Why doesn't chemistry refer to heat flow simply as 'heat flow'? Why 'enthalpy change'? Heat is not an inherent property or condition of a system, so it is not proper to refer to 'heat energy'. Heat refers to a transfer of energy. However, by specifying constant pressure, we can conceptualize a new state function for the system, the enthalpy, H, where H = U + PV. However, when you say enthalpy change, you do mean heat flow. Think about it. To say that enthalpy change equals heat flow is simply the 1st law of thermodynamics, i.e. the heat flow results from the change in internal energy and work.
Hess' Law of Heat Summation provides the rationale underlying the use of standard enthalpies to compute the enthalpy change of a chemical reaction.
However, when you say enthalpy, as something in itself, you are not referring to heat. That would make no sense. Heat is not a state function. What you are referring to when you refer to enthalpy in itself is a property of the system that includes the internal energy plus the work involved to push back the environment to create the space the system occupies. Enthalpy can be thought of as the 'thermal potential' of the system.
Enthalpy is a pretty good stand-in for internal energy in chemical discussion. It differs from internal energy in that when it changes, heat flows by the same amount. Enthalpy change equals internal energy change if the volume is constant.
The big advantage that comes from describing heat flow in terms of enthalpy change in chemistry is that, because enthalpy is a state function, the difference in enthalpy doesn't depend on the path between two states of the system. In other words, describing heat flows in terms of enthalpy change allows us to use Hess' Law of Heat Summation, through which discussions like the Born-Haber cycle are relevant and tables of standard enthalpies are possible.
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