Concentration of reactants

In addition to the reaction rate constant, the concentration of reactants influences the reaction rate significantly as shown in Equation (3-5). For example, assume that the reaction A — P is a first-order reaction with respect to A. Then, from Equation (3-5), the reaction rate becomes r = kcA- For a concentration twice as high, the reaction rate increases by a factor of two. Dilution, then, is a method to lower the reaction rate and to moderate the increases in temperature and pressure. Dilution