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I'd just like to thank you for posting this, your comment to Toni's post was really good and helped me with my Chem coursework, which I was really struggling with, thanks:)
Limescale is mainly composed of calcium carbonate, CaCO3. All acids react with carbonate compounds to liberate CO2 gas.
Ethanoic (acetic), citric and sulfamic acids are weak acids, however, they are capable of supplying H+ ions. The H+ ions react with CaCO3 in the following way:
CaCO3(s) + 2H+ --> Ca2+ + CO2(g) + H2O
The limescale is dissolved. The anion of the acid is also in solution with the calcium ions. This solution can be easily washed away, and the limescale is gone. Weak acids like the acetic acid are in vinegar.
This doesn't exactly answer HOW the acids remove the limescale :/
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Thanks for posting this, very helpful