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The experiment is described in the following link: http://www.sciencekids.co.nz/experiments/invisibleink.html

I carried out a small research but I was unable to find what exactly happens. In other words which particular acids, present in lemon juice, are oxidized (e.g. citric acid, malic acid etc.)? And what causes the brownish colour?

Any kind of help would be appreciated.

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Lemon juice contains sugars (carbohydrates) and acid (lemon acid). Sugars turn into carbon+water when heated in presence of acid. This is a standard thin layer chromatography analysis for sugars (spray plate with acid and heat up - black spots are sugars). The reaction is

C12H22O11 (sucrose) + H$^+$ (catalytic) -> 12C (charcoal) + 11 H2O (steam).

Paper also has polysugars (cellulose), but cellulose is more robust. Eventually even paper will turn black by the same reaction.

You can use sugar + vinegar as the ink. Result will be the same. It proves that decomposition of sugars in presence of acid is the reaction responsible for revealing this ink.

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