Why does paraffin burn with a dirty flame?

Answer 1

It doesn't, always. Sometimes it does. Paraffin is a series of complex hydrocarbons of varying lengths. C31H64 is one common paraffin chain. Several different chains may also contain other elements. Often, paraffin molecules are notated as CxHxXx, where the xs are replaced with the number of elements in the chain and the X is an added element.

Most paraffin waxes used for burning are done so as candles, these paraffins are usually highly refined, containing mostly carbon and hydrogen atoms. These paraffins typically burn with a clean smokeless flame. The reason candles burn with a smoky flame are two fold. First the wick which is often cotton thread doesn't burn cleanly. Secondly, the paraffin itself, doesn't burn completely, due to a lack of sufficient oxygen in the 'combustion zone'. This lack of oxygen creates a yellow-orange flame, an incandescent light, which is the primary purpose of a candle. This incomplete combustion aside from producing light, also produces "soot", or smoke, the result of unburnt carbon atoms. This is the source of a 'dirty' flame.

If enough oxygen were present or added to the flame by mechanical means the paraffin would burn completely and with a nearly invisible blue flame giving off little to no light. This is why candles (and lanterns) burn with smoky flames.