In an exothermic chemical reaction the energy gained by the surroundings must be the energy lost by the reaction

In an exothermic reaction the energy gained by the surroundings must be equal to the energy lost by the reaction.

Explanation:

Exothermic reactions occur by the loss of energy in the form of heat to the surroundings (apparatus and the system).

The heat gained can be quantitatively analysed and measured  provided no product escapes the system and it is numerically equal to the amount of heat lost by the reaction.

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