Formic acid reaction with potassium permanganate
"Cr_2 O_7 + 8H + 3HCOOH \u2192 2Cr_3 + 3CO_2 + 7H_2 O"
Formic acid is not a true acid, hence it reduces Tollen's reagent to metallic silver.
Acetic acid reaction with potassium permanganate
"K_2Cr_2O_7 + 8CH_3COOH \u2192 2CH_3COOK + 2(CH_3COO)3Cr + 4H_2O + \\frac{3}{2}O_2"
Acetic acid, propionic acid and butyric acid do not react with Tollen's reagent.
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