General rate of reaction

Kinetic investigations using rising temperature techniques Since, in general, rates of reaction vary with both a and T, i.e. 

To avoid the ambiguity of more than one rate, chemists have defined a general rate of reaction equal to the rate of consumption of a reactant or formation of a product divided by its coefficient in the balanced chemical equation. Thus, for the reaction... 

We introduce the axial dispersion of mass and heat for a single reaction in a tubular reactor that operates at a steady state with the generalized rate of reaction r per unit volume. 

Increasingly, Monte-Carlo calculations become available, which try not only to describe the general rate of reactions but also the sites of attack within the... 

This observation suggests that we can define a more general rate of reaction for any chemical reaction with any stoichiometry in terms of the rate of consumption or production of any of the reactants or products ... 

Thus, the rates of reaction of a single reaction can be all expressed in terms of one rate of reaction as long as the stoichiometric numbers for this single reaction are all known. We will define the generalized rate of reaction (r) in a later section. 

Of course, we could have used Rg, Rq, or R as the basis rather than To avoid this multiplicity of choices, we can define a rate of reaction that does not depend on the component. It is only related to the reaction let us call this rate the generalized rate of reaction, r ... 

There are M equations having N reactions (rj, j = 1,2,N) and cry is the stoichiometric number of component i in reaction j. The generalized rate of reaction for reaction j is given by rj. Note that rj is the overall rate of reaction for the whole unit (it is not per unit volume or per unit mass of catalyst and so on that is why our equations are mass balance equations, not design equations as shown later). 

We can also express Q in terms of AHr and the generalized rate of reaction... 

Note that for this irreversible single reaction, we always take the absolute values for rates of reaction and stoichiometric numbers, because the sign of Q is determined by the sign of the heat of reaction (whether the reaction is exothermic or endothermic) and not by whether we are referring to a product or a reactant. However, when we use the generalized rate of reaction (r), this issue is automatically addressed because r is always positive, as we have shown in the previous section. 

Note 3 The heat generation (or absorption) term will always have the sign of (AHr) or AHra, because it is always multiplied by the generalized rate of reaction r, which is always positive. 

The rates of reaction can be given for the production or consumption of the components or they can be given for the reactions that lead to the generalized rates of reaction studied earlier. 

The generalized rates of reactions r and r 2 (moles per unit volume per unit time) can be defined as explained in the following very simple steps. 

Here, r j is the generalized rate of reaction for reaction j [in mol/(time x volume)] (it is equal to rj for a unit volume of reactor). For a single reaction, the design equation simply becomes... 

Tj = overall generalized rate of reaction for reaction j in phase II = stoichiometric number of component i in reaction j in phase II K = total number of output streams for phase II L = total number of input streams for phase II N = total number of reactions in phase II... 

When we refer to the rate of reaction (20.1), which of the four quantities described should we use To avoid confusion in this matter, the International Union of Pure and Applied Chemistry (lUPAC) recommends that we use a general rate of reaction, which, for the hypothetical reaction represented by the balanced equation,... 

If the rate data in Table 20.3 were based on the disappearance of HgCl2 instead of 2042 , Rj in this setup would be twice as great and k for the general rate of reaction would be based on —5 X A[HgCl2]/Af. Note the units on the rate constant are M 2 min which are appropriate units for a third-order rate constant. Checking the units in an answer is one way to ensure that we have not made any mistakes. 

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