C + O = CO2 . This is because carbon has valency of 4 while oxygen has valency of 2. When they react the valencies are criss crossed which means we will get C2O4 but this is simplified to CO2.
But my textbook say that C + O2 = CO2.
So how is it possible that C + O2 and C + O both get the same product of CO2?
Also you can say that the reaction of C + O = CO2 is not balanced but the balanced chemical reaction would be C + 2O = CO2 not C + O2 = CO2 which is the reaction that my textbook says.
When thinking about chemical reactions it is very important to know which chemicals may react with each other. Jun-Goo Kwak already pointed out the nature of oxygen.
A quick reminder: The ground state of elementary oxygen is the triplet biradical $\ce{o2}$, which is a gas. This is what we have on the surface of the earth. Carbon however comes in many different forms in nature. The most popular and often is graphite. Other forms include diamond, fullerenes and graphene. At one point in your life you haw almost certainly come in contact with graphite: coal. As the principle repeating unit is carbon itself, its formula will be written as $\ce{C}$.
As for the binary combination of oxygen and carbon, there are also many different modifications. The most important of them are carbonmonooxide ($\ce{CO}$) and carbondioxide ($\ce{CO2}$). Like Uncle Al stated there are also suboxides known, which are usually byproducts of incomplete combustion (if not targeted explicitly).
Having said all that, if you burn coal, the following main reaction will happen (1):
$$\ce{C + O2 -> CO2}$$
However, given the right conditions (excess carbon) also carbonmonoxide may be formed (sum of reaction, 2):
$$\ce{2C + O2 -> 2CO}$$
The reaction itself will detour via the Boudouard reaction, which is very important in blast furnace processes. First forming carbondioxide via 2 and then convertin excess carbon to carbonmonoxide via 3: $$\ce{C + CO2 <=> 2CO}$$
Let's first take a look at the allotropes of oxygen, and look into dioxygen more in depth.
From NASA, http://www.nasa.gov/topics/technology/features/atomic_oxygen.html, regarding atomic oxygen:
Atomic oxygen doesn't exist naturally for very long on the surface of Earth, as it is very reactive. But in space, where there is plenty of ultraviolet radiation, $\ce{O2}$ molecules are more easily broken apart to create atomic oxygen. The atmosphere in low Earth orbit is comprised of about 96% atomic oxygen. In the early days of NASA's space shuttle missions, the presence of atomic oxygen caused problems.
Dioxygen, or triplet oxygen, is the most commonly known allotrope of oxygen. It has the molecular formula $\ce{O2}$. Oxygen has 8 electrons with 2 in the 1s, 2 in the 2s, 4 in the 3p orbitals. Alternatively, there are 6 valence electrons. If there are another oxygen molecules, oxygen will pair up, form a double bond with bond order of two. In short, the potential energy of dioxygen is far less than that of atomic oxygen.
One interesting aspect of oxygen is that it exhibits paramagnetism unlike $\ce{N2}$ and it can exist in two different electronic states called singlet oxygen. The picture of the molecular orbital (MO) diagram of oxygen makes this more clear:
The MO diagrams above are for the singlet oxygen $a^1\Delta g$ excited state, the singlet oxygen $b^1\Sigma \text{g+}$ excited state, and the triplet ground state $X^3\Sigma \text{g-}$ respectively.
What you may notice is a spin flip in the $b^1\Sigma \text{g+}$ excited state.
This definition taken from Purdue University summarizes Hund's rule of maximum simplicity nicely: every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.
The two first diagrams are in violation of the 1.) spin-selection rule: spin-flips are foridden, and 2.) Laporte selection rule: trasnsitions between orbitals of the same parity are forbidden, where parity means symmetry with respect to inversion. There is a german notation, gerade - which refers to symmetric with respect to inversion and ungerade - antisymmetric with respect to inversion.
There are many ways to produce ozone. https://en.wikipedia.org/wiki/Ozone#Production Ozone is a triatomic molecule with 3 oxygens. It is much less stable than dioxygen and often breaks down into dioxygen.
What you may have been confused with is Dalton's incorrect "rule of greatest simplicity." Dalton was trying to resolve the issue of the correct ratio and number of atoms in respect to the chemical formula.
He assumed that:
$$ \ce{H + O -> H2O}$$
However, we know that:
$$ \ce{H2 + O2 -> 2H2O}$$
It wasn't until Avogadro and Gay-Lussac who stated the Law of Multiple Proportions and postulated the existence of diatomic molecules, that we can now resolve Dalton's incorrect hypothesis.
When two elements form a series of compounds, the masses of one element that combine with a fixed mass of the other element are in the ratio of small integers to each other.
The common products of carbonaceous materials' combustion are carbon monoxide and carbon dioxide. The products determine the equation. The equation does not dictate the products.
Carbon suboxide $\ce{C2O3}$ is known. Benzene hexacarboxylic acid trianhydride is a carbon oxide. Combustion generally outputs simple molecules in deep thermodynamic holes.
