On treatment with permanganate, cis-2-butene yields a glycol of m.p. \(34^{\circ}\), and trans-2-butene yields a glycol of m.p. \(19^{\circ}\). Both glycols are optically inactive. The glycol of m.p. \(19^{\circ}\) is resolvable (through reaction with optically active salts) into two fractions of equal but opposite rotation. The glycol of m.p. \(34^{\circ}\) is not. (a) What are the configurations of the two glycols? (b) Assuming these results are typical (they are), what is the stereochemistry of hydroxylation with permanganate? (syn or anti?) (c) Treatment of the same alkenes with peroxy acids gives the opposite results: the glycol of m.p. \(19^{\circ}\) from cis-2-butene, and the glycol of m.p. \(24^{\circ}\) from trans-2- butene. What is the stereochemistry of hy droxylation with peroxy acids?

Syn addition refers to a chemical reaction where two substituents are added to the same side of a double bond, resulting in a cis configuration. In the context of our exercise with hydroxylation, when we treat an alkene with permanganate, the hydroxyl groups both add to the same side of the original double bond. This happens because permanganate attacks the double bond from one side, leading to the addition of both hydroxyl groups from that side. Syn addition is an important concept in organic chemistry as it helps predict the stereochemical outcome of reactions involving alkenes.

Syn addition is associated with certain reagents such as osmium tetroxide (OsO4) and cold potassium permanganate (KMnO4), which facilitate the addition of atoms or groups of atoms to the same side of the double bond, leading to a specific geometric configuration of the product.

On the flip side, anti addition involves the addition of two substituents across opposite sides of a double bond, leading to a trans configuration. This is showcased in the treatment of alkenes with peroxy acids, as described in our exercise. Here, each hydroxyl group ends up on opposite sides of the original double bond. This outcome results in the formation of two new chiral centers and can lead to the creation of products that are enantiomers of each other.

Typically, reagents that induce anti addition include bromine (Br2) in a non-polar solvent or peroxy acids such as m-CPBA (meta-chloroperoxybenzoic acid). Understanding anti addition is crucial for predicting the stereochemical results of reactions and potentially the biological activity of the synthesized compounds.

Cis-trans isomerism, also known as geometric isomerism, refers to a type of stereoisomerism where molecules with the same structural formula have different spatial orientations of atoms due to the presence of a double bond or ring structure. The 'cis' isomer has substituents on the same side of the double bond or ring, while the 'trans' isomer has them on opposite sides.

In our textbook exercise, we compared cis-2-butene with trans-2-butene. Their different physical properties like the melting point and their disparate reaction outcomes upon hydroxylation highlight the significant impact of the cis-trans arrangement on molecular behavior and chemical reactions. Identifying cis-trans isomerism is crucial for understanding the physical and chemical properties of molecules.

Optical activity is a property of chiral molecules where they have the ability to rotate the plane of polarized light. A substance is considered optically active if it contains chiral centers but lacks an internal plane of symmetry. Typically, optical activity is quantified by measuring the angle of rotation using a polarimeter.

In the given exercise, the glycol with a melting point of 19 degrees Celsius is said to be resolvable into two fractions of equal but opposite optical rotation, meaning it is optically active. On the other hand, the glycol with a melting point of 34 degrees Celsius is optically inactive, indicating an absence of chiral centers or the presence of symmetry that cancels out any optical activity.

A racemic mixture is a 50:50 mixture of two enantiomers of a chiral molecule. Enantiomers are chiral molecules that are non-superimposable mirror images of each other. In a racemic mixture, the effects of one enantiomer's rotation of polarized light are completely counterbalanced by the other's, resulting in no net optical rotation.

For example, in the textbook exercise, the glycol derived from trans-2-butene is optically inactive because it forms a racemic mixture. The presence of each enantiomer in equal quantities causes their individual optical rotations to cancel out, thereby resulting in an overall optically inactive mixture.

A meso compound is a special type of stereoisomer that is achiral despite having multiple chiral centers; it has an internal plane of symmetry that bisects the molecule. This symmetry allows for the cancellation of optical activity within the same molecule, which means meso compounds do not rotate the plane of polarized light.

In the context of our study exercise, the glycol with a higher melting point would be a meso compound. The symmetry could arise because the added hydroxyl groups from the syn addition of permanganate to cis-2-butene allow for a plane of symmetry to exist through the molecule.

Alkene reactions encompass various chemical reactions where the carbon-carbon double bonds in alkenes undergo transformations. These reactions are highly diverse, and alkenes can react in several ways, including addition, polymerization, and oxidation reactions.

The hydroxylation reaction seen in the exercise is a type of addition reaction where alkenes react with a reagent, resulting in the addition of hydroxyl groups to the double bond carbons. The stereochemistry of these reactions (whether it is syn or anti addition) will dictate the three-dimensional arrangement of the resulting product. Knowledge of these reactions helps chemists to synthesize a wide range of compounds with specific desired properties tailored for different applications in science and industry.