I3,
You ask: "is there any basic equation or is there some element(apart from oxygen) that is necessary to make a fire?"
The answer to that last question is no, not even oxygen. The confusion you are experiencing is typical of what happens when you do not quite understand the thing that you are asking questions about. In this case you do not even understand some of the things about the thing that you asking questions about. Let's see whether we can get down to basics and if so, dispel the confusion.
1: What is fire? Any time that I can react substances that give off so much heat that they not only go on reacting without my doing anything to encourage them, but also produce mixtures of hot gases in which much of the reaction takes place. The volume in which we find those hot gases, we call a flame, and the process of reaction we call a fire. There are funny exceptions to this, such as when some metals burn in air, but they do not really affect the argument. Think of a candle flame. You heat enough of the wax hot enough to produce vapour and make it start reacting with the air. The heat given off heats more wax and starts it reacting in its turn. This goes on till you run out of wax or air. That is what we call a process. Right? If instead of burning wax in air, I burnt white phosphorus in chlorine, none of the elements would be the same, but the process would be very much the same. For a couple of contrasting examples imagine burning a jet of hydrogen in oxygen, producing water. If you introduce a jet of oxygen into hydrogen, the jet of oxygen would burn exactly as fiercely. And no one would be in any doubt that any of those processes would be fire: reacting chemicals going in, giving off enough heat to keep the process going, and producing non-reacting chemicals as products.
2: If you think that the process consists of elements, ask yourself what a race is made of. What is a race? We might have a lot of people beginning at one place and seeing who can be the first to get to another place, right? A process, right? But, you ask that race is made up of people isn't it? Well come with me to the finishing line, where we gather up all the competitors and display them to someone who wants to know what a race is made up of, right? So he points at this group of people and says: "You say that is a race? But I saw a lot of other people this morning, and nobody said they were a race; what makes this group of people a race? And why don't those people have aircraft? Isn't a race made up of aircraft?" You know, I think the person asking that question has a point. Just as I can have a flame containing oxygen and a flame containing chlorine, but I can have oxygen without any flame and chlorine without any flame, so I can have a race with wild horses and no people, or people in aircraft or boats. What makes it a flame is not what it is made up of, but the nature of the process, and the same applies to racing. If you can't get your head around the process concept, then don't bother thinking about fire.
3: You speak about the fire having a state, namely a plasma state, and you say that to have a state something must be made of something. However, that makes no sense for example processes can have all sorts of states without being made on anything; processes can be self-sustaining (or not) fast (or slow) abstract (or material) and so on. The plasma state in this case is not even the state of the fire, but a state consequent on the fire, caused by the fire if you like; what it means is that some of the electrons have been stripped from some of the atoms or groups of atoms in the gas and more or less move along with them, helping them to react. But this has nothing to do with whether the flame is the reaction of oxygen with hydrogen, or the reaction of phosphorus with chlorine, even though every single atom in each of those processes is different from the other process.
4: Georg mentioned that classically fire was regarded as a substance, that the Greeks called an element. I do not know whether that is what you were thinking of when you ask the question, but it is not an idea that makes sense when one understands the abstract concept of a process. It is a bit like asking "What kind of wood is floating made of?" We know that we can make floats of at least some kinds of wood, but floating is a state or a process, depending on how you look at it, and it is very little to do with wood as such. For example wood floats nicely on mercury or concentrated brine, but not on liquid nitrogen, although an empty, light glass shell could float on it quite nicely.
Is this helping you?
