a. Propose a mechanism for the following reaction:

Question

b. Use the bond-dissociation enthalpies given in Table 4-2 (page 167) to calculate the value of ΔH° for each step shown in your mechanism. (The BDE for CH₂=CHCH₂―Br is about 280 kJ/mol, or 67 kcal/mol.) Calculate the overall value of ΔH° for the reaction. Are these values consistent with a rapid free-radical chain reaction?

Accepted Answer

Hey everyone. Let's do this problem and says propose a mechanism for the reaction shown below. Use the appropriate bond association and therapies to find the value of delta H. Or the entropy for each step shown in the mechanism you propose and calculate the value of delta H. For the overall reaction. If the bond association entropy for fennel ch two to be our bond is approximately 2 80 kg per mole. Are these values appropriate for a rapid free radical chain reaction? So we have to propose a mechanism for the reaction below. And this problem actually gives us a hint as to what that mechanism is going to look like because in part two of this question, it mentions a free radical chain reaction and if we look more closely we see that we have a halogen reacting with an al cane in photochemical condition. So we have the presence of light. So that is going to result in the substitution of that hydrogen with a browning in a free radical substitution mechanism. So in a free radical mechanism we have initiation is the first step where we will make our radical. So we have that Bram mean bro mean the di atomic bombing in the presence of light to form two bromine radicals and we have to draw our electron arrows. So remember we use the single headed arrows for the movement of one electron. So we are going to have each electron from this bond go onto a bromine atom. So two single headed arrows and that is step one of the free radical mechanism. Step two We move on to propagation and that is sort of a chain reaction that will create a different radical. So now we have one of our bromine radicals we just created with our reactant C. H three coming off of that benzene ring. Oops. And we're going to have three single headed arrows in this step. So we're forming an Hbr bond and then we're creating a radical on this carbon. So we're going to have this free radical electron meet up with this electron from that carbon hydrogen bond and the other electron from that bond will go onto that carbon. Okay, so we're getting rid of that hydrogen in order to make this carbon a free radical which will then allow that bro mean to attach to that carbon in the end of our reaction. So this will form hbr and our radical like we mentioned. But this radical has some resonance stabilization. So let's draw the resonance forms of this radical. So we have these pi bonds that can switch alternating locations. They can also change again to form a double bond. If we have this radical come with one electron from this pi bond and then we'll have one electron from the remaining double bonds to meet with each other inform those double bonds. Except this one will form a new radical on this carbon over here neighboring that methyl group. So we will have ch two double bonded to the ring in our radical is out here. So those are the possible resonance structures for the step to product. And the last step is actually still a propagation step here because we are still creating a new radical from it. So we have another di atomic protein bro mean molecule with our new radical that we just formed. And again we're going to have 31 sided arrows. So we are creating a broom in radical and we want to attach this broom into this carbon so they will each donate one electron to that bond which gives us our product ch to be our attached to that fennel group and another bro mean radical. Okay, so those are steps to in step three which are both propagation steps Okay, so that is our mechanism for part one. Now, Part two asks us to use the bond entropy is given to calculate delta H. For each step and for the overall reaction. So remember that when we break a bond, that value will be positive. Right? We are absorbing the energy and when we make a bond, the value will be negative. Okay, so in step one, what bonds are we breaking or making? Well, we're simply breaking one br br bond. So breaking means a positive value. So the entropy for this step will be kg joules per mole for step one. All right Now, step two, we are making a hydrogen and broening bond. Okay, so that will be negative. 366. Tell jules per mole. And we are also breaking a fennel ch two and hydrogen bond. Right, We are severing the bond between this carbon and hydrogen. So that is a positive 376 joules per mole. So, for step two, the delta H value will be positive 10 kg joules per mole. All right. and looking at step three, we are breaking a B r b R bond. So that will be positive 190 kg per mole. And we are making that CBR bond here. So that will be minus 280 kg joules per mole. All right. And for step three, let me move this over. So, for step three the Delta H value will be negative 90 kg joules per mole. Okay, we're not done yet. We still need to calculate the overall delta H value. Now for free radical mechanisms. The delta H. For the overall reaction is going to be the sum of the independent propagation steps. So, just the propagation steps. So in that case we will be adding negative 90 kg joules per mole plus 10 kg joules per mole. Which means that the delta H for the overall reaction Will be negative 80 kg joules per mole. And the question also asks, are these values appropriate for a rapid free radical chain reaction? Well, negative 80 kg joules per mole is a large and negative value. So that means this reaction is very X. A thermic. And the second step only adds kg joules per mole in order to complete this step. So that suggests that there is a small activation energy, right? If we only need a little bit of energy added to get that step completed, then that means small activation energy and a rapid reaction. Okay, so the reaction is expected to be very rapid, which leaves choice a to be the correct answer for this problem. That's it for this one. I hope this video is helpful and thank you for watching.

Key Concepts

Free Radical Mechanism

Bond Dissociation Enthalpy (BDE)

Enthalpy Change (ΔH°)

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