Reversible and Irreversible Reactions
Irreversible Reactions in Parallel:
Consider the simplest case, A decomposingby two competing paths, both elementary reactions:
The k values are found using all three differential rate equations. First of all,Eq. 34, which is of simple first order, is integrated to give:
When plotted as in flowingfigure, the slope is :k1+ k2.
Then dividing Eq. 35 by Eq.36 we obtain the following Figure.
Irreversible Reactions in Series:
We first consider consecutive unimoleculartypefirst-orderreactions such as:
The time at which the maximum concentration of R occursis thus:
The maximum concentration of R is found by combining Eqs. 49 and 51 to give:
Homogeneous Catalyzed Reactions
Suppose the reaction rate for a homogeneouscatalyzed system is the sum of rates of both the uncatalyzed and catalyzedreactions:
with corresponding reaction rates:
This means that the reaction would proceed even without a catalyst present andthat the rate of the catalyzed reaction is directly proportional to the catalystconcentration. The overall rate of disappearance of reactant A is then
On integration, noting that the catalyst concentration remains unchanged, we have:
Making a series of runs with different catalyst concentrations allows us to findk1and k2. This is done by plotting the observed k value against the catalystconcentrations as shown in Figure below. The slope of such a plot is k2and theintercept k1.
Homework:
Autocatalytic Reactions
A reaction in which one of the products of reactionacts as a catalyst is called an autocatalytic reaction. The simplest such reaction is
For an autocatalytic reaction in a batch reactor some product R must be presentif the reaction is to proceed at all. Starting with a very small concentration ofR, we see qualitatively that the rate will rise as R is formed. At the other extreme,when A is just about used up the rate must drop to zero. This result is given inFigure below, which shows that the rate follows a parabola, with a maximum wherethe concentrations of A and R are equal.
To test for an autocatalytic reaction, plot the time and concentration coordinatesof Eq. 42 or 43, as shown in Figure below and see whether a straight line passingthrough zero is obtained.
First-Order Reversible Reactions:
The simplest case is the opposed unimolecular-type reaction
= (k1+ k2) t
A plot of -In (1 - XA/XAe)vs .t, as shown in Fig. 3.13, gives a straight line.
Figure 3.13 Test for the unimolecular typereversible reactions of Eq. 53.
The similarity between equations for the first-order irreversible and reversiblereactions can be seen by comparing Eq. 12 with Eq. 54
or by comparing Fig. 3.1with Fig. 3.13.
Thus, the irreversible reaction is simply the special case of thereversible reaction in which CAe = 0, or XAe = 1, or Kc=?.
Q) The first-order reversible liquid reaction
takes place in a batch reactor. After 8 minutes, conversion of A is 33.3%while equilibrium conversion is 66.7%. Find the rate equation for this reaction.
Solution:
Homework:
Q)
Q)
Second-Order Reversible Reactions:
For the bimolecular-type second-order reactions:
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