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For example, $MnCO_3 → MnO + CO_2$ is endotermic, and occurs at 473 K

the polymerization of ethylene $H_2C=CH_2$ to $n(H_2C=CH_2)$ is exotermic

I suspect it has something to do with the standard enthalpy of formation of the different terms of the equation (right side - left side = $\Delta H$ if negative, the reaction is exotermic and releases $\Delta H$ to the environment as heat, if positive, it is endotermic and needs $\Delta H$ to happen.

Is this correct?

If not, What am I missing?

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You are correct. If you have enthalpies of formation of each reagent and each product then you sum up enthalpies of each product multiplied by stoichiometric coefficient and subtract enthalpies of each reagent multiplied by stoichiometric coefficient. If the result is negative then the reaction is exothermic and vice versa.

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