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Carbon steel is iron containing some carbon in various forms of iron carbide.
When it rusts (oxidises), the iron becomes part of all kinds of crystalline and amorphous iron oxides and hydroxides, mostly as Fe3+.
Where does the carbon go in this process? Does it also oxidise to carbon dioxide or monoxide and leaves the system as a gas? Does it combine with the iron to form siderite (iron carbonate)? Does it remain as graphite or some other form of elemental carbon? Something else?
Cast iron has considerable free carbon as graphite, but carbon steel has iron carbide in cementite, $\ce{Fe3C}$ in a ferrite ($\ce{α-F}$e) matrix, along with other phases and additives. In a corrosive environment, the ferrite and cementite form a galvanic couple, causing increased corrosion of the $\ce{α-F}$e while effectively protecting the $\ce{Fe3C}$. According to Acta Metallurgica Sina,, "So, the ferrite phase diminishes gradually, and the accumulated cementite multiplies on the surface of the specimens along with the development of corrosion."
That said, what now happens to the remaining $\ce{Fe3C}$? Wikipedia states, "While cementite is thermodynamically unstable, eventually being converted to austenite [$\ce{γ-Fe}$] and graphite at higher temperatures, it does not decompose on heating at temperatures below... 723 °C..."
So, at room temperature, the remaining carbon would be specks of cementite amid the rust.
