Hess's Law
Introduced| English |
|---|
| state function/steɪt ˈfʌŋkʃn/ |
| Hess's law/ˈhesɪz lɔː/ |
Adding reactions like recipes
- Some reactions are too hard to measure directly.
- But you can build them from steps you already know.
- Add those steps up and their heats add up too.
- The total heat depends only on start and end, not the route.
A path-independent quantity
- $\Delta H$ is a state function 状态函数: it depends only on start and end.
- The route taken does not change the total heat.
- So any path from reactants to products gives the same $\Delta H$.
$\Delta H$ is a state function, which means it depends only on...
A state function ignores the path between start and end.
Adding known steps
- Hess's law 赫斯定律 adds known reactions to reach a target.
- Sum their $\Delta H$ values to get the target $\Delta H$.
- Choose steps that cancel to leave the reaction you want.
When you reverse a reaction step, its $\Delta H$...
The reverse step has the opposite $\Delta H$.
If you double a reaction step, you double its $\Delta H$.
Scaling the amounts scales $\Delta H$ by the same factor.
Steps are chosen so the ____ cancel, leaving the target reaction.
Intermediates on opposite sides cancel when the steps are added.
Flip and scale
- Reverse a step and flip the sign of its $\Delta H$.
- Multiply a step and multiply its $\Delta H$.
- Then add the adjusted steps together.
Hess's law cycle
Enthalpy is a state function, so any route from reactants to products gives the same total.
Step 1 has $\Delta H = -100$; step 2 has $\Delta H = -50$; their sum is the target.
- Add them: $\Delta H_{target} = -100 + (-50) = -150\ \text{kJ}$.
- The intermediates cancel out.
Two steps have $\Delta H = -120\ \text{kJ}$ and $+30\ \text{kJ}$. Their sum (in kJ)?
$-120 + 30 = -90\ \text{kJ}$.
Hess's law works because enthalpy is a state function.
Path-independence is exactly why the step $\Delta H$ values add.
When you reverse a step, flip the sign of its $\Delta H$; when you scale it, multiply $\Delta H$ too. Line the steps up so the intermediates cancel. And Hess's law works only because $\Delta H$ is a state function -- the path does not matter.
Because $\Delta H$ is a state function (path-independent), Hess's law lets you add known reactions to find an unknown $\Delta H$. Reverse a step and flip its sign; scale a step and scale its $\Delta H$; then sum so the intermediates cancel.