No-Flow Batch System

then a 10-degree temperature rise will nearly quintuple the rate, whereas at 10,000 K the rate is barely raised by 1.5 times its initial value  

We have not discussed the issue of the dimensions of the rate constant. The reason is that the dimensions change with the change in the rate dependence upon concentration. Hence we have postponed consideration of dimensions until we reach that point. 

Reactions take place in a localized region of space, that is, a system defined by a control volume. The control volume can be real or abstract such as a cell or organelle, or a region of an organelle. They can be macrosized such as a reactor or abstractly macrosized as in the case of the reactions that take place within the nucleus of a star. We choose the control volume according to the dictates of the analysis that we are undertaking. The control volume should be one phase or it may be abstract and treat more than one phase as if it would behave as a single phase. 

We will begin with the case of the batch reactor. In this case the vessel defines the control volume. We will move to systems with flow in and both flow in and out. The former is the case of semibatch operation while the latter will be treated as the continuous stirred tank reactor (CSTR) and the plug flow reactor (PFR). All the chemical kinetics that we will need can be introduced within the context of these four different kinds of reactors. 

We know from the conservation of mass that when we run a reaction in a batch reactor the mass of products must be equal to the mass of reactants so long as nothing has escaped from the reactor. This holds absolutely and is independent of the chemical reaction type, mechanism, or stoichiometry. All that chemical reactions do is to rearrange the atoms and mass in the molecules. In essence the labels on the mass change but that is all. If the reaction in solution leads to a gas such as the reaction of baking soda with vinegar water (that is, sodium bicarbonate with dilute acetic acid), then a mass change can take place because one of the products is a gas and can escape the vessel  

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