Reversible reactions during cooling

Geologists often must deal with chemical reactions during cooling. The quantitative aspects for a simple case of reaction kinetics during cooling, and the qualitative aspects for more complicated reactions during cooling, were presented in Chapter 1. In this section, the quantitative aspects of reversible reactions are presented. A simple first-order reversible reaction is used as an example to de- 

1 Analytical solution for a first-order reversible reaction 

Consider the following first-order reversible reaction (Reaction 2-1)  

Because T depends on t, kf and kf, depend on f. The analytical solution of Equation 2-35 is complicated  

To integrate the above equation, the functional form of the dependence of T on t, T(t), must be assumed. Usually, two functions are used, one is referred to as asymptotic cooling, and the other as exponential cooling. The two functions are 

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The similarity theory and an exact mathematical theory of the course of the reversible reaction during cooling of the explosion products are set forth. A universal relationship between the ratio of the yield to the equilibrium... 

This scheme (in which the reversible arrows are not meant to imply that equilibrium is attained) provides an excellent qualitative, and reasonably semiquantitative, description of the formation of products during the cool-flame oxidation at 523° to 580°K. of 2-methylpentane (24). Also, because of the different energy requirements for the various modes of Reactions 4 and 5, the scheme is capable of explaining, at least in principle, the complex dependence of rate on temperature during cool-flame oxidation (24, 51). 

This calorimetric test shows that the reaction is reversible, but only 61 % of the energy which has been stored is recovered during cooling. But it will be also necessary to work with a slower scanning rate, to know its influence on the efficiency of the reaction. 

The ore is first treated with caustic soda under pressure. The aluminium largely dissolves as the aluminate, the iron oxide is insoluble and the silica also remains in the form of a sodium aluminium silicate, which leads to a loss of aluminium. Hence the best bauxites are those low in silica. After filtration, the hydrated aluminium oxide is reprecipitated by seeding and the caustic soda solution may be re-used. The alumina is washed and then heated at 1200°C to remove water. The final step in the production of aluminium metal has to be electrolytic since the reduction of alumina with carbon is only possible at very high temperatures and the reverse reaction occurs on cooling. Moreover, because of the chemistry of aluminium, the electrolysis medium cannot be water in fact almost all commercial production of aluminium during the last ninety years has used an electrolysis in molten cryolite (Na3AlF5). 

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