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Q: What state of matter is 'fire', solid, liquid, gas, or plasma?
Krishna:  A flame is glowing combustion products. Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products.
For the most part, fire is a mixture of hot gases. Flames are the result of a chemical reaction, primarily between oxygen in the air and a fuel, such as wood or propane. Depending on what material is used to produce it, a flame can also be  a mixture of reacting gases and solids. 
Simply defined (3), fire is a chemical reaction in a mixture of incandescent gases, typically luminous with intense heat. But candle flames, wood fires, and propane fires aren’t created equal. What constitutes fire depends on the fuel being burned. The chemistry of each type of fire is different. All fires eventually burn themselves out, unlike solids, liquids, and gases, which can exist indefinitely in the same state.
In many cases, such as the burning of organic matter, for example wood, or the incomplete combustion of gas, incandescent  solid particles called soot (1) are produced. Flames though consist primarily of carbon dioxide, water vapour, oxygen and nitrogen.
In addition to other products, the reaction produces carbon dioxide, steam, light, and heat. If the flame is hot enough, the gases are ionized and become yet another state of matter: plasma. Burning a metal, such as magnesium, can ionize the atoms and form plasma. This type of oxidation is the source of the intense light and heat of a plasma torch.
While there is a small amount of ionization going on in an ordinary fire, most of the matter in the flame is a gas. Or, you can say it's mostly gas, with some amount of plasma at high temperatures.
Forest fire : Source: nj.gov.

There are several parts of a flame; each is made up of different chemicals (2).

  • Near the base of a flame, oxygen, and fuel vapor mix as unburned gas. The composition of this part of the flame depends on the fuel that is being used.
  • Above this is the region where the molecules react with each other in the combustion reaction. Again, the reactants and products depend on the nature of the fuel.
  • Above this region, combustion is complete, and the products of the chemical reaction may be found. Typically these are water vapour and carbon dioxide. If combustion is incomplete, a fire may also give off tiny solid particles of soot or ash. Additional gases may be released from incomplete combustion, especially of "dirty" fuel, such as carbon monoxide or sulfur dioxide.

While it's difficult to see it, flames expand outward like other gases. In part, this is hard to observe because we only see the portion of the flame that is hot enough to emit light. A flame isn't round (except in space) because the hot gases are less dense than the surrounding air, so they rise up.

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