Energy Diagrams A Review

Energy Diagrams are a plot of the reaction steps, or “Reaction Coordinate” (X-axis) versus the Energy (Kcal or KJ)

In a spontaneous reaction, the product(s) are more stable than the reactant(s), thus the products are at a lower energy than the reactants. For a single step reaction, the energy diagram would look like:

“Spontaneous” refers to the total Gibbs Free Energy (  G) during a reaction, taking into account bond energies (Enthalpy,  H) and disorder changes (Entropy,  S).  G =  H - T  S When enthalpy is focused on, the term is “exothermic” for a reaction/reaction step.

In an exothermic reaction or reaction step, the product bonds are more stable than the reactant bonds, thus the products are at a lower energy than the reactions. Energy Diagram for Exothermic: Note the drop in Energy!

The energy is determined by: E(products)- E(reactants). The sign for spontaneous/exothermic reaction steps is always negative, when energy is being given off.

Exothermic Reaction – heat is given off – Product bonds are more stable than reactant bonds –  H value is negative, – heat coming out of system

In a non-spontaneous reaction, the products are less stable than the reactants, thus the products are at a higher energy than the reactants. For a single step reaction, the energy diagram would look like:

As before, “Non-Spontaneous” refers to the total Gibbs Free Energy during a reaction, taking into account bond energies (Enthalpy) and disorder changes (Entropy). When enthalpy is focused on, the term is “endothermic” for a reaction/reaction step.

In an endothermic reaction or reaction step, the product bonds are less stable than the reactant bonds, thus the products are at a higher energy than the reactions. Energy Diagram for Endothermic: Note the climb in energy!

Again, the energy is determined by: E(products)-E(reactants). The sign for non- spontaneous/endothermic reaction steps is always positive, when energy must be added in.

Endothermic Reaction – heat is required – Reactant bonds are more stable than product bonds –  H value is positive – heat must be added to system

On a side note… Very often, organic chemists estimate overall  G as being approximately the same as  H. Values are a close approximation but not exactly the same (missing  S factor) Bonds energies are calculated for gas phase reactions (but we do everything in solutions) and do not indicate rate of reaction (may seem favorable mathematically but could take two months!!)

Entropy (  S) Entropy –  S (Disorder) A  B + C –  S increasing as one becomes two or more pieces A + B  C –  S decreasing as two become one in a reaction

 S decreases when the world is less chaotic, as in the reaction shown below, as two molecules add together to become one molecule: Entropy is not viewable on an energy diagram.

So… Energy Diagrams… What to recognize…? Spontaneous steps are Exothermic and Non- Spontaneous steps are Endothermic.

Notice the high-energy points in a diagram:

Transition States This high-energy point in the diagram step is what is called a “transition state” in the step

Transition States Transition States are high energy, unstable species which cannot be isolated, therefore they are only theoretical Being “theoretical”, their structures are not physically proven, but thought to exist based on evidence in reaction, what the starting material looks like as well as the product.

Transition States Every mechanistic step in a reaction process has a transition state On an energy diagram, every transition state is recognized as every high point in the diagram. On the following energy diagram, how many transition states are present? (or alternatively, how many mechanism steps are in the process? Same answer for both!)

Transition States How many transition states?

Every high point is a transition state. 4 total Every transition state = a step. 4 steps shown.

Notice the low points, between the high points:

Intermediates The low points are energy values for intermediates.

Intermediates Intermediates are species like anions, cations (cations on carbons are called carbocations) or radicals. These are also higher in energy, in general, as they are an unstable species (too many electrons, not enough electrons or odd- numbered, unpaired electrons). Intermediates, unlike transition states, are species that can be physically isolated.

Intermediates The definition of an intermediate is “a species that forms during a reaction, that then continues to react to form something else”. How many intermediates are shown on the following energy diagram?

Intermediates How many intermediates are shown?

Intermediates How many intermediates are shown on the following energy diagram? There are 3 (notice all of the “valleys”, between the “hills”).

