Why does the enthalpy change for the reverse of a reaction have an opposite sign?

The enthalpy change for the reverse of a reaction has an opposite sign because it involves energy being absorbed or released in the opposite direction.

In a chemical reaction, the enthalpy change, represented as ΔH, is a measure of the amount of energy absorbed or released by the reaction. If a reaction is exothermic (releases heat), the enthalpy change is negative, indicating that energy has been lost to the surroundings. Conversely, if a reaction is endothermic (absorbs heat), the enthalpy change is positive, indicating that energy has been gained from the surroundings.

When a reaction is reversed, the direction of energy transfer is also reversed. An exothermic reaction in the forward direction becomes an endothermic reaction in the reverse direction, and vice versa. This is why the sign of the enthalpy change is reversed for the reverse reaction.

For example, consider the combustion of methane, which is an exothermic reaction. The enthalpy change for this reaction is negative, indicating that energy is released. If we consider the reverse reaction, which is the formation of methane from carbon and hydrogen, this is an endothermic process. The enthalpy change for this reaction is positive, indicating that energy is absorbed.

This concept is a fundamental aspect of thermodynamics in chemistry, and it is crucial for understanding how energy changes affect the feasibility and direction of chemical reactions. It's also important to remember that the magnitude of the enthalpy change remains the same for a reaction and its reverse, only the sign changes. This is because the amount of energy involved in breaking and forming bonds remains the same, only the direction of energy transfer changes.

In summary, the sign of the enthalpy change for the reverse of a reaction is opposite because it signifies a reversal in the direction of energy transfer. This is a key concept in understanding the energy changes that occur during chemical reactions.