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q refers to heat whereas H refers to enthalpy. Enthalpy is known as a state function, meaning that if you knew the state of a reaction (how the reaction was before and after it occurred), the enthalpy can be calculated. On the other hand, heat is not a state function and cannot be calculated from the starting and ending states of a reaction.
q is the measurement of heat (transfer of heat energy) and H is the measurement of enthalpy! Enthalpy is a state function but heat is not. If the system in question is at constant pressure, then I believe delta H is equal to q.
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