transition state energy, can differ. In the image below, the R enantiomer has a lower and would thus react faster than the S enantiomer. The ideal kinetic resolution is that in which only one enantiomer reacts, i.e. kR>>kS. The selectivity (s) of a kinetic resolution is related to the rate constants of the reaction of the R and S enantiomers, kR and kS respectively, by s=kR/kS, for kR>kS. This selectivity can also be referred to as the relative rates of reaction. This can be written in terms of the free energy difference between the high- and low-energy transitions states, . The selectivity can also be expressed in terms of ee of the recovered starting material and conversion (c), if first-order kinetics (in substrate) are assumed. If it is assumed that the S enantiomer of the starting material racemate will be recovered in excess, it is possible to express the concentrations (mole fractions) of the S and R enantiomers as where ee is the ee of the starting material. Note that for c=0, which signifies the beginning of the reaction, , where these signify the initial concentrations of the enantiomers. Then, for stoichiometric chiral resolving agent B*, Note that, if the resolving agent is stoichiometric and achiral, with a chiral catalyst, the [B*] term does not appear. Regardless, with a similar expression for R, we can express s as If we wish to express this in terms of the enantiomeric excess of the product, ee", we must make use of the fact that, for products R' and S' from R and S, respectively From here, we see that which gives us which, when we plug into our expression for s derived above, yield Additionally, the expressions for c and ee can be parametrized to give explicit expressions for C and ee in terms of t. First, solving explicitly for [S] and [R] as functions of t yields which, plugged into expressions for ee and c, gives Without loss of generality, we can allow kS=1, which gives kR=s, simplifying the above expressions. Similarly, an expression for ee″ as a function of t can be derived Thus, plots of ee and ee″ vs. c can be generated with t as the parameter and different values of s generating different curves, as shown below. As can be seen, high enantiomeric excesses are much more readily attainable for the unreacted starting material. There is however