Chapter 4, Problem 46DSP

Consider two chemical changes: one occurring at a tetrahedral $s{p}^3$ carbon $\text{C}\left(\text{x,x,y,z}\right)\text{,}$ the other at a trigonal $s{p}^2$ carbon $\text{C}\left(\text{x,y,z}\right)$, where x, y, and z is different atoms or groups attached to C. Each reactant is achiral; both are converted to the chiral product $\text{C}\left(\text{w,x,y,z}\right)$. In the first case w replaces one of the x atoms or groups, in the other w add to the trigonal carbon.

Both transformations convert C in each achiral reactant to a chirality center in the product. The two achiral reactants are classified as prochiral. C is a prochirality center in $\text{C}\left(\text{x,x,y,z}\right)$ and has two prochiral faces in $\text{C}\left(\text{x,y,z}\right)\text{.}$

In achiral molecules with tetrahedral prochirality centers, substitution of one of the two x groups by w gives the enantiomer of the product that results from substitution of the other. The two x groups occupy mirror-image sites and are enantiotopic.

Enantiotopic groups are designated as pro-R or pro-S by a modification of Cahn–Ingold– Prelog notation. One is assigned a higher priority than the other without disturbing the priorities of the remaining groups, and the R,S configuration of the resulting chirality center is determined in the usual way. If it is R, the group assigned the higher rank is pro-R. If S, this group is pro-S. Ethanol and citric acid illustrate the application of this notation to two prochiral molecules.

Citric acid played a major role in the development of the concept of prochirality. Its two ${\text{CH}}_2{\text{CO}}_2\text{H}$ chains groups behave differently in a key step of the Krebs cycle, so differently that some wondered whether citric acid itself were really involved. Alexander Ogston (Oxford) provided the answer in $1948$ when he pointed out that the two ${\text{CH}}_2{\text{CO}}_2\text{H}$ groups are differentiated when citric acid interacts with the chiral environment of an enzyme. The two prochiral faces of a trigonal atom $\text{C}\left(\text{x,y,z}\right)$ are enantiotopic and designated Re and Si according to whether x, y, and z trace a clockwise (Re) or counterclockwise (Si) path in order of decreasing Cahn–Ingold–Prelog precedence. An acetaldehyde molecule that lies in the plane of the paper, for example, presents either the Re or Si face according to how it is oriented.

The stereochemical aspects of many enzyme-catalyzed reactions have been determined. Then enzyme alcohol dehydrogenase catalyzes the oxidation of ethanol to acetaldehyde by removing the pro-R hydrogen (abbreviated as HR). When the same enzyme catalyzes the reduction of acetaldehyde to ethanol, hydrogen is transferred to the Re face.

What are the pro-R and pro-S designations for the enantiotopic hydrogens in $1$-propanol?