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What is the action of carbon on the following metal oxide $F{{e}_{2}}{{O}_{3}}$ in a blast furnace?

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Hint: Blast furnace is used to get pure iron. The cast iron is heated at elevated temperatures of about 500 to 2200K at different levels of the blast furnace. The main aim of blast furnaces is to reduce the iron by the removal of oxygen.

Complete answer:
Iron is extracted from iron ore in a huge container called a blast furnace.
Extraction of iron from its ore is the third and the penultimate step in the process of metallurgy. The few steps of extraction and isolation are: Concentration of ore, Extraction of metal from concentrated ore, Purification of the metal.
The purpose of the blast furnace is to reduce the concentrated ore chemically to its liquid state.The blast furnace is gigantic, steel stack lined with refractory brick, in here concentrated iron ore,coke and limestone are dumped from the top, and hot air is blown into the bottom.

\[F{{e}_{2}}{{O}_{3}}+3C\xrightarrow{\Delta }2Fe+3CO(g)\]
The oxygen must be removed from the iron(III) oxide in order to leave the iron behind. Reactions in which oxygen is removed are called reduction reactions.

Note: Wrought iron is the purest form of iron available commercially, and is prepared from the cast iron by heating the cast iron in a furnace line with Haematite ($F{{e}_{2}}{{O}_{3}}$). Limestone is also added in a blast furnace as flux and it creates the slag. Impurities such as S, Si pass into the slag and the slag late can be easily separated to yield pure iron.