When wood burns, a small amount of ash is made. Why is the mass of the wood before the fire not equal to the mass of the wood after the fire?

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The burning of fuel (in this case wood) in the presence of oxygen to produce energy in the form of fire is called combustion.  Combustion requires three things, a source of fuel (hydrocarbon based), oxygen (usually from the atmosphere), and a spark to initiate it.  The products of combustion are carbon dioxide, water vapor, and energy in the form of fire.  The reason that a smaller amount of ash remains than wood that was there to start with is because much of the mass of wood was converted to carbon dioxide and water vapor and dissipated into the air.  During complete combustion, there would be no ash remaining since all of the fuel would have been completely consumed.  Some ash remains behind for two reasons.  One is that there are some elements in wood that are not carbon, hydrogen, or oxygen and thus cannot be converted to CO2 or H2O.  Second is that in the real world we experience incomplete combustion so some of the carbon remains behind as carbon soot (ash).

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