Why is it sometimes kJ only, and in other times kJ/mol? What's the difference? [closed]








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Here is an example in my book. Computing the enthalpy of formation $\Delta{}H\_\mathrm{f}$ *via* multiple enthalpies of reaction $\Delta{}H\_\mathrm{r}$ I notice some of the equations run by $\pu{kJ/mol}$ and others by $\pu{kJ}$ only. I'm puzzled about the conceptual difference between these values. How do they relate to each other?


[![1](https://i.stack.imgur.com/5PbPj.jpg)](https://i.stack.imgur.com/5PbPj.jpg)


[![2](https://i.stack.imgur.com/gZrEk.jpg)](https://i.stack.imgur.com/gZrEk.jpg)




The keyword is [dimension analysis](https://en.wikipedia.org/wiki/Dimensional_analysis).


For instance, in example 1-7, the aim is to determine the *standard* enthalpy of formation $\Delta{}H\_\mathrm{f}$ for $\ce{SO2}$ (note the subscript is `f`) determined with equations 1, 2, and 3. After rearrangement $3 \rightarrow 4$ you add the equations to obtain equation #5 which however describes the enthalpy of *reaction* (note subscript is `r`) to yield $\pu{2 mol}$ of $\ce{SO2}$ instead of the conventionally tabulated enthalpy of *formation* (again subscript `f`) for $\pu{1 mol}$ of $\ce{SO2}$.


Thus, $$\Delta{}H\_\mathrm{r} = \pu{2 mol} \times \Delta{}H\_\mathrm{f} = \pu{2 mol} \times(\pu{-296 kJ/mol}) = \pu{-592 kJ}.$$ One may argue the publisher was sloppy when writing `2` instead of `2 mol` in this line.


You may retain that $\Delta{}H\_\mathrm{r}$ as a special case (mathematically speaking, a [subset](https://en.wikipedia.org/wiki/Subset)) of the more general $\Delta{}H\_\mathrm{r}$. That is to say, for a reaction yielding $\pu{4.2 mol}$ of $\ce{SO2}$, the reaction enthalpy $\Delta{}H\_\mathrm{r}$ is:


$$\Delta{}H\_\mathrm{r} = \pu{4.2 mol} \times \Delta{}H\_\mathrm{f} = \pu{4.2 mol} \times(\pu{-296 kJ/mol}) = \pu{-1243.2 kJ.}$$


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