0.11 Measuring energy changes in chemical reactions  (Page 7/8)

We could study many reactions in a similar manner to see if this pattern holds up. We find experimentally that it does. The pattern is therefore a new natural law called Hess’ Law. Stated generally (but wordily), the energy of a reaction is equal to the sum of the energies of any set of reactions which, when carried out in total, lead from the same reactants to the same products. This is a powerful observation! (It is important to note here that we have omitted something from our observations. Hess’ Law requires that all reactions considered proceed under similar conditions like temperature and pressure: we will consider all reactions to occur at constant pressure.)

Why would Hess’ Law be true? Why doesn’t it matter to the energy whether we carry out a reaction in a single step or in a great many steps which produce the same products? We might have guessed that more steps somehow require more energy or somehow waste more energy. But if so, our guess would be wrong. As such, it would be helpful to develop a model to account for this law to improve our intuition about reaction energies.

[link] gives us a way we can make progress based on the work we have already done. This is a just a picture of Hess' Law showing all of [link] , [link] , and [link] . (Remember that the total reaction in [link] is exactly the same as the original reaction in [link] .) In [link] , the reactants C(s) + 2 H2O (g) + O ₂ (g) are placed together in a box, representing the reactant state of the matter before [link] occurs. The products CO2(g) + 2H2(g) + O ₂ (g) are placed together in a second box representing the product state of the matter after [link] . The reaction arrow connecting these boxes is labeled with the heat of [link] (which is also the heat of [link] ), since that is the energy absorbed when the matter is transformed chemically from reactants to products in a single step.

Also in [link] , we have added a box in which we place the same matter as in the reactant box but showing instead the products of carrying out [link] . In other words, we will first do [link] , producing CO ₂ (g) but leaving the H ₂ O(g) unchanged. Notice that the reaction arrow is labeled with the energy of [link] . Now we can also add a reaction arrow to connect this box to the product box, because that reaction is just [link] , producing H ₂ (g) and O ₂ (g) from the H ₂ O(g). And we can label this reaction arrow with the energy of [link] .

This picture of Hess' Law makes it clear that the energy of the reaction along the "path" directly connecting the reactant state to the product state is exactly equal to the total energy of the same reaction along the alternative "path" consisting of two steps which connect reactants to products. (This statement is again subject to our restriction that all reactions in the alternative path must occur under the same conditions, e.g. constant pressure conditions.)

Now let’s take a slightly different view of [link] . Visually make a loop by beginning at the reactant box and following a complete circuit through the other boxes leading back to the reactant box, summing the total energy of reaction as you go. If you go “backwards” against a reaction arrow, then reverse the sign of the energy, since a reverse reaction has the negative energy of the forward reaction. When we complete a loop and do the sum, we discover that the net energy transferred around the loop starting with reactants and ending with reactants is exactly zero. This makes a lot of sense when we remember the Law of Conservation of Energy: surely we cannot extract any energy from the reactants by a process which simply recreates the reactants. If this were not the case, in other words if the sum didn’t equal zero, we could endlessly produce unlimited quantities of energy by following the circuit of reactions which continually reproduce the initial reactants. Experimentally, this never works since energy is conserved.