The enthalpy H of a thermodynamic system is defined as: 
The importance of this magnitude in chemistry lies in the fact that its variation coincides with the heat exchanged at constant pressure. It is very common for a chemical reaction to take place in an open vessel (at atmospheric pressure) and the heat exchanged will be an enthalpy change.
We start from the first law of thermodynamics: 
, the subscript p indicates constant pressure. 
Clearing the heat and grouping terms we obtain: 
Now let's see what happens when the volume of the system remains constant: 
At constant volume the work is zero and the heat exchanged at constant volume coincides with the change in internal energy. 
In any chemical process that maintains the constant volume, the heat exchanged coincides with the change in internal energy of the system.