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What is the correct name for a reaction like this?

$$ \ce{ 4MnO2 ->[500\ ^\circ \text{C}] 2Mn2O3 + O2 ^}$$

Is it a synthesis, or a Decomposition? I tried to find it out with http://en.wikipedia.org/wiki/Chemical_reaction but i did not get the link between the formula and the nomenclature as it seems to be both.

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This is a decomposition reaction. Synthesis requires a minimum of two reactants. Decomposition is where a reactant breaks down into two or more products. Here, one reactant (MnO2) goes to two products. It seems like it may not be decomposition because MnO2 is becoming MnO3, but it is still one reactant to two products.

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This reaction is definitely decomposition. Decomposition reactions involve taking one reactant and destabilizing its bonds in order to produce 2 or more products. In this case, the 500 degree Celsius condition (indicated above the reaction arrow) indicates that heat energy is being added to decompose the molecule of MnO2. This is more commonly called "thermal decomposition" (Check out this link: http://en.wikipedia.org/wiki/Thermal_decomposition).

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