Most candles today are made from paraffin wax, a solid mix of hydrocarbons each with between 20 and 40 carbon atoms per hydrocarbon chain. When you light the wick with a match or lighter a small amount of the wax is melted and that is drawn up the wick by capillary action where it combusts, giving a flame. That flame melts more wax and so the candle will burn until it’s put out or the flame is otherwise stifled it runs out of fuel.
The hydrocarbons and oxygen from the air react exothermically (giving off heat and light) and producing water vapour and carbon dioxide, just as Michael Faraday demonstrated in his original chemical history of a candle. However, although we know the basics, chemists still don't understand or even know every chemical reaction that is taking place in that simple flame.
via Chemistry of the advent candle.
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