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For example, I have a question below that I know the correct answer to, but I don't know why it's positive rather than negative.

When $\ce{NaOH}$ is neutralized by $\ce{HCl}$:

$$\ce{NaOH(aq) + HCl(aq) + H2O(l) -> NaCl(aq)}\qquad{\Delta H = \pu{-56.2kJ/mol}}$$

How much heat is produced when $\pu{195 mL}$ of $\pu{0.667 M }\ce{NaOH}$ are mixed with $\pu{125 mL 1.750 M }\ce{HCl}$?

a. $\pu{−14.6 kJ}$
b. $\pu{14.6 kJ }$
c. None of these.
d. $\pu{7.31 kJ}$

I know that the answer is (d), but I'm not sure why it is correct. I thought the correct answer was $−7.31$, but there was no answer choice for $−7.31$.

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    $\begingroup$ I suspect that your instructor was trying to include the semantic difference between enthalpy change and amount of heat produced. It's kind of like if you asked what the temperature was and I told you -10°. You could then ask how many degrees below zero it is, and I would answer 10°. Both answers mean the same thing, but the negative sign is included verbally rather than arithmetically. $\endgroup$ – Jason Patterson Oct 9 '15 at 2:52
  • $\begingroup$ An enthalpy change of -7.31 kJ means that this is the amount of heat you need to remove from the system so that the final temperature of the system is equal to the initial temperature. So that must be the amount of heat produced. $\endgroup$ – Chet Miller Oct 9 '15 at 3:02
  • $\begingroup$ @Jason is entirely right. An alternative way of putting it is: You can have a negative enthalpy change (ΔH), and you can have a negative bank balance. But you can't produce a negative amount of heat, just like you can't owe someone a negative amount of money. The negative sign of ΔH is already implied by the word "produced", because if ΔH were to be positive, the appropriate word would be "absorbed". $\endgroup$ – orthocresol Oct 9 '15 at 7:04
  • $\begingroup$ I want to restate my previous comment because, as written, it's a little ambiguous. When we say that the enthalpy change of a reaction is -7.31 kJ, it means that we have to add -7.31 kJ to the system (i.e., remove +7.31 kJ from the system) in order for the final temperature to be equal to the original temperature. So, if we have to remove 7.31 kJ, this must be the amount of heat produced by the reaction. $\endgroup$ – Chet Miller Oct 9 '15 at 10:41

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