A Nomograph for the Estimation of the ~ c t i v a G oEnergies i of Unimolecular Reactions EARL WARRICK Department of Chemistry, Carnegie Institute of Technology, Pittsburgh, Pennsylvania
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To establish the value of D, one uses the scales marked "A" and connects 570 on the frequency scale with the C-Cl value on the Do scale by a straight line and reads 78 kilocalories on the D, scale. Shifting to the scales marked "B," one connects the value 78 kilocalories on the D. scale with the value 570 on the P scale. This straight line when extrapolated to the D, is the spectroscopic energy of dissociation for the E scale gives 47 kilocalories for the energy of activation. bond characterized by frequency G and is related to the The observed energy of activation is 46 kilocalories. thermochemical bond energy, Do, by the equation The calculated value for E is accurate within the limits of experimental error. The use of the nomograph seems to be limited by The numerical constants given in both equations are the quadratic nature o: the equation. However, only valid when ? is expressed in cm.-I, and D. and Do it may be noted that, for energies of activation smaller than 50 kilocalories, the two possible frequencies differ are given in calories. It is convenient to set up both equations in nomo- by a multiple of four or greater. Obviously the graphic form and suitable nomographs are shown in higher frequency is an impossible value. For higher energies of activation the two frequencies may ditrer the accompanying graph. The use of the nomograph may be illustrated by only by a multiple of two or less. Here both freconsidering the decomposition of tertiary butyl chlo- quencies are physically possible and, in fact, do exist ride (2). This molecule decomposes into isobutylene for the C-H bond. It is impossible to state which frequency is the correct one for this case. and hydrogen chloride. In the reaction the C-H and C-
