in calorimetry, is the heat exchanged with the surroundings the same as the enthalpy change of the reaction???
That's right. If you think about the equation we use in measuring enthalpy change:
q (energy) = MCdT (mass * specific heat capacity * change in temperature)
In using the equation, you're measuring the energy increase (or decrease) or a reaction mixture, e.g copper sulfate (aq) and magnesium, making the assumption that:
The energy given out (or taken in) by a reaction is the same as the energy gained (or lost ) by the reaction mixture.
In truth, the errors in measuring the increase in energy of the reaction mixture mean that in an environment, such as a lab with imprecise equipment, mean that the value you measure is unlikely to be the true value of the enthalpy change of the reaction.