Determine Whether a Sock Would Be Chiral or Achiral
Chirality and Optical Activity
Chiral Stereoisomers
The cis/trans or E/Z isomers formed by alkenes aren't the only example of stereoisomers. To understand the second example of stereoisomers, it might be useful to start by considering a pair of hands. For all practical purposes, they contain the same "substituents" 
four fingers and one thumb on each hand. If you clap them together, you will find even more similarities between the two hands. The thumbs are attached at about the same point on the hand; significantly below the point where the fingers start. The second fingers on both hands are usually the longest, then the third fingers, then the first fingers, and finally the "little" fingers.
In spite of their many similarities, there is a fundamental difference between a pair of hands that can be observed by trying to place your right hand into a left-hand glove. Your hands have two important properties: (1) each hand is the mirror image of the other, and (2) these mirror images are not superimposable. The mirror image of the left hand looks like the right hand, and vice versa, as shown in the figure below.
Objects that possess a similar handedness are said to be chiral (literally, "handed"). Those that do not are said to be achiral. Gloves are chiral. (It is difficult, if not impossible, to place a right-hand glove on your left hand or a left-hand glove on your right hand.) Mittens, however, are often achiral. (Either mitten can fit on either hand.) Feet and shoes are both chiral, but socks are not.
In 1874 Jacobus van't Hoff and Joseph Le Bel recognized that a compound that contains a single tetrahedral carbon atom with four different substituents could exist in two forms that were mirror images of each other. Consider the CHFClBr molecule, for example, which contains four different substituents on a tetrahedral carbon atom. The figure below shows one possible arrangement of these substituents and the mirror image of this structure. By convention, solid lines are used to represent bonds that lie in the plane of the paper. Wedges are used for bonds that come out of the plane of the paper toward the viewer; dashed lines describe bonds that go behind the paper.
If we rotate the molecule on the right by 180 around the CH bond we get the structure shown on the right in the figure below.
These structures are different because they cannot be superimposed on each other, as shown in the figure below.
CHFClBr is therefore a chiral molecule that exists in the form of a pair of stereoisomers that are mirror images of each other. As a rule, any tetrahedral atom that carries four different substituents is a stereocenter, or a stereogenic atom. However, the only criterion for chirality is the nonsuperimposable nature of the object. A test for achirality is the presence of a mirror plane within the molecule. If a molecule has a plane within it that will cut it into two symmetrical halves, then it is achiral. Therefore, lack of such a plane indicates a molecule is chiral. Compounds that contain a single stereo-center are always chiral. Some compounds that contain two or more stereocenters are achiral because of the symmetry of the relationship between the stereocenters.
The prefix "en-" often means "to make, or cause to be," as in "endanger." It is also used to strengthen a term, to make it even more forceful, as in "enliven." Thus, it isn't surprising that a pair of stereoisomers that are mirror images of each are called enantiomers. They are literally compounds that contain parts that are forced to be across from each other. Stereoisomers that aren't mirror images of each other are called diastereomers. The prefix "dia-" is often used to indicate "opposite directions," or "across," as in diagonal.
The cis/trans isomers of 2-butene, for example, are stereoisomers, but they are not mirror images of each other. As a result, they are diastereomers.
Chirality Tutorial
The Difference Between Enantiomers on the Macroscopic Scale
If you could analyze the light that travels toward you from a lamp, you would find the electric and magnetic components of this radiation oscillating in all of the planes parallel to the path of the light. However, if you analyzed light that has passed through a polarizer, such as a Nicol prism or the lens of polarized sunglasses, you would find that these oscillations were now confined to a single plane.
