How do scientist obtain the value of enthalpy of formation? [closed]








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Do they do it experimentally or do/can they use bond enthalpy to figure it out? For example $\ce{C2H4 + H2 -> C2H6}$. The enthalpy of formation, $\Delta\_fH$ of formation for the product is listed as -84, however if I use bond enthalpy to calculate the $\Delta\_fH$, it gives be a value of -222, which is considerably different. Shouldn't the difference between bonds formed and bonds broken account for the heat given off my the reaction? With this discrepancy I can only conclude that I mixed up the two concept. 


Also if $\ce{C2H4}$ enthalpy of formation $\Delta\_fH$ equals to 52, $\ce{H2}$ = 0 and $\ce{C2H6}$ = -84, the difference between the product and reactant is -136. I am confused about the 3 numbers (-84, -222 and -136) and their significance.


Also, how is $\Delta\_fH^\circ$ different from $\Delta\_RH^\circ$ of reaction? When do I use each one?


I would really appreciate it if someone can clear this up concisely




There is a consent to start with: the standard enthalpies of formation of elements (like $\ce{H2}$), at standard conditions ($\pu{1 bar}$, $\pu{298.15 K}$) are set to zero. If there are several forms of one element, than the most stable polymorph is chosen as reference (except for phosphor, [ref](https://en.wikipedia.org/wiki/Standard_enthalpy_of_formation)).


More generally, to determine the $\Delta{}\_fH^\circ{}$ of other compounds, you may embark experiments by [calorimetry](https://en.wikipedia.org/wiki/Calorimetry). By means of a calorimeter, you are able to record the energetic changes that occur in the course of a reaction. For example for the exhaustive combustion of carbon with oxygen:


$$\ce{C + O2 -> CO2}$$


all the heat recorded is due to the formation of carbon dioxide. Since *this* reaction equation was balanced that it equals only one mol of product ($\ce{CO2}$), the more general standard *reaction* enthalpy ($\Delta\_{\text{R}}H^\circ{}$) equals to the standard enthalpy of formation ($\Delta\_fH^\circ{}$). And by one experiment, after an other, the body of *experimentally determined* enthalpies grows.


Based on other experiments than combustion, one was able to determine how much energy is necessary to break a bond between atoms which is called [bond dissociation energy](https://en.wikipedia.org/wiki/Bond-dissociation_energy). Conversely, this value expresses how much energy *over all* is released if two atoms establish a bond with each other. In some instances, these energies are (comparatively) small, for example single bonded $\ce{Cl-Cl}$ ($\pu{242 kJ/mol}$), in other instances (comparatively) large, like triple bonded $\ce{N#N}$ ($\pu{945 kJ/mol}$).


If one knows the structure of a compound, which atoms are connected with each other and how (single, double, triple bond), than these bond dissociation energies may be used to *estimate* the standard enthalpy of formation of the new compound, for example by [an increment system](https://en.wikipedia.org/wiki/Benson_group_increment_theory). Alternatively, by virtually setting up for example a combustion reaction *of exactly one mole* of the new compound into $x$ moles of $\ce{H2O}$ and $y$ moles of $\ce{CO2}$. Then, the calculation to perform is 


$$\Delta\_{\text{R}}H^\circ{} = \sum\_{\text{all products}}{\Delta\_fH^\circ{}} - \sum\_{\text{all starting materials}}{\Delta\_fH^\circ{}}$$


where $\Delta\_{\text{R}}H^\circ{}$ again is the overall reaction enthalpy. Since these *estimations* are based on some empiric data, they do not a substitute for an experimentally determined value for your newly prepared compound. Often, increment systems leave some of inter- and intramolecular interactions unconsidered (e.g., ring strain, possible existence of polymorphism) which then yields a difference between the estimated, and the actual value of $\Delta\_{\text{R}}H^\circ{}$ or $\Delta\_fH^\circ{}$.


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