# How do you determine the sign of heat flow q as compared to DeltaH? How do their units relate and what is the difference between "kJ" and "kJ/mol"?

Feb 17, 2017

It always depends on context, but it is never the case that $- q = \Delta H$.

By definition, $q = n \Delta H$ at constant pressure, and both $q$ and $\Delta H$ are typically in units of $\text{J}$ or $\text{kJ}$, as long as they agree.

$q$ and $\Delta H$ are ALWAYS the same sign, for the SAME process. i.e. ${q}_{\text{rxn}} > 0$ implies that $\Delta {H}_{\text{rxn}} > 0$, ${q}_{\text{cal}} > 0$ implies $\Delta {H}_{\text{cal}} > 0$, because the number of $\text{mol}$s is always positive.

If you see $\Delta H$ in $\text{kJ/mol}$, then it's an entirely different context than $q$ if $q$ is in $\text{J}$. The units are necessarily different if we are talking about $n$ $\text{mol}$s of gas ($\text{J}$ or $\text{kJ}$, an extensive unit), compared to some nonspecific quantity of gas ($\text{J/mol}$ or $\text{kJ/mol}$, an intensive unit).

This can be seen by simply using the units. If $q = n \Delta H$, then:

$\text{J" = "mol" xx "J"/"mol}$

Thus, if $q$ is units of $\text{J}$, we must have from $q = n \Delta H$ that $\Delta H$ is in $\text{J/mol}$. If it's anything else, and $q$ is chosen arbitrarily to be in $\text{J}$, it's simply incorrect use of units on $\Delta H$, or there was a conversion to different units that was not stated, i.e.

$\text{2500 J"/"mol" xx "1 kJ"/"1000 J" = "2.5 kJ"/"mol}$