The chemical reactions involved in the conversion from carbon to carbon dioxide to sodium carbonate to sodium bicarbonate back to carbon dioxide can be represented as follows:

C + O2 -> CO2
CO2 + NaOH -> Na2CO3
Na2CO3 + H2O + CO2 -> 2 NaHCO3

Therefore, the overall reaction would be:
C -> CO2 -> Na2CO3 -> NaHCO3 -> CO2

This series of reactions involves the combustion of carbon to form carbon dioxide, the reaction of carbon dioxide with sodium hydroxide to form sodium carbonate, and the reaction of sodium carbonate with water and carbon dioxide to form sodium bicarbonate. The sodium bicarbonate can then decompose back into carbon dioxide, completing the cycle.