Under what conditions is the change in internal energy, δe rxn , equal to the heat evolved in a chemical reaction?

 the first law says that  the change in internal energy of a system is given by: 

δE = δq + δw

where δE is the i change in internal energy, 

δq is the amount of thermal energy added to the system from the surroundings 

δw is the l work done *on* the system *by* the surroundings. 

For a system only undergoing expansion work,
δw = -pδV, so: 

δE = δq - p δV 
when δV = 0, then δe=δq

Solubility would be your answer.