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Composition

The Chemistry of fireworks is based on the simple theory of combustion. The composition inside the firework must however contain 6 vital ingredients

Fuel
Charcoal, commonly known in the pyrotechnic industry as black powder is the most common fuel used in fireworks. Normally, all fuels will contain an organic element such as charcoal or thermite.
The mechanism by which the fuel functions in the firework is relatively simple. The fuel loses electrons to atoms within the oxidizer (thereby reducing the oxidizer) and releasing atoms from the oxidizer. During this process, bonds are formed between the fuel and oxygen atoms forming a product which is relatively stable. However, only a minimal amount of energy is required to start the combustion of this fuel-oxidizer compound. When combustion does start, the result is a massive release of energy as the solid mixture liquefies and vaporizes into the flame of ignition. This maximizes the probability of reaction of the oxidizer as it is brought into the close proximity of the flame.
Oxidizing Agents
The function of the oxidizing agent is to produce the oxygen needed in order for the mixture inside the firework to burn. These oxidizers can be nitrates, chlorates or perchlorates.

Nitrates only give up a third of their oxygen as the equation above illustrates.
On the contrary, Chlorates get completely reduced as they are better oxidizing agents and so cause an even more spectacular reaction. This however does cause the reaction to become extremely explosive.

Perchlorates contain even more oxygen but are less likely to explode than chlorates due to their increase in stability. 

They follow the reaction below:

Reducing Agents
The second part to a firework is the reducing agent. These burn the oxygen provided by the oxidizing agents to produce hot gasses.
Common reducing agents are Sulphur and Charcoal. These react with the oxygen to form Sulphur dioxide and Carbon dioxide respectively as illustrated below.
By mixing both the reducing agents, the speed of the reaction can be controlled.
Regulators
Metals can be added to regulate the speed at which the reaction. The larger the surface area of the metal, the faster the reaction will proceed (collision theory).
Coloring Agents
Different chemicals are used to produce different colored fireworks. Therefore, in order to produce a firework of a certain color, the correct corresponding chemical or as the case may be, mixture of chemicals can be used:
Metal
Color
Strontium
Red
Copper
Blue
Barium
Green
Sodium
Yellow/Orange
Calcium
Orange
Gold
Iron
Hence Strontium used in conjunction with Copper will yield a purple firework. 

The incandescence from the elements occurs when solid particles are heated in the flame to extremely high temperatures. These release excess energy in the form of light (hv) at the broad end of the spectrum. The higher the temperature, the shorter the wavelength at which light is emitted, and the nearer it tends toward the blue end of the colored spectrum. This is why blue colored fireworks are so hard to synthesize, as they only occur at very high temperatures.
Binders
Binders are used to hold what is essentially the mixture of the firework together in a paste like mixture. The most commonly used binder is known as dextrin, a type of starch which holds the composition together. Parron can also be used in binding; however, it is less common and only used in conjunction with red and green fireworks as it helps to enhance their color. The binders do not actually begin to work until the firework has been lit as they are too unstable for storage within the firework and are hence potentially dangerous.


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