Half-life of reaction

Problem 1.18 A second order reaction with initial concentration of each reactant as 0.5 mol dm 3 was carried out in presence of acid as catalyst. At pH 4.0 the half-life of reaction was found to be 60 min. Calculate the observed and true rate constant for the reaction. 

Half-life of reaction, i.e. time for half reactant to be ... 

The reaction rate must be slow so that the half-life of reaction is much longer than the time required for sample introduction into and sealing of the pressure vessel, and for thermal equilibration following heating of the sample caused by compression, as noted above. 

The rate of oxidation of N3- by HO is nearly diffusion controlled (Table VI), so that with only 10 mmol dm of N3-, the half-life of reaction 48 is just 6 ns. The overall result is that the yield ( uimol J ) of N3 is 0.55, with a residual yield of hydrogen atoms of 0.06. The H atoms react only slowly with the basic solution components, and adjustments for their contribution can be made. The rate constant for oxidation of phenol is about two orders of magnitude smaller than that for oxidation of phenoxide, again illustrating the powerful effect of protonation of the electron donating center. 

The addition of H2 to an alkaline solution thus doubles the yield of e m which is observed. However, the half-life of Reaction 2 with H2 dissolved at 1 atm. is some 25 /xsec. and if the loss of OH radicals by the competing reaction,... 

With these possibilities in mind we attempted the photo-oxygenation of norbornene. With either methylene blue or hematoporphyrin as sensitizer and methanol or pyridine as solvent, we obtained no evidence of any reaction by infrared or NMR spectrum, by gas chromatography, or by spot test for hydroperoxide (potassium iodide/starch in 2-propanol/ acetic acid) or peroxide (hydriodic acid/starch in 2-propanol). While the half-life of reaction of cyclohexene was only about one day under our reaction conditions, no evidence of reaction of norbornene was obtained in a period of one month. Assay of norbornene by gas chromatography with benzene as internal standard failed to show any depletion of norbornene over the attempted reaction interval. 

The resulting expressions for the half-life of reactions of different orders (n) are as follows ... 

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