If the breaking of bonds requires an input of energy (which it always does), how is it possible that some chemical reactions (like the burning of gasoline, for instance) can release energy into the environment?
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Answer:
The breaking of chemical bonds never releases energy to the external environment. Energy is only released when chemical bonds are formed. In general, a chemical reaction involves two steps: 1) the original chemical bonds between the atoms are broken, and 2) new bonds are formed. These two steps are sometimes lumped into one event for simplicity, but they are really two separate events. For instance, when you burn methane (natural gas) in your stove, the methane is reacting with oxygen to form carbon dioxide and water.
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Other answers
The total energy input or output of a reaction equals the energy released in forming new bonds minus the energy used in breaking the original bonds. If if takes less energy to break the original bonds than is released when new bonds are formed, then the net energy of the reaction is positive. This fact means that the energy will flow out of the system as the reaction proceeds. This fact also means that the reaction can proceed on its own without any external energy once started. Such reactions are known as exothermic.
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