2012년 12월 2일 일요일

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2012년 11월 30일 금요일

원운동

v = dl/dt = rd(theta)/dt = r*omega

a = dv/dt = r*d(omega)/dt
  = r*alpha
tau = F*r = mar = mr^2*alpha = I*alpha
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2012년 11월 29일 목요일

Epoxides

II. Epoxides
Epoxides are compounds containing the three-membered ring:
They are ethers, but the three-membered ring gives them unusual properties which make them an exceedingly important class of compounds. Epoxides are commonly made by the oxidation of alkenes by peroxy compounds, such as benzoic acid:
When allowed to stand in ether or chloroform solution, the peroxy acid and the unsaturated compound -- which need not be a simple alkene -- react to yield benzoic acid and the epoxide. For example:
Epoxides owe their importance to the ease of opening of the highly strained three-membered ring. They undergo acid-catalyzed reactions with extreme ease and -- unlike ordinary ethers -- can even be cleaved by bases.
A polymer made of epoxide units is called a polyepoxide or an epoxy. Epoxy resins are used as adhesives and structural materials; one such example is epoxyethane.
Acid-catalyzed Cleavage  
Like other ethers, an epoxide is protonated by acid.
 
The protonated epoxide can then undergo attack by any number of nucleophilic reagents.                            
An important feature of the reactions of epoxides is the formation of compounds that contain two functional groups. Thus, reaction with water yields a 1,2-diol. Reaction with an alcohol yields a compound that is both ether and alcohol.
The two-stage process of epoxidation followed by hydrolysis is stereoselective, and gives 1,2-diols corresponding to anti-addition to the C=C double bond. The same stereochemistry was observed for hydroxylation of alkenes by formic acid. There, an epoxide is formed as a reaction intermediate which is rapidly cleaved in the acidic medium. The interpretation is exactly the same as that given to account for anti-addition of halogens. Indeed, epoxides and their hydrolysis served as a model on which the halonium ion mechanism was patterned.  
Base-catalyzed Cleavage  
Unlike ordinary ethers, epoxides can be cleaved under alkaline conditions. Here it is the epoxide itself -- not the protonated epoxide -- which undergoes nucleophilic attack.
The lower reactivity of the non-protonated epoxide is compensated for by the more basic, more strongly nucleophilic reagents that are compatible with the alkaline solution (e.g. alkoxides, phenoxides, ammonia, etc.).
Like alkyl halides and sulfonates, and like carbonyl compounds, epoxides are an important source of electrophilic carbon -- of carbon that is highly susceptible to attack by a wide variety of nucleophiles. (E.G. Epoxides generated form carcinogenic hydrocarbons are even attacked by the nucleophilic portion of the genetic material DNA and thereby induce mutation and tumors).  
Cleavage Orientation
There are tow C atoms in an epoxide ring. In principle, either one can suffer nucleophilic attack. In a symmetrical epoxide like ethylene oxide, the two carbons are equivalent, and attack occurs randomly at either site. But in an asymmetrical epoxide molecule, the C atoms are not equivalent, and the product obtained depends upon which one is preferentially attacked.
It turns out that the preferred point of attack depends chiefly on whether the reaction is acid-catalyzed or base-catalyzed. Consider, for example, two reactions of isobutylene oxide:
Here (as in general) the nucleophile attacks the more substituted carbon in an acid-catalyzed cleavage, and the less substituted carbon in a base catalyzed cleavage.
Our first thought might be that there are two different reaction mechanisms (e.g. SN1 vs. SN2). But the evidence indicates clearly that both are of the SN2 type. This is characterized typically by cleavage of the C-O bond and attack by the nucleophile in a single step.
How, then, are we to account for the difference in orientation -- particularly for the SN2 attack at the more hindered position in acid-catalyzed cleavage ?
The answer to this query lies in the transition state (or reaction intermediate).
In the transition state of most SN2 reactions, bond-breaking and bond-making have proceeded to about the same extent, and carbon has not become appreciably positive or negative. Therefore steric factors, not electronic factors, chiefly determine reactivity.
But in acid-catalyzed cleavage of an epoxide, the C-O bond, already weak because of the angle strain of the three-membered ring, is further weakened by protonation. The leaving group is a very good one -- the weakly basic alcohol hydroxyl (OH) group. Alternatively, the nucleophile is a poor one (e.g. water, alcohol). In the transition state, bond-breaking has proceeded further than bond-making, and thus carbon has acquired a considerable positive charge.
Since both leaving group and nucleophile are far away, crowding is relatively unimportant here. The stability of the transition state is determined chiefly by electronic factors and not steric factors. Thus the reaction has considerable SN1 character. In this case:
    Attack occurs at the C atom that can best accommodate the positive charge.
In base-catalyzed cleavage, the leaving group is a poorer one -- a strongly basic alkoxide oxygen -- and the nucleophile is a good one (e.g. hydroxide, alkoxide).
Bond-breaking and bond-making are more nearly balanced, and reactivity is controlled in the more usual way -- by steric factors. In this case:
                                  Attack occurs at the less hindered carbon.
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케톤의 알파-카본

