Kevin B. answered 12/08/22
Enthusiastic Orgo Professor Can Help You Unlock Organic Chemistry
This is a good example of a nice, short multi-step synthesis problem, with a little bit of "retrosynthetic" thinking thrown in. Solving this kind of problem requires a strong foundation in the basic substitution, elimination and addition reactions involving alcohols, alkyl halides and alkenes, so if those are not a strength, you should head to a textbook (or lecture/notes) to firm up those reactions.
The key to this synthesis is that you do not only need to be able to answer the question, "What compounds can I make from cyclopentanol?" You also need to answer the question, "From what reactant can I make 1,2-epoxycyclopentane?" While the first question is essentially a "synthetic" question, the second question is a "RETRO-synthetic" question. Being equipped to think about a synthesis like this BOTH ways is CRITICAL to being able to solve questions like this!
First, what the heck is "1,2-epoxycyclopentane"? (I am going to assume you know what cyclopentanol is.) Well answering that would be easier with a drawing program, but here's a verbal description. An "epoxide" is a 3-membered ring in which one atom is an oxygen (and the other two are carbons). So "1,2-epoxy" cyclopentane is bicyclic molecule -- like a pentagon with a triangle fused to one side (they share a side), in which the "point" of the triangle is an oxygen atom. That's 1,2-epoxycylopentane.
The next thing you need to know is how to make an epoxide from other kinds of molecules. There are two decent answers to that question. One answer is that you can react an alkene with a peroxyacid (RCO3H) to make an epoxide -- the pi bond between the two C=C carbons breaks, and each of those carbons forms a bond to a new oxygen atom (coming from the RCO3H) to make the triangle/epoxide. There are any number of different peroxyacids which could accomplish this reaction, but the most common one presented in typical sophomore organic textbooks is meta-chloroperbenzoic acid, or "mCPBA". In one step (usually without specifying any other reaction conditions), you can transform an alkene into an epoxide. In this particular case, in order to make the 1,2-epoxycyclopentane, you would simply need to react cyclopentene with mCPBA.
You can also make an epoxide from a vicinal-halohydrin (a compound with a halide and an -OH on carbon atoms which are adjacent to each other) in a reaction with base -- the base removes the O-H proton, and the negative oxygen "leans over" to do an SN2 reaction on the adjacent halide, resulting in the 3-membered ring epoxide. This then begs the question -- from what reactant can you make the vicinal halohydrin? The answer to that is ALSO an alkene -- X2/H2O will add to an alkene to put an -X on one of the C=C alkene carbons, and an -OH on the other (which results in a vicinal halohydrin). So basically, there are two ways to make an epoxide from an alkene -- a one-step synthesis with RCO3H, and a two step synthesis of reaction with X2/H2O (probably Br2/H2O) followed by a base (could be NaOH, or NaH, or NaOEt -- just about anything that can remove the O-H proton from the halohydrin). But both of those syntheses require starting with an alkene (in this specific case, cyclopentene).
Well, you weren't instructed to start with an alkene! So that takes the "retrosynthesis" back one MORE step, to be "From what reactant(s) can I make cyclopentene?" And fortunately, this time, one of the answers IS your starting reactant! You can do an elimination (E1 mechanism, if you were wondering) on cyclopentanol with a strong acid (H2SO4, or H3PO4 -- probably best would even be a mixture of the two -- but for the purposes of this synthesis, it probably doesn't matter exactly which acid you use, and your textbook probably says H2SO4).
Of course, there is a DIFFERENT retrosynthesis of cyclopentene, where it could be made from an alkyl halide (or tosylate) with a strong base (E2 reaction). In this case, to make cyclopentene, you would start with cyclopentyl bromide and react with sodium ethoxide in hot ethanol (protic solvent and high temperature reduce competition from SN2 reaction). Then, once again, you have to ask, "From what reactant can I make cyclopentyl bromide?" And the answer is, once again, now the alcohol, cyclopentanol (which can be most simply converted into the bromide with PBr3).
So there are SEVERAL routes from cyclopentanol to 1,2-epoxycyclopentane! You can go directly to the alkene by an E1 reaction with H2SO4 (one step), or you could first make the bromide and then do E2 with base (two steps). Then, you could go directly from the alkene to the epoxide with mCPBA (one step), or by first making the bromohydrin (with Br2/H2O) then reacting with base to close the epoxide. There is often more than one way to skin a cat! (Though seriously, why would anyone need to skin a cat? Somebody call PETA....)
So the shortest synthesis starting with cyclopentanol is only TWO steps! 1. H2SO4, then 2. mCPBA. But the question (inexplicably) requests a "three-step synthesis". Well, there are TWO POSSIBLE 3-step syntheses: 1. H2SO4, then 2. Br2/H2O, then 3. NaH (or some other base). OR: 1. PBr3, then 2. NaOEt/EtOH and heat, then 3. mCPBA. Both of those syntheses are good, three-step syntheses for 1,2-epoxycyclopentane from cyclopentanol. And, of course, if you have time and chemicals to burn, you could do a FOUR-step synthesis (1. PBr3, 2. Base/heat, 3. Br2/H2O, 4. NaH).
Often is can be VERY helpful to be able to propose multiple ways to accomplish the same multi-step synthesis! In the context of a much longer synthetic route, one of the two paths may lend itself more readily to combination with other reactions you might need to do. So spend time now learning how to use the chemistry you know to propose multiple syntheses, and then consider which one(s) are better/worse than the other ones! That skill will come in very handy! Honestly, if I were picking from these options, I would pick the two-step synthesis, rather than either one of the 3-step ones (though the 3-step route forming the halide, then doing E2 before reacting with mCPBA is also excellent).
Finally, if these reactions/words are unfamiliar to you (halohydrin, PBr3, E2/E1/SN2, etc.), then you are probably not well-equipped to be able to solve synthetic questions like this. You will need to go back and review earlier material to get there. Organic chemistry is inherently VERY cumulative -- you pretty much can't forget anything! And you can skim over things and never really learn them -- that will come back and bite you REALLY fast....
Good luck in your pursuit of organic chemistry!!