Oxydation of glycerine by potassium permanganate

Potassium permanganate reacts with glycerine (glycerol, propane-1,2,3-triol,$C_2H_8O_3$) to form a mixture of potassium carbonate, carbon dioxide, manganese dioxide and water. Write the formulas of these substances!

$KMnO_4$, $K_2CO_3$, $MnO_2$, $CO_2$, $H_2O$

Equilibrate the equation of this reaction !

$14KMnO_4$ $+$ $3C_2H_8O_3$ $\longrightarrow$ $7K_2CO_3$ $+$ $14MnO_2$ $+$ $2CO_2$ $+$ $12 H_2O$

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