7321 I ' ,,4 I I \ /' 0 -9 I -1 3 7 II 15 PH Figure 4. Experimental and calculated racemization rate constants for phenylalanine at various pH values and 142 O C : (A) experimental observed rate constants by Bada and Show2 (A) calculated observed rate constants using the six absolute rate constants from this study; and (B) calculated observed rate constants using the four absolute rate constants from Bada and Shou.Z Bada and Shou's2 data points are shown by the A' s in all three plots. Curve B is the computer-calculated curve using only the four rate constants k,, k2, k4, and k6 calculated by Bada and Shou.'Curve A is the one obtained by using all six rate constants, which follows the experimental points precisely.The pK, values used in the calculations of both curves A and B were those obtained in this study using computer analysis. However, there was very little effect on the plots when using pK, values reported by Bada and Shou2 or obtained by applying Robinson and stoke^'^ equations. Experimental SectionAbsolute Rate Constants and pK,'s. The values of different pH's and observed rate constants were entered into the computer. The concentrations of H+, OH-, and each ionic species of the amino acids (using the Henderson-Hasselbach e q~a t i o n )~ were then calculated for each pH. After this, a minimization routine (ZXSSQ from the IMSL Library) using least-squares analysis was called to calculate the best six absolute rate constants. The px"s of the amino acids were determined by manually varying the pK values until the differences between the calculated and experimental values of observed rate constants were minimal.Observed Rate Constants. The calculated observed rate constants were obtained by entering previously determined pK, values and absolute rate constants in the computer program and then calculating the resultant observed constants at various values of pH. The pH profile data (A points in all plots) are those reported by Bada and Shou.2 Curve B was obtained by using Bada and Shou's equation (2) with only their four rate constants. Curve A was obtained by using eq 1 with all six rate constants from this study. W e thank NASA for research Grant NSG-7038 and the Research Office a t Utah State University for computer time. Registry No. Alanine, 56-41-7; valine, 72-18-4; leucine, 61-90-5; phenylalanine, 63-91-2. Acknowledgment.( 5 ) Eisenberg, D.; Crothers, D. Physical Chemistry with Applications to the Lqe Sciences; Benjamin/Cumming: Abstract: Dipeptides, their methyl esters, diketopiperazines (DKP), and N-substituted derivatives were racemized at high

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