides of the equation. This is necessary because you can't create or destroy matter.
After a little trial and error, here is what a balanced form of this same equation looks like:
2H2 + O2 → 2H2O
The number in front of a chemical symbol indicates that many of that particular molecule. So 2H2 means two hydrogen molecules.  So now we have 4 hydrogens on the left side of the equation and 4 hydrogens on the right side. But now we have two oxygens on the left and two oxygens on the right. The equation is "balanced."
4. The process can also happen in reverse in a "decomposition" reaction. If you put electricity through water (electrolysis), water will begin to decompose into hydrogen and oxygen gas molecules. The balanced decomposition reaction looks like the following:
2H2O → 2H2 + O2
5. Two other kinds of reaction are single replacement reactions and double replacement reactions. In a single replacement reaction, an element in one compound trades places with an element in another:
AB + C → AC + B
For example, if you take silver nitrate (AgNO3)  and add it to copper in solid form (Cu), the copper trades places with the silver, forming copper or "cuprous" nitrate (CuNO3)  and the silver coming out in solid form. The balanced formula looks like the following:
AgNO3(aq) + Cu(s) → CuNO3 + Ag(s) 
When a solid comes out of solution, as the silver does here, we call it a "precipitate."
6. Another way of thinking about many single replacement reactions is as oxidation-reduction reactions or redox reactions. "Oxidation" refers to some component of a reaction losing electrons (OX-loss). "Reduction" refers to some component of a reaction reducing its charge or gaining electrons. "OIL RIG" might help a person remember what the definitions mean. "Oxidation is loss, Reduction is gain" of electrons.
So in the silver nitrate reaction, silver gains electrons (it goes from +1 to 0) and copper loses electrons (it goes from 0 to +1). So the copper is "oxidized" because it loses electrons. The silver is "reduced" because it gains an electron and gets more negative, in a sense. We say that the silver is an "oxidizing agent" and the copper is a "reducing agent."
Elements are assigned an "oxidation number" somewhat depending on what column they are in on the periodic table. Any element in column 1 has an oxidation number of +1. Any element in column 7 has an oxidation number of -1. The rest is predictable. Oxygen is -2. Nitrogen is -3. Carbon can be either +4 or -4.
7. In a double replacement reaction, two elements in two compounds trade places:
AB + CD → AC + BD
For example, if you take sodium chloride (NaCl) and mix it with silver nitrate (AgNO3), the sodium and the silver will trade places, yielding sodium nitrate (NaNO3) and silver chloride (AgCl), which will come out of solution as a precipitate. The balanced formula is:
AgNO3(aq) + NaCl (aq) → NaNO3(aq) + AgCl(s)
8. A slightly more complicated example is when you dissolve marble, calcium carbonate (CaCO3), in sulfuric acid (H2SO4). The calcium will take the place of the hydrogen, yielding calcium sulfate (CaSO4), and the hydrogen combines with some of the oxygen to form water (H2O). Carbon dioxide is also formed (CO2).
The equation is CaCO3 + H2SO4 → CaSO4 + CO2 + H2O
9. In the previous post, we mentioned that acids are compounds that want to give a proton and most typically have hydrogen ions as part of their formulas. Bases are then compounds that attract protons, often having an OH- ion at the end of their formula.
One special kind of double replacement reaction involves the neutralization of an acid with a base.  One example would be the neutralization of sulfuric acid (H2SO4) with sodium hydroxide (NaOH):
H2SO4 + 2NaOH → NaSO4 + 2H2O
Next Week: Math/Science 7: The Basic Tools of Algebra
 Some radioactive degenerations involve one type of atom deteriorating into two lighter atoms.
 One molecule of hydrogen (H) consists of two hydrogen atoms (H2). We say that it is a "diatomic" molecule for this reason. The reason there are two is because with each hydrogen sharing its one electron with the other, the outer shell of the hydrogen is full. Hydrogen and helium don't follow the octet rule because they only have one "s" shell, which only can take two electrons.
 Ag is the symbol for silver because it is an element that has been known long enough to go by its Latin name argentum. The ion NO3 is the nitrate ion. It has a negative one charge.
 Some elements, like the transition metal copper, has more than one ionic charge. So copper can either take on a +1 charge or a +2 charge. When the +1 form combines to form a compound, it is called "cuprous" something. When the +2 form combines it is called "cupric" something.
 (aq) means that the compound is dissolved in water and is "in solution."
 One way to neutralize is by a method called titration, where an acid or a base is dripped into the other until the resulting solution is completely neutralized.