0.9 Energetics of chemical reactions  (Page 5/7)

The concept of a state function is somewhat analogous to the idea of elevation. Consider the difference inelevation between the first floor and the third floor of a building. This difference is independent of the path we choose toget from the first floor to the third floor. We can simply climb up two flights of stairs, or we can climb one flight of stairs, walkthe length of the building, then walk a second flight of stairs. Or we can ride the elevator. We could even walk outside and have a crane lift us to the roof of the building, from which we climb downto the third floor. Each path produces exactly the same elevation gain, even though the distance traveled is significantly differentfrom one path to the next. This is simply because the elevation is a "state function." Our elevation, standing on the third floor, isindependent of how we got to the third floor, and the same is true of the first floor. Since the elevation thus a state function, theelevation gain is independent of the path.

Now, the existence of an energy state function $H$ is of considerable importance in calculating heats of reaction. Considerthe prototypical reaction in , with reactants $R$ being converted to products $P$ . We wish to calculate the heat absorbed or released in this reaction, which is $\Delta (H)$ . Since $H$ is a state function, we can follow any path from $R$ to $P$ and calculate $\Delta (H)$ along that path. In , we consider one such possible path, consisting of two reactionspassing through an intermediate state containing all the atoms involved in the reaction, each in elemental form. This is a usefulintermediate state since it can be used for any possible chemical reaction. For example, in , the atoms involved in the reaction are C, H, and O, each of whichare represented in the intermediate state in elemental form. We can see in that the $\Delta (H)$ for the overall reaction is now the difference between the $\Delta (H)$ in the formation of the products $P$ from the elements and the $\Delta (H)$ in the formation of the reactants $R$ from the elements.

The $\Delta (H)$ values for formation of each material from the elements are thus of general utility in calculating $\Delta (H)$ for any reaction of interest. We therefore define the standard formation reaction for reactant $R$ , as $$\text{elements in standard state}\to R$$

and the heat involved in this reaction is the standard enthalpy of formation , designated by $\Delta (H_f^{°})$ . The subscript $f$ , standing for "formation," indicates that the $\Delta (H)$ is for the reaction creating the material from the elements in standard state. The superscript ° indicates that the reactions occurunder constant standard pressure conditions of 1 atm. From , we see that the heat of any reaction can be calculated from

Extensive tables of $\Delta (H_f^{°})$ have been compiled and published. This allows us to calculate withcomplete confidence the heat of reaction for any reaction of interest, even including hypothetical reactions which may bedifficult to perform or impossibly slow to react.

Observation 3: bond energies in polyatomic molecules

The bond energy for a molecule is the energy required to separate the two bonded atoms togreat distance. We recall that the total energy of the bonding electrons is lower when the two atoms are separated by the bonddistance than when they are separated by a great distance. As such, the energy input required to separate the atoms elevates the energyof the electrons when the bond is broken.