In chemistry there are millions of chemical reactions. But most reactions can be classified as one of four types of reactions:

Synthesis: A + B -> AB
Decomposition: AB -> A + B
Single Replacement: A + BC -> AC + B
Double Replacement: AB + CD -> AD + CB
 
Here is a short explanation and examples of each type of reaction.
 
 -------------------------------------- Synthesis (Composition) --------------------------------------
In a synthesis reaction (also known as a composition reaction), two substances combine to form a larger substance.
synthesis
A good analogy of these reactions are dancers. In a synthesis reaction boy A walks into the dance, sees girl B and ask her to dance. They then form couple AB.

In the simplest type of synthesis reaction, two elements combine to form a compound. When writing these be sure to include a subscript 2 under any diatomic elements (hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine).

Here are four synthesis reactions:
Hydrogen + oxygen yields water
2H2 + O2 -> 2H2O
Magnesium + nitrogen yields magnesium nitride
3Mg + N2 -> Mg3N2
Iron + sulfur yields iron(II) sulfide
Fe + S -> FeS
Barium + phosphorus yields barium phosphide
3Na + P -> Na3P
IMPORTANT: You must recognize diatomic elements when writing any equation. Diatomic elements are nonmetal elements that form a covalent bond between two atoms. The diatomic elements are: hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine. As elements they always travel in pairs of atoms and therefore you must write then as:
H2 N2 O2 F2 Cl2 Br2 and I2
diatomic elements
 
Sometimes an element and a compound can combine to produce a bigger compound. Here are some examples:
Carbon dioxide + oxygen yields carbon dioxide
2CO + O2 -> 2CO2
Oxygen + water yields hydrogen peroxide
O2 + 2H2O -> 2H2O2

And sometimes two compounds can combine to form an even bigger compound.

Water + carbon dioxide yields carbonic acid
H2O + CO2 -> H2CO3
In this class you will only encounter synthesis reactions involving two elements. So it will be easy to identify synthesis reactions since the only thing two elements can do is combine to form a compound.
 
 -------------------------------------- Decomposition--------------------------------------
 
In a decomposition reaction, a larger substance breaks apart and forms two or more simpler substances.
decomposition

In our dancers analogy, boy A steps on girl B's toe. She gets upset and walks away.

The first thing you may notice about a decomposition reaction is that it is the complete opposite of a synthesis reaction. In fact many synthesis reactions can be reversed into a decomposition reaction.
 
When you burn hydrogen gas, the hydrogen combines with oxygen to produce water.
2H2 + O2 -> 2H2O Synthesis Reaction
 
With an electrical current, water can be decomposed into hydrogen and oxygen gas.
2H2O -> 2H2 + O2 Decomposition Reaction
electrolysis
 --------------------------------------Single Replacement--------------------------------------
 
In a single replacement reaction, a more active element replaces a less active element in a compound.
single replacement

In our dance analogy, Boy A and Girl B are dancing. In walks boy C, who happens to wish to dance with Girl B. If he is strong enough he can push out Boy A and dance with girl B. Now boy A is by himself. In this analogy the boys are metals and the girl is the nonmetal.

What do you think would had happened if Boy C wasn't strong enough to push out Boy A? You go it - nothing would have happened. Same goes with a single replacement reaction. If the element is not more chemically active than the element (in the compound) it is trying to replace, no reaciton will occur.
Generally, as you go across the periodic table (from I-A to IIIV-A) metals become less chemically active. A metal such as magnesium is more chemically active that transition metals such as copper, tin or zinc. An easier way to identify the activity of element is to use an activity series which shows the chemical activity of both metals and nonmetals.

Activity Series

Metals

Nonmetals

lithium

fluorine

potassium

chlorine

calcium

bromine

sodium

iodine

magnesium

oxygen

aluminum

nitrogen

zinc

chromium

iron

nickel

tin

lead

hydrogen*

copper

mercury

silver

platinum

gold

*hydrogen behaves like a metal
For the metals to replace each other, the compound containing the metal ion must be dissolved in water. Dissolving ionic compounds in water breaks up the crystalline lattice and allows the ions to move about freely. This allows the elements to replace each other.
 
Aqueous solution is a term used by chemist to denote that a compound is dissolved in water. An aqueous solution of salt is salt water. The symbol (aq) is used in chemical reactions to show that a substance is dissolved in water. So NaCl(s) is solid salt while NaCl(aq) is a solution of salt water.
crystalline lattice / aqueous
You know that when you place a piece of copper (or any other metal) in water it does not dissolve. This is because metal atoms are not soluble in water. But most metal ions (atoms that have lost electrons and become cations) are usually soluble in water. In a single replacement reaction a metal atom switches places with a metal ion in a compound. Let's see an example.
 
