Rate versus concentration

A plot of rate versus concentration for the decomposition of N2O5 is a straight line. The... 

A plot of the initial reaction rate versus concentration, on logarithmic scales. The reaction is the polymerization of methyl methacrylate, and the concentration is that of the initiator, azobisisobutyronitrile. The slope is 0.496, showing that the reaction is half-order with respect to the initiator concentration. 

Figure 5.4-26. Reaction rate versus concentrations product.

Figure 5.4-29. Initial rate versus concentration for different processes controlling.

The tabulated data of rate versus concentration refer to a reaction that is believed of the second order in the forward direction and first order in reverse. Initial concentrations of the two reactants were 1.2 mol/cuft each and there was no product to start with, [a) Find the specific rates (b) How long does it take to convert 60% of the reactants ... 

Figure 3. Schematic view of the substrate uptake rate versus concentration relationship as described by the whole-cell Michaelis-Menten kinetics. Q is the substrate uptake rate, <2max the biologically determined maximum uptake rate per biomass, c the substrate concentration, and Kj the whole-cell Michaelis constant, i.e. the concentration resulting in 2max/2 (mass of substrate per volume). At c

Figure 3.5 Determination of order graphs of rate versus concentration, (concentration)2 and (concentration)1/2...

Pig. The plot of rate versus concentration for a zero-order reaction The reaction rate does not vary with concentration of reactant. Reaction and Half-lifetime... 

Thus, if the double-logarithmic plot of rate versus concentration gives a straight line, then the slope gives the value of n and the intercept gives in k. 

Figure 8. Sensory heat ratings versus concentration of oleoresin capsicum on paprika for a set of 15 artificial red peppers. Reproduced with permission from Ref. 4, copyright 1984, Institute of Food Technologists.

FIGURE 15B Typical rate versus concentration curve for autocatalytic reactions of the iype -rA = k Cf), A is the polymer. 

A guideline for choosing a suitable method is to avoid approximations as much as possible. Thus, plots of concentration, or a function of concentrations, versus time or reactor space time are preferred for evaluation of experiments with batch, tubular, and differential recycle reactors, in which concentrations are directly measured and rates can only be obtained by a finite-difference approximation (see eqns 3.1, 3.2, 3.5, 3.6, and 3.8). On the other hand, plots of the rate, or a function of the rate, versus concentration or a function of concentrations serve equally well for evaluation of results from CSTRs or differential reactors without recycle (gradientless reactors), where concentrations and rate are related to one another by algebraic equations that involve no approximations (see eqns 3.3, 3.4, or 3.7). 

During metal-RNa exchange (Fig. 17) the selectivity of the resin for the metals Cu, Ni is always high so that the rate of mass transfer depends only on the concentration factor. The rate versus concentration dependencies is close to linear for these cases (Fig. 17). The small difference in rates for Ni/Na and Cu/Na exchange is due to the difference in difiiisivity of Cu and Ni ions. 

Figures 19 and 20 show the dependence of rates on the concentration foctor for Cl/[Ag(S20j)2] and Cl/[Cu(S203)2] exchange in the weak base resin, AN-18. The foct that rate versus concentration dependence exhibited in Fig. 20 is not linear is attributable to a complicated influence of Cg concentration on the selectivity factor. It follows from the IE isotherms obtained in static experiments [72] that the selectivity factor for the displacement of Ag(S20j) and Cu(S20j) ions decreases with increase of Cg concentrations. The significant decrease of Me(S203) ion selectivity explains the rate versus concentration Cg dependence observed in Fig. 20 when Cg concentration varies from 0.5 N to 2.5 N. But this decrease does not follow a simple pattern for the Ag(S203) ion and, as a consequence, the rate versus concentration dependence in Fig. 20 for the Cl[Ag(S203)2] IE system is not simple as well.

Write a rate law using experimental rate-versus-concentration data from a chemical reaction. 

The rate of the reaction depends on the concentration of N205(g). Figure 18.4 shows the graph of rate versus concentration to be a straight line that can be extrapolated to pass through the origin. So, the rate can be written... 

The following data have been obtained for the rate —versus concentration C. ... 

Copper(II) forms a 1 1 complex with the organic complexing agent R in acidic medium. The formation of the complex can be monitored by spectrophotometry at 480 nm. Use the following data collected under pseudo-first-order conditions to construct a calibration curve of rate versus concentration of R. Find the concentration of copper(Il) in an unknown whose rate under the same conditions was 7.0 X 10 A s . ... 

Since an increase in the surfactant concentration results in a higher fraction of substrate bound to the aggregate, an increase of the rate effects is expected, as seen in the above example, as [surfactant] increases and when [surfactant] >cac. Consequently, an enzymelike rate versus concentration profile is anticipated with a tendency of the curve to plateau when all the substrate is transferred into the aggregate. However, this is correct only in case (3) and in case (1) when the counterion of the added ionic surfactant is the reactive species (Figure 7, right). In case (1) when the reactive ion is not added as the counterion of the ionic surfactant (and is, consequently, kept constant in concentration) and in case (2), reaction profiles go through a maximum as the concentration of surfactant is increased (Figure 7, left). 

Figure 1. Log-log plot of initial rate versus concentration X, Xj is the parametric concentration held constant in this case at a value of Xj. Ln/, is the value of the intercept, and the slope represents the kinetic order of the reaction with respect to X,. The value of the slope in this case is 2.

There are two important results from this analysis. First, the rate constants for binding and dissociation can be obtained from the slope and intercept, resp>ec-tively, of a plot of the observed rate versus concentration. In practice this is possible when the rate of dissociation is comparable to ki [S] under conditions that allow measurement of the reaction. At the lower end, resolution of i is limited by the concentration of substrate required to maintain pseudo-first-order kinetics with substrate in excess of enzyme and by the sensitivity of the method, which dictates the concentration of enzyme necessary to observe a signal. Under most circumstances, it may be difficult to resolve a dissociation rate less than 1 sec by extrapolation of the measured rate to zero concentration. Of course, the actual error must be determined by proper regression analysis in fitting the data, and these estimates serve only to illustrate the magnitude of the problem. In the upper extreme, dissociation rates in excess of 200 sec make it difficult to observe any reaction. At a substrate concentration required to observe half of the full amplitude, where [S] = it., the reaction would proceed toward equilibrium at a rate of 400 sec. Thus, depending upon the dead time of the apparatus, much of the reaction may be over before it can be observed at the concentrations required to saturate the enzyme with substrate. 

Figure 4.7 Reaction rate versus concentration fornth-order kinetics, r kc, n > 0.

Figure 8.29 Reaction rate versus concentration of iimitmg reactant rate expression is neither convex nor concave.

It is quite common in experimental studies to operate a PFR as a so-called differential reactor. A differential reactor is a PFR in which the reactants experience only a small (differential) change in the extents of the reactions. The differential reactor is modeled using a limiting form of the PFR material balance design equation and generates data of the form rate versus concentration. Rate versus concentration data may prove useful in certain kinetic parameter studies. The PFR design equation is... 

Inverse of reaction rate versus concentration optimal se quence to achieve 95% conversion is PFR-CSTR-PFR. 

Figure 4J0 Reaction rate versus concentration for nth-order kinetics, r = kc% n < 0.

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