In 1813 Jean Baptiste Biot noticed that plane-polarized light was rotated either to the right or the left when it passed through single crystals of quartz or aqueous solutions of tartaric acid or sugar. Because they interact with light, substances that can rotate plane-polarized light are said to be optically active. Those that rotate the plane clockwise (to the right) are said to be dextrorotatory (from the Latin dexter, "right"). Those that rotate the plane counterclockwise (to the left) are called levorotatory (from the Latin laevus, "left"). In 1848 Louis Pasteur noted that sodium ammonium tartrate forms two different kinds of crystals that are mirror images of each other, much as the right hand is a mirror image of the left hand. By separating one type of crystal from the other with a pair of tweezers he was able to prepare two samples of this compound. One was dextrorotatory when dissolved in aqueous solution, the other was levorotatory. Since the optical activity remained after the compound had been dissolved in water, it could not be the result of macroscopic properties of the crystals. Pasteur therefore concluded that there must be some asymmetry in the structure of this compound that allowed it to exist in two forms.
Once techniques were developed to determine the three-dimensional structure of a molecule, the source of the optical activity of a substance was recognized: Compounds that are optically active contain molecules that are chiral. Chirality is a property of a molecule that results from its structure. Optical activity is a macroscopic property of a collection of these molecules that arises from the way they interact with light. Compounds, such as CHFClBr, that contain a single stereocenter are the simplest to understand. One enantiomer of these chiral compounds is dextrorotatory; the other is levorotatory. To decide whether a compound should be optically active, we look for evidence that the molecules are chiral.
The instrument with which optically active compounds are studied is a polarimeter, shown in the figure below.
Imagine a horizontal line that passes through the zero of a coordinate system. By convention, negative numbers are placed on the left and positive numbers on the right of zero. Thus, it isn't surprising that levorotatory compounds are indicated with a negative sign (-).and dextrorotatory compounds are with a positive sign (+).
The magnitude of the angle through which an enantiomer rotates plane-polarized light depends on four quantities: (1) the wavelength of the light, (2) the length of the cell through which the light passes, (3) the concentration of the optically active compound in the solution through which the light passes, and (4) the specific rotation of the compound, which reflects the relative ability of the compound to rotate plane-polarized light. The specific rotation of the dextrorotatory isomer of glucose is written as follows:
When the spectrum of sunlight was first analyzed by Joseph von Fraunhofer in 1814, he observed a limited number of dark bands in this spectrum, which he labeled A-H. We now know that the D band in this spectrum is the result of the absorption by sodium atoms of light that has a wavelength of 589.6 nm. The "D" in the symbol for specific rotation indicates that it is light of this wavelength that was studied. The "20" indicates that the experiment was done at 20C. The "+" sign indicates that the compound is dextrorotatory; it rotates light clockwise. Finally, the magnitude of this measurement indicates that when a solution of this compound with a concentration of 1.00 g/mL was studied in a 10-cm cell, it rotated the light by 3.12.
The magnitude of the rotations observed for a pair of enantiomers is always the same.
The only difference between these compounds is the direction in which they rotate plane-polarized light. The specific rotation of the levorotatory isomer of this compound would therefore be -3.12.
The Difference Between Enantiomers on the Molecular Scale
A strategy, which is based on the Latin terms for left (sinister) and right (rectus), has been developed for distinguishing between a pair of enantiomers.
- Arrange the four substituents in order of decreasing atomic number of the atoms attached to the stereocenter. (The substituent with the highest atomic number gets the highest priority.) The substituents in 2-bromobutane, for example, would be listed in the order: Br > CH3 = CH2CH3 > H.
- View the enantiomer from the direction that places the substituent with the lowest priority as far from the eye as possible. In the following example, this involves rotating the molecule counterclockwise around the CCH2CH3 bond and tilting it slightly around an axis that lies in the plane of the paper. When this is done, the substituent that has the lowest priority is hidden from the eye.
In this example, the path curves to the left, so this enantiomer is the (S)-2-bromobutane stereoisomer.
It is important to recognize that the (R)/(S) system is based on the structure of an individual molecule and the (+)/(-) system is based on the macroscopic behavior of a large collection of molecules. The most complete description of an enantiomer combines aspects of both systems. The enantiomer analyzed in this section is best described as (S)-(-)-2-bromobutane. It is the (S) enantiomer because of its structure and the (-) enantiomer because samples of the enantiomer with this structure are levorotatory; they rotate plane-polarized light clockwise. Note that the sign of the optical rotation is not correlated to the absolute configuration.
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Determine Whether a Sock Would Be Chiral or Achiral
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