Label them all now Label the reactant (R), product (P), transitions states (TS) and intermediates ( I ).

Label them all now The transition states and intermediates are numbered here for each step.

Label them all now Notice that Step 1 starts with the reactant, R, and ends with I 1. Step 2: I 1  I 2. Step 3: I 2  I 3. Step 4: I 3  P.

Let’s talk energy now… Now, the higher in energy a species is, the more unstable it is. Transition states are the high points in energy in the middle of each step. A certain amount of energy is required in order for that transition state to form. This energy value is called the Activation Energy or Activation Barrier, or  G ‡.

Activation Barrier The activation barrier is the increase in energy from the start of the step to the TS of the step

Activation Barriers Every step has an activation barrier

Activation Barriers The step with the largest Activation Barrier requires the most energy and is the slowest step in the process. Which step is that?

The Slowest Step… Starting at the beginning of the step and rising up to each TS, you can see that Step 1 has the largest rise, thus this is the slowest step.

The RDS… The slowest step is always referred to as the RATE-DETERMINING STEP or RDS.

Other Energy Values to Find? The overall reaction, or each individual step, has a change in energy as the reactant for the start of the step is converted into the product. We alluded to this when we initially talked about exothermic and endothermic steps (spontaneous or non-spontaneous, if you like).

Other Energy Values to Find? These values are usually referred to as  G, the Gibbs Free Energy of the step. You should be able to find  G for any single step or the overall reaction, on an Energy Diagram.

Label all values of  G (for each step and the overall reaction):

 G begins at each reactant for a step/reaction and ends at each product for a step/reaction. Every step has an energy value and the overall reaction has an energy value:

Which steps are exothermic/spontaneous? Which steps are endothermic/non- spontaneous? Is the overall reaction exo or endo?

If energy increases  endothermic If energy decreases  exothermic

Application to reactions? Consider the addition of HBr to an alkene.

Application to reactions? Consider the addition of HBr to an alkene. This is a two-step process, R  I and I  P.

Step 1: Reactant forms Intermediate In Step 1, the alkene attacks the HBr to form a carbocation intermediate: The molecules must approach each other. Enough energy must be present to overcome electron cloud repulsions between the neutral alkene and the neutral HBr. Energy rises…

Energy rises as the pi bond begins to break and attack the HBr (think high energy - TS!), and then collision occurs! If the orientation of the alkene with the HBr is correct, (i.e. the alkene finds the H, not the Br), the pi bond and H-Br break and a new sp 3 C-H forms! Intermediate forms…

The intermediate that forms will be higher in energy than the starting materials, as it is a charged species, not neutral. It needs to react to become stable again… so here comes Step 2…

Step 2: Intermediate forms Product In Step 2, the bromide attacks the carbocation intermediate: Again, the molecules must approach each other and enough energy must be present to overcome electron cloud repulsions but this step has less electron repulsions as the TS forms. Lower Activation barrier!

Step 2: Intermediate forms Product This time one species is electron-poor (the carbocation) and the other one is electron- rich (the Br - ) so this has a lower energy barrier to overcome! sp 3 C-Br Bond Formation!

Step 2: Intermediate forms Product Formation of a stable, neutral product will lower the energy in the system again. What would the energy diagram look like?

Energy Diagram – Adding HBr to Alkenes Here’s the basic energy diagram for this type of reaction: Note the larger activation barrier for step 1. Endothermic. Step 2, small activation barrier. Exothermic. This particular reaction is exothermic, overall.

Overview: For any Energy Diagram, you should be able to find:  G for each individual step or for overall reaction – Difference in Energy between the Product and Reactant of each step, or overall reaction – Spontaneous/Non-spontaneous or Exothermic/Endothermic  G ‡ for each step (fastest step, slowest step) – Difference in Energy between reactant of a step and the Transition State for the step Identify all transition states (TS) and intermediates (I)

All the basic pieces: