Imagine that the product of one reaction serves as the reactant for another reaction. Now imagine that the product of the second reaction serves as the reactant for a third reaction. What you have is a set of coupled reactions, connected in series like the cars of a train:
![image0.jpg](https://www.dummies.com/wp-content/uploads/476541.image0.jpg)
Therefore,
![image1.jpg](https://www.dummies.com/wp-content/uploads/476542.image1.jpg)
You can think of these three reactions adding up to one big reaction
![image2.jpg](https://www.dummies.com/wp-content/uploads/476543.image2.jpg)
What is the overall enthalpy change associated with this reaction
![image3.png](https://www.dummies.com/wp-content/uploads/476544.image3.png)
Here's the good news:
![image4.jpg](https://www.dummies.com/wp-content/uploads/476545.image4.jpg)
Enthalpy changes are additive. But the good news gets even better. Imagine that you're trying to figure out the total enthalpy change for the following multistep reaction:
![image5.jpg](https://www.dummies.com/wp-content/uploads/476546.image5.jpg)
Here's a wrinkle: For technical reasons, you can't measure this enthalpy change
![image6.jpg](https://www.dummies.com/wp-content/uploads/476547.image6.jpg)
directly but must calculate it from tabulated values for
![image7.jpg](https://www.dummies.com/wp-content/uploads/476548.image7.jpg)
and
![image8.jpg](https://www.dummies.com/wp-content/uploads/476549.image8.jpg)
No problem, right? You simply look up the tabulated values and add them. But here's another wrinkle: when you look up the tabulated values, you find the following:
![image9.jpg](https://www.dummies.com/wp-content/uploads/476550.image9.jpg)
Gasp! You need
![image10.jpg](https://www.dummies.com/wp-content/uploads/476551.image10.jpg)
but you're provided only
![image11.jpg](https://www.dummies.com/wp-content/uploads/476552.image11.jpg)
Relax. The enthalpy change for a reaction has the same magnitude and opposite sign as the reverse reaction. So if
![image12.jpg](https://www.dummies.com/wp-content/uploads/476553.image12.jpg)
then
![image13.jpg](https://www.dummies.com/wp-content/uploads/476554.image13.jpg)
It really is that simple:
![image14.jpg](https://www.dummies.com/wp-content/uploads/476555.image14.jpg)
Thanks be to Hess.
Try an example. Calculate the reaction enthalpy for the following reaction:
![image15.jpg](https://www.dummies.com/wp-content/uploads/476556.image15.jpg)
Use the following data:
![image16.jpg](https://www.dummies.com/wp-content/uploads/476557.image16.jpg)
Reaction enthalpies are given for two reactions. Your task is to manipulate and add Reactions 1 and 2 so the sum is equivalent to the target reaction. First, reverse Reactions 1 and 2 to obtain Reactions
![image17.jpg](https://www.dummies.com/wp-content/uploads/476558.image17.jpg)
and
![image18.jpg](https://www.dummies.com/wp-content/uploads/476559.image18.jpg)
and add the two reactions. Identical species that appear on opposite sides of the equations cancel out (as occurs with species P4 and Cl2):
![image19.jpg](https://www.dummies.com/wp-content/uploads/476560.image19.jpg)
Finally, divide the sum by 4 to yield the target reaction equation:
![image20.jpg](https://www.dummies.com/wp-content/uploads/476561.image20.jpg)
So, the reaction enthalpy for the reaction is 83.8 kJ.