When a piece of magnesium is placed in a solution of lead(II) nitrate, a single replacement reaction occurs. The magnesium is more active than lead and replaces it in the compound. Lead crystals grow on the side of the magnesium and magnesium nitrate solution is produced.
Mg + Pb(NO3)2
If fluorine gas is bubbled through a solution of potassium chloride, the fluorine will replace the chlorine.
2KCl + F2 --> 2KF + Cl2
This is why there are two columns on the activity series. Element A will replace another element B (that is in a compound) only if: Element B is in same column and below element A. The metals (and H because in many ways it behaves like a metal) are in the first column while the nonmetals are in the second column. More actice metals replace less active metals, while more active nonmetals replace less active nonmetals.
 
 --------------------------------------Double Replacement--------------------------------------
 
 
In a double replacement reaction, two metal ions (in aqueous compounds) switch places.
double rep.

To use our analogy of dancers: Two couples are dancing . The two girls look over and state they wish to switch partners. And so...they do.

Of course you know it is a bit more complex than that - and here is how:

For a double replacement reaction to occur, one of the products must be insoluble and form a solid. This solid, called a precipitate, is more dense than the surrounding solution and falls to the bottom of the test tube. An arrow down is used to identify a precipitate. If both products are soluble (remain dissolved) then there is no reaction.

 
When writing double replacement reactions, both reactants must be dissolved in water (aqueous). This frees-up the ions (that normally would be locked in place in a crystalline lattice) and allows them to exchange places. If either of the reactants are not soluble, the reaction will not occur.
 
To determine if a compound in soluble (will dissolve in water) or insoluble (will not dissolve in water) you must consult a solubility table. When using the table below, look for the anion (negative ion) in the compound and then see if the cation (positive ion) is soluble with it.
SOLUBILITY TABLE

Anion

Solubility

nitrates

all soluble

nitrites

all soluble except with Ag+

chlorides

all soluble except with Ag+, Hg+, Pb+2, Cu+

bromides

all soluble except with Ag+, Hg+, Pb+2,

iodides

all soluble except with Ag+, Hg+, Pb+2,

sulfates

all soluble except with Ag+, Ba+2, Sr+2, Ca+2

sulfites

all INSOLUBLE except with any alkali metal, NH4+

sulfides

all INSOLUBLE except with any alkali metal, alkaline earth metal, NH4+

phosphates

all INSOLUBLE except with any alkali metal, NH4+

carbonates

all INSOLUBLE except with any alkali metal, NH4+

oxides

all INSOLUBLE except with any alkali metal, alkaline earth metal

hydroxides

all INSOLUBLE except with any alkali metal, alkaline earth metal, NH4+

 
In a reaction between sodium chloride solution (NaCl (aq)) and silver nitrate solution (AgNO3 (aq)) the products are sodium nitrate(NaNO3 (aq)) solution and silver chloride solid (AgCl (s)).
double replacement reaction
Since silver chloride is insoluble (won't dissolve in water) it forms a white solid and sinks to the bottom of the test tube. A solid that forms in a double replacement reaction is called a precipitate. Here is a photo of this reaction:
AgCl
Here are some other double replacement reactions:
NaCO3 (aq) + BaCl2 (aq) --> 2NaCl (aq) + BaCO3 (s)
K3 PO4 (aq) + 3MgF2 (aq) --> 3KF (aq) + Mg3PO4 (s)
2NH4 OH(aq) + CuCl2 (aq) --> 2NH4 Cl(aq) + Cu(OH)2 (s)
Pb(NO3)2 (aq) + CaBr2 (aq) --> Ca(NO3)2 (aq) (aq) + PbBr2 (s)

IMPORTANT : If both products are soluble in water (remain dissolved and do not form a solid) then there is no reaction. Here are some examples of where that occurs:
NaNO3(aq) + AlCl3(aq) --> No Reaction (both the products NaCl + Al(NO3)3 are soluble in water and do not form a precipitate.)

BaBr2(aq) + KI(aq) --> No Reaction (both the products BaI2 + KBr are soluble in water and do not form a precipitate.)

MgSO4 + Fe(NO3)2 --> No Reaction (both the products Mg(NO3)2 + FeSO4 are soluble in water and do not form a precipitate.)

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