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I've seen a few videos on cola being used to remove rust, I've tried it myself too so I know that it works.

Now the thing that's bothering me is that this apparently contradicts what I've learnt about corrosion in class. If I'm not wrong, cola contains phosphoric acid, and therefore would most probably have free H+ ions floating around in there. I've been taught that H+ promotes (catalysis) the rusting of iron.

Then how come coke removes rust instead of promoting its formation? Also, why doesn't coke form rust on iron?

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Rust is a hydrated iron oxide that has a volume greater than the iron it contains. When iron rusts, the oxide grows in layers and curls away from the iron, exposing it to more corrosion.

Phosphoric acid is a moderately strong acid, but it forms an iron phosphate that is insoluble but adherent to iron (and steel). In that sense, phosphoric acid deactivates corrosion on iron (not perfectly, but pretty good), and there are commercial products (like Naval Jelly) which are essentially gelled phosphoric acid, designed to rub on iron and steel to give some corrosion protection. It is a sort of passivation.

Phosphate ions adhere to rust, making rust particles negative and promoting dispersion in the liquid and disadhesion from the iron metal. Some elbow grease is generally needed.

Overall, the extra corrosion from Coke or other phosphoric acid is minimal, and the dispersive effect is helpful, and the iron is better protected after the treatment than before.

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Well, yes, $\ce{H+}$ ions accelerate rusting. The coke has phosphoric acid and $\ce{CO2}$.

The phosphoric acid is used for rust removal industrially.
The rate of acceleration of rusting of iron (with $\ce{H+}$ ions) is very slow and all the rust will have already reacted with phosphoric acid to form iron phosphate.

All the rust is already destroyed and the $\ce{H+}$ ions just increase the rate catalytically, but now there is no rust left for this effect to work.

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