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It's necessary to identify this because we treat the systems differently. For example, in an open system, there will always be constant pressure, so we can treat q as deltaH, where as in a closed system or isolated system, this may be different.
The system gives you insight into where the energy of the reaction is going. In a closed system, since no heat or energy is lost to the environment, delta H is equal to delta U, the internal energy of the system. For closed or open systems it is much more difficult to quantify how much heat is lost to the environment, so calculations lose accuracy. It is still possible to do open system, constant pressure calorimetry calculations, but the approach changes based on the system.
It is important to know what kind of system is present because the type of system will determine whether energy and pressure have to be constant or if they can change so that you can complete accurate calculations and choose the correct equations to use.
Identifying different types of systems allows you to understand how the flow of energy is moving and determine how to calculate reaction energy; for example, it is extremely difficult to determine the heat lost or gained in an open calorimetry system.
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