Reaction rate against concentration graphs

Tangents can be drawn at various points and Table 16.7 shows the values calculated for the rate at five different concentrations of acid. These results are then plotted as a graph of rate against concentration graph. They produce a curve, indicating that the reaction is second order (Figure 16.6). 

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. 

The order of reaction can be determined from graphs of reaction rate against concentration. 

Chemical reactions are classified according to the number of reactants. In the simplest case, the first-order reaction, there is just one reactant and the rate of the reaction is proportional to the concentration of that reactant. Hence, a graph of reaction rate against reactant concentration is a straight line for a first-order chemical reaction (Fig. 7.5). 

These types of inhibition are shown by simple enzymes (also called Michaelis-Menten enzymes). Some enzymes show much more complex behavior toward inhibitors and may also respond to activators. Such enzymes do not yield such simple graphs of reaction rate against substrate concentration. 

Figure 11.32 A graph of initial rate against concentration for a first-order reaction (decomposition of dinitrogen pentoxide) 2N20s(g) 4N02(g) + 02(g)... 

Worked Example 8.2 yields a value for the rate constant k, but an alternative and usually more accurate way of obtaining k is to prepare a series of solutions, and to measure the rate of each reaction. A graph is then plotted of reaction rate (as y ) against concentration(s) of reactants (as V) to yield a linear graph of gradient equal to k. 

From the data shown in Figure 7.9 it is possible to produce a different graph which direcdy shows the rate of the reaction against concentration rather than the time taken for the reaction to occur against concentration. To do this, the times can be converted to a rate using ... 

Figure 7.10 Graph to show the rate of reaction against concentration.

To simplify the kinetics, we will start by considering only the reaction rate right at the beginning of the reaction. The reaction rate at time 0, VO, is the initial slope of the graph of product concentration against time (Fig. 7.6). 

The Michaelis-Menten equation developed in 1913 ushered in the era of enzyme kinetics and mechanism (chapter 2). Experimentally, its application involves graphing rates (velocities) of reaction (v) against trial concentrations of substrate ([S]). A "saturation" curve is usually observed in which there is a leveling off of v, so as to approach the maximum rate (V a ) as [S] reaches saturation concentration. In practice, it is difficult to accurately determine the onset of saturation and this led to considerable uncertainty in the values of Vmax as well as the enzyme-substrate binding constants (K in chapter 2). 

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. 

It is important in kinetics to discover how the rate of reaction varies with concentration of the reactants. It allows chemists to deduce the order and the rate expression for the reaction (Chapter 16). One simple, but not very precise, approach is to draw a number of tangents on a concentration-time graph (Figure 6.28) and then plot a graph of the rates (the numerical value of the gradients) against concentration. Many reactants show a directly proportional relationship between concentration and rate (reactions in which this is the case are said to be first order for that reactant (Chapter 16)). 

A graph of the concentration of HCI(aq) against time is shown in Figure 16.5. Note that the concentrations of both the acid and methanol fall at the same rate over time. Tangents can then be drawn to the curve to find the reaction rate. Figure 16.5 shows the tangent that corresponds to [HCI(aq)] =... 

A graph of rate of reaction against concentration of cyclopropane (Figure 22.8) shows us that the rate is directly proportional to the concentration of cyclopropane. So, if the concentration of cyclopropane is doubled the rate of reaction is doubled, and if the concentration of cyclopropane falls by one-third, the rate of reaction falls by one-third. 

In the magnesium/acid reaction, processing could involve plotting a graph of rate against the relative concentration of the acid. Inspection of the graph would allow a deduction to be made about the order with respect... 

Figure 8.9 Kinetics of a second-order reaction the racemization of glucose in aqueous mineral acid at 17 °C (a) graph of concentration (as y ) against time (as V) (b) graph drawn according to the linear form of the integrated second-order rate equation, obtained by plotting 1 / A, (as V) against time (as V). The gradient of trace (b) equals the second-order rate constant k2, and has a value of 6.00 x 10-4 dm3mol 1s 1...

Figure 8.15 The rate constant of a pseudo-order reaction varies with the concentration of the reactant in excess graph of k (as V) against [alkene]0 (as V). The data refer to the formation of a 1,2-diol by the dihydrolysis of an alkene with osmium tetroxide. The gradient of the graph yields k2, with a value of 3.2 x 10 2 dm3 mol-1 s-1...

FIGURE 13.10 We can test for a first-order reaction by plotting the natural logarithm of the reactant concentration against the time. The graph is linear if the reation is first order. The slope of the line, which is calculated by using the points A and B, is equal to the negative of the rate constant. 

The reaction begins without delay. The rate decreases as the degree of conversion increases. A graph showing vinyl concentration according to second order kinetics plotted against time gives a linear relationship (Fig. 5). 

The rate of a chemical reaction is usually described in terms of the rate of change of concentration c with respect to time t. The gradient of a graph of c against t is thus given by the derivative dddt. 

The essential feature of the procedures described above is that the test employed to decide whether or not a given rate equation represents the kinetics of a particular reaction is based on the values of the rate coefficients obtained at a number of different values of [A]o Rnd [B]q. If the rate coefficients show no systematic variation with one or other of the initial concentrations, the assumed rate equation is applicable and the orders a and b postulated from the preliminary examination of the data are confirmed. Linearity of the graph of a particular form of f(a) against (t—to) at one pair of values of [A]o and [B]o is not conclusive proof of the applicability of the chosen rate equation since it is a matter of fairly common experience that kinetic data may fit a particular equation quite well at one set of initial concentrations only to show significant deviations when the initial concentrations are changed. 

When two reactants are mixed together (for example, in a beaker) the rate of reaction is greatest at the start of the reaction. As the reaction continues, the rate continues to fall. If the concentration of reactant (such as bromine. Fig. 14.1) or product is plotted against time, a graph like Fig. 14.2(a) is produced. (If the reaction is an equilibrium reaction, the concentration of reactants in Fig. 14.2(a) will level out when equilibrium has been achieved, but will not fall to zero.)... 

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