Zero-order reactions rate-concentration graphs

When we measure the rate (also called the velocity) of an enzymatic reaction at varying substrate concentrations, we see that the rate depends on the substrate concentration, [S]. We measure the initial rate of the reaction (the rate measured immediately after the enzyme and substrate are mixed) so that we can be certain that the product is not converted to substrate to any appreciable extent. This velocity is sometimes written or Vq to indicate this initial velocity, but it is important to remember that aU the calculations involved in enzyme kinetics assume that the velocity measured is the initial velocity. We can graph our results as in Figure 6.8. In the lower region of the curve (at low levels of substrate), the reaction is first order (Section 6.3), implying that the velocity, V, depends on substrate concentration [S]. In the upper portion of the curve (at higher levels of substrate), the reaction is zero order the rate is independent of concentration. The active sites of aU of the enzyme molecules are saturated. At infinite substrate concentration, the reaction would proceed at its maximum velocity, written kJnax-... 

A second-order reaction is one for which the overall reaction order is 2. If a second-order rate law depends on the concentration of only one reactant, then rate = k[A], and the time dependence of [A] is given by the integrated form of the rate law 1/[A], = 1/[A]q + kt. In this case a graph of 1/[A] t versus time yields a straight line. A zero-order reaction is one for which the overall reaction order is 0. Rate = fc if the reaction is zero order. 

Figure 6.23 shows a graph of the amount or concentration of a reactant against time. (This form of graph is obtained in most reactions, with the exception of autocatalysis or zero order reactions (Chapter 16).) You can see that the gradient of the graph continually decreases with time and, hence, the rate of reaction decreases with time. The reaction rate is zero when the reactants are all consumed and the reaction stops. 

Figure 16.9 Rate-concentration graphs for zero-order, first-order and second-order reactions... 

For a zero-order reaction, the graph is a descending straight line. The rate of reaction is the slope (gradient) of the graph. The reaction proceeds at the same rate whatever the concentration of the reactant. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

In zone a of Figure 2.5, the kinetics are first order with respect to [S], that is to say that the rate is limited by the availability (concentration) of substrate so if [S] doubles the rate of reaction doubles. In zone c however, we see zero order kinetics with respect to [S], that is the increasing substrate concentration no longer has an effect as the enzyme is saturated zone b is a transition zone. In practice it is difficult to demonstrate the plateau in zone c unless very high concentrations of substrate are used in the experiment. Figure 2.5 is the basis of the Michaelis-Menten graph (Figure 2.6) from which two important kinetic parameters can be approximated ... 

With the neutral [(RCN)2PdCl2] pro-catalyst system (Fig. 12.3, graph iv), computer simulation of the kinetic data acquired with various initial pro-catalyst concentrations and substrate concentrations resulted in the conclusion that the turnover rates are controlled by substrate-induced trickle feed catalyst generation, substrate concentration-dependent turnover and continuous catalyst termination. The active catalyst concentration is always low and, for a prolonged phase in the middle of the reaction, the net effect is to give rise to an apparent pseudo-zero-order kinetic profile. For both sets of data obtained with pro-catalysts of type B (Fig. 12.3), one could conceive that the kinetic product is 11, but (unlike with type A) the isomerisation to 12 is extremely rapid such that 11 does not accumulate appreciably. Of course, in this event, one needs to explain why the isomerisation of 11 now proceeds to give 12 rather than 13. With the [(phen)Pd(Me)(MeCN)]+ system, analysis of the relative concentrations of 11 and 13 as the conversion proceeds confirmed that the small amount of... 

The available data are the reactant concentration as a function of time for a single experiment, so we will need to use graphical techniques to determine the order of the reaction. There are three possibilities we can explore using the integrated rate laws we ve examined. The reaction could be zero order, first order, or second order with respect to NO2. We will need to manipulate and plot the data in various ways to determine whether there is a good fit with any of these models. (Other orders are also possible, so we should be aware that all three tests could conceivably fail.) With a spreadsheet or a graphing calculator, such manipulation of data is easy. For this example, first we will calculate all of the data needed for all three plots and then make the appropriate graphs to find the linear relationship and determine the rate law. 

A graph of reaction rate against concentration tells us whether a reaction is zero, first, second or third order with respect to a particular reagent (or overall). It is very rare to obtain an order with respect to a particular reagent higher than second order. Figure 22.9 shows the shapes of the graphs expected for different orders of reaction. 

But the slope of the second graph is zero The rate-determining step does not involve NaOH so adding more of it docs not speed up the reaction. The reaction shows first-order kinetics (the rate is proportional to one concentration only) and the mechanism is called S l, that is, Substitution, Nucleophilic, 1st order. 

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