Reactions at the α-Carbon

Many aldehydes and ketones undergo substitution reactions at an alpha carbon, as shown in the following diagram (alpha-carbon atoms are colored blue). These reactions are acid or base catalyzed, but in the case of halogenation the reaction generates an acid as one of the products, and is therefore autocatalytic. If the alpha-carbon is a chiral center, as in the second example, the products of halogenation and isotopic exchange are racemic. Indeed, treatment of this ketone reactant with acid or base alone serves to racemize it. Not all carbonyl compounds exhibit these characteristics, the third ketone being an example.
alpharx1.gif
Figure 1: Reactions at the carbon
Two important conclusions may be drawn from these examples. First, these substitutions are limited to carbon atoms alpha to the carbonyl group. Cyclohexanone (the first ketone) has two alpha-carbons and four potential substitutions (the alpha-hydrogens). Depending on the reaction conditions, one or all four of these hydrogens may be substituted, but none of the remaining six hydrogens on the ring react. The second ketone confirms this fact, only the alpha-carbon undergoing substitution, despite the presence of many other sites. Second, the substitutions are limited to hydrogen atoms. This is demonstrated convincingly by the third ketone, which is structurally similar to the second but has no alpha-hydrogen.

Mechanism of Electrophilic α-Substitution

Kinetic studies of these reactions provide additional information. The rates of halogenation and isotope exchange are essentially the same (assuming similar catalysts and concentrations), and are identical to the rate of racemization for those reactants having chiral alpha-carbon units. At low to moderate halogen concentrations, the rate of halogen substitution is proportional (i.e. first order) to aldehyde or ketone concentration, but independent of halogen concentration. This suggests the existence of a common reaction intermediate, formed in a slow (rate-determining step) prior to the final substitution. Acid and base catalysts act to increase the rate at which the common intermediate is formed, and their concentration also influences the overall rate of substitution.
From previous knowledge and experience, we surmise that the common intermediate is an enol tautomer of the carbonyl reactant. Several facts support this proposal:
  1. Compounds that do not have any α-hydrogen atoms cannot enolize and do not undergo any of the reactions described above.
  2. The carbon-carbon double bond of an enol is planar, so any chirality that existed at the α carbon is lost on enolization. If chiral products are obtained from enol intermediates they will necessarily be racemic.
  3. In simple aldehydes and ketones enol tautomers are present in very low concentration. Reactions that involve enol reactants will therefore be limited in rate by the enol concentration. Increasing the amounts of other reactants will have little effect on the reaction rate.
  4. Enolization is catalyzed by acids and bases. These catalysts will therefore catalyze reactions proceeding via enol intermediates.
The reactions shown above, and others to be described, may be characterized as an electrophilic attack on the electron rich double bond of an enol tautomer. This resembles closely the first step in the addition of acids and other electrophiles to alkenes. Therefore, if electrophilic substitution reactions of this kind are to take place it is necessary that nucleophilic character be established at the alpha-carbon. A full description of the acid and base-catalyzed keto-enol tautomerization process (shown below) discloses that only two intermediate species satisfy this requirement. These are the enol tautomer itself and its conjugate base (common with that of the keto tautomer), usually referred to as an enolate anion.
ketenleq.gif
Figure 2: Keto-enol tautomerization
Clearly, the proportion of enol tautomer present at equilibrium is a critical factor in alpha substitution reactions. In the case of simple aldehydes and ketones this is very small, as noted above. A complementary property, the acidity of carbonyl compounds is also important, since this influences the concentration of the more nucleophilic enolate anion in a reaction system. Ketones such as cyclohexanone are much more acidic than their parent hydrocarbons (by at least 25 powers of ten); nevertheless they are still very weak acids (pKa = 17 to 21) compared with water. Together with some related acidities, this is listed in the following table. Even though enol tautomers are about a million times more acidic than their keto isomers, their low concentration makes this feature relatively unimportant for many simple aldehydes and ketones.
Table 1: Acidity of α-Hydrogens in Some Activated Compounds
 
Compound RCH2–NO2 RCH2–COR RCH2–C≡N RCH2–SO2R
pKa 9 20 25 25
In cases where more than one activating function influences a given set of alpha-hydrogens, the enol concentration and acidity is increased. Examples of such doubly (and higher) activated carbon acids are given elsewhere.
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conjugate ketone


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