Quantitative Laws Arrhenius

A15. Arrhenius, S., Quantitative Laws in Biological Chemistry. Harcourt, New York, 1915. 

Kinetics is concerned with the rates of chemical reactions and the factors which influence these rates. The first kinetic measurements were made before 1820, but interpretation in terms of quantitative laws began with the studies on the inversion of sucrose by Wilhelmy/ the esterification of ethanol with acetic acid by Bethelot and St. Gilles, and the reaction between oxalic acid and potassium permanganate by Harcourt and Esson. These investigations established the relations between rate and concentration of reactants. The important contribution of Arrhenius for the effect of temperature was also made in the nineteenth century. 

Arrhenius and Madsen, Z. phys. Chem.y 1903, xliv, 7 Arrhenius, Z. phys. Chem.y 1903, xlvi, 415 Madsen, Brit. Med. y.y 1904, II, 567-74 Craw, Z. phys. Chem.y 1905, lii, 569 Arrhenius, Immunochemistryy New York, 1907 id.y Quantitative Laws in Biological Chemistryy 1915 Thorvald Madsen was Director of the Serum Institute, Copenhagen. 

In summaiy, the mathematical formulation of a mechanism will provide us with the means to find the quantitative laws of evolution (extent-time, speed-time and speed-extent) as well as the influence of concentrations on speeds. The influence of temperature will only show up by making Arrhenius law explicit on the different rate coefficients. 

Several points are worth noting about these formulae. Firstly, the concentrations follow an Arrhenius law except for the constitutional def t, however in no case is the activation energy a single point defect formation energy. Secondly, in a quantitative calculation the activation energy should include a temperature dependence of the formation energies and their formation entropies. The latter will appear as a preexponential factor, for example, the first equation becomes... 

In this chapter, we describe how experimental rate data, obtained as described in Chapter 3, can be developed into a quantitative rate law for a simple, single-phase system. We first recapitulate the form of the rate law, and, as in Chapter 3, we consider only the effects of concentration and temperature we assume that these effects are separable into reaction order and Arrhenius parameters. We point out the choice of units for concentration in gas-phase reactions and some consequences of this choice for the Arrhenius parameters. We then proceed, mainly by examples, to illustrate various reaction orders and compare the consequences of the use of different types of reactors. Finally, we illustrate the determination of Arrhenius parameters for die effect of temperature on rate. 

Figure 7.5 is quantitatively correct only for the special case of the exponential approximation to the Arrhenius rate law. However, the figure is also qualitatively correct for the exact Arrhenius form with non-zero y, provided y < 4. No new stationary-state patterns are introduced. 

Work of recent years has shown that typical vital processes obey quantitatively the laws of ordinary chemical dynamics. Examples are found especially in publications by Osterhout and by Hecht. The demonstration of this principle was possible only when the velocities of organic activites were measured, and treated as presenting problems in mass action kinetics. In this way, as Loeb and Arrhenius foresaw and in a measure illustrated, it is possible to get around the otherwise insuperable obstacle arising from the fact that the quantities of reacting substances controlling protoplasmic activity may be extraordinarily minute, inaccessible and that gross analysis is in any case impossible while the material is alive. These difficulties are especially conspicuous if one contemplates the investigation of so delicate a matter as the adjustor functions of the central nervous system. 

According to the theory of Arrhenius, the variations of A with concentration are due to shifts in equilibrium between undissociated and dissociated species. This idea was expressed quantitatively by the Russian-German physical chemist Friedrich Wilhelm Ostwald (1853-1932) in terms of a dilution law. Consider an electrolyte AB which exists in solution partly as the undissociated species AB and partly as the ions A" and B""... 

During the first decade of the 20th century, kinetics and thermodynamics were combined in order to make predictions of chemical behavior. Toward the end of the 19th century Arrhenius had quantitated the dependence of reaction rate on temperature (k = Aexp[-E/RT]) Rates increase with increasing temperature (often roughly doubling with every 20°F [10°C] increase). For a chemical system (e.g., a reaction), the second law can be expressed as follows ... 

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