Kinetic reaction profiles

units of moles per litre can also be expressed a.s moles per dm, or mol dm - , 

Both mol I and mol dm are widely used as concentration units. However, the litre is not part of the SI system of units. Mol dm has a more formal status and is the concentration unit we use here. 

after 2 000 s of reaction the magnitudes of the changes in the concentrations of reactants and products in Reaction 3.1 are the same, although there is a decrease for reactants and an increase for products. In fact, this type of result would have been obtained irrespective of the time period selected. This means that the stoichiometry of Reaction 3.1 applies throughout the whole course of reaction that is it has time-independent stoichiometry. 

It might be tempting to conclude that intermediates are not present for a reaction that has time-independent stoichiometry. However, this is not the case. Time-independent stoichiometry simply means that, within the accuracy of the chemical analysis used, intermediates cannot be detected and so they do not affect the stoichiometric relationship between reactants and products. In fact. Reaction 3.1 is thought to be composite with a three-step mechanism in which case intermediates must be involved. 

How would you summarize (in a single sentence) the features we have determined, so far, for Reaction 3.1  

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Examples of the application of MCR to both 2D DOSY NMR data23 and 3D [jH-15N] HSQC NMR data24 can be found. In the latter case, the reaction between 15N-labelled cisplatin and the amino acid-nucleotide hybrid (Phac-met-linker p5 dG) is monitored and both analysis of the individual 2D HSQC spectra as well as the simultaneous analysis of all 2D HSQC spectra over time is performed in which case the kinetic reaction profiles can be obtained. The authors found that sub-structures involved in local unfolding as a consequence of the addition of denaturant could be identified, and that this would hardly have been possible without multivariate analysis of the data. 

Figure 3.1 A kinetic reaction profile for Reaction 3.1 at 25 °C. Smooth curves have been drawn through the experimental data points. The behaviour for BrO and Cl is represented by a single curve.

Figure 3.3 plots a kinetic reaction profile for BrO and shows the tangent drawn to the curve at 1 500 s. 

Clearly, d[BrO-]/dt and d[Cl-]/dr will be equal in value since the kinetic reaction profiles for BrO and Cl- are identical. They are also both positive quantities since they represent th formation of product species. Thus, if we represent the rate of Reaction 3.1 at any time by the symbol /, then one possible definition would be... 

This question uses the Kinetics Toolkit. The experimental data that were used for plotting Figure 3.1, the kinetic reaction profile for Reaction 3.1, is given in Table 3.1. It is presented in a form suitable for direct entry into the graphplotting software, although you should note that the E format must be used for inputting powers of ten. For example, 3.230 x 10-3 is input as 3.230E-3. When you have input your data, you should store it in an appropriately named file.)... 

Data used for plotting the kinetic reaction profile in Figure 3.1 ... 

One special case of the rate of reaction is that corresponding to the start of the reaction. This is referred to as the initial rate of reaction and is represented by Jq (V subscript zero ). Figure 3.4 plots a kinetic reaction profile for Cl and shows the tangent (labelled initial tangent ) drawn to the curve so that the initial rate of change of concentration of Cl can be determined. 

If you would like to look at this definition in more detail then information for plotting a kinetic reaction profile for Reaction 3,4 is given in Exercise 3.1 at the end of this section. 

A kinetic reaction profile is a plot of the concentrations of reactants or products in a reaction, individually or combined, as a function of time under isothermal conditions. 

The instantaneous rate of change of the concentration of a reactant, or a product, at a particular instant in a chemical reaction is equal to the slope of the tangent drawn to the kinetic reaction profile at that time. 

Table 3.2 Data for plotting a kinetic reaction profile for the gas-phase decomposition of NO2 (Reaction 3.4) at 300 °C...

This, in outline, is the strategy we shall adopt here. It is assumed that the stoichiometry of the reaction has been established and that kinetic reaction profiles are to be measured at a fixed temperature. 

A kinetic reaction profile for N2O5 measured at 63.3 °C is shown in Figure 5.2. (If you wish to plot this kinetic reaction profile for yourself using the Kinetics Toolkit, the data are given in Table 5.1.)... 

It would be convenient if the kinetic reaction profile in Figure 5.2 could be used directly, without the need for any further processing of the data, to obtain information about the experimental rate equation for the decomposition of N2O5. In fact, a preliminary check can be carried out using a method based on the idea of reaction half-life, which is denoted by fi/2. This approach was suggested many years ago by Wilhelm Ostwald who was Professor of Chemistry at Leipzig (1887-1906) and a Nobel prizewinner (1909). 

For the purposes of our preliminary check it is useful to extend the idea of reaction half-life a little further. As shown schematically in Figure 5.3, successive half-lives can be defined on the same kinetic reaction profile of a reactant A with initial concentration [A]q ... 

A kinetic reaction profile for N2O5 measured for the decomposition of this compound in the gas phase at 63.3 °C. A smooth curve is drawn through the experimental data points. 

A preliminary half-life check of the kinetic reaction profile for NO2 shows that the reaction is not first-order. (You may wish to confirm this for yourself by returning to Exercise 3.1.)... 

The rate of reaction can therefore be determined from the kinetic reaction profiles for NO2, NO or O2 and you should recall that you were asked to find values of J at different times for the decomposition reaction in Exercise 3.1. These values are repeated in Table 5.2 which also includes the initial rate of reaction and two further determinations at 250 s and 750 s. You should note that this table includes the values of d[N02]/dt from which J is calculated (although values of d[NO]/dr or d[02]/dt could equally well have been used for this purpose). In addition the table gives the values of [NO2] at the selected times these values are simply taken from the kinetic reaction profile for NO2. 

The kinetic reaction profile (Figure 3.1) we discussed for this reaction was one for which the initial concentrations of C10 and Br were relatively small and similar in magnitude (3.230 x 10 moldm 3 and 2.508 x 10 moldm 3, respectively). However, the reaction can be investigated over a much wider range of reactant concentrations a specific example is shown in Figure 5.7. (The temperature is reduced to 15 °C so that the reaction is slow enough to be monitored by conventional techniques.)... 

Figure 5.7 Kinetic reaction profiles for (a) C10 and (b) Br for the reaction between these ionic species in aqueous solution at 15 °C. In each plot, a smooth curve has been drawn through the experimental data points.

Table 5.6 provides information taken from the kinetic reaction profile for Br" in Figure 5.7b. Use this information to determine a value for the pseudo-order rate constant in Equation 5.22. 

You may have noticed in Table 5.8 that the initial concentrations of CIO" and Br" in Experiment I are the same as those used in plotting the kinetic reaction profile in Figure 3.1 (Table 3.1, Section 3.1). In all three experiments, at least within experimental error, the initial concentration of Br- is fixed, but it is not in excess. This is an important feature of the initial rate method it is not necessary to have reactants in excess. 

Determine at a given instant during the progress of a chemical reaction the rate of change of concentration of a reactant or product species with respect to time from a suitable kinetic reaction profile. (Question 3.2 and Exercise 3.1)... 

Given information about the initial tangent to a kinetic reaction profile, determine the initial rate of reaction. (Question 3.3)... 

From the information given, albeit limited, it can be seen that 7/[An] is constant within experimental uncertainty and so it can be concluded that /3, the partial order with respect to the anhydride (An), is 1. (It would in practice be important to check this result using data from the full kinetic reaction profile.)... 

Your kinetic reaction profile should be similar to that in Figure E.2. 

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