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Since they are interchangeable, I do not believe it matters which notation you use. However, since Dr. Lavelle has been using deltaH almost exclusively in lecture so far, I take it that we would mainly use deltaH.
For all intents and purposes, I think it is just important to know the concept behind their interchangeability. q is used to describe values of released or absorbed heat, and using the subscript p to create "qp" just means you are looking at the change in heat at a constant pressure. This is the definition behind enthalpy, as enthalpy can be described in terms of heat (q).
I do not think there will be a specific case where you are obligated to use "qp" instead of the deltaH notation but it is still important to understand the concept that they are equal to each other since it provides you with a definition of what the meaning of deltaH actually is.
qp is the heat released or absorbed at constant pressure, you would use this format in certain situations when looking at systems at constant pressure whereas the other equation where it is just q is the heat released or absorbed under certain conditions not necessarily at constant pressure. I recommend looking into it and asking a TA just to be sure, I think the previous replies do a good job of explaining all of this.
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