Why Q = -DH.

 
Throughout the explanation, imagine a man with hot hands and a woman with cold hands.

1st Point of View: Man is reaction; woman is environment. Man releases or loses heat; he is

an exothermic reaction. DH for man is (-). Woman feels heat; she absorbs it, and her temperature increases. Her Q = (+) . Recall that Q = mc DT, where DT = T_f - T_i.

Note DH = -Q.

2nd Point of View: Woman is reaction; man is environment. Woman takes heat from man. She is an endothermic reaction. She steals or absorbs heat from the man. DH for woman is (+).

Man feels a cold hand; he loses heat to the woman, so his temperature drops. His Q = (-).

Again DH = -Q; the signs are again opposite of one another.

Chemical Case.

Suppose that NaOH_(aq) is neutralizing HCl_(aq). Both are dilute solutions in water. When they react they release heat into the surrounding water, just like the man. Their DH =(-). But you record an increase in temperature because you are inserting a thermometer into the water. The water is like the woman in the previous analogy. So for water, Q = (+).

If NaNO₃ dissolves in water, the sodium nitrate absorbs or steals heat from the water. The DH for the reacting nitrate is (+), just like the woman's when she is regarded as the reactant. The water is now like the man; it experiences a drop in temperature and its Q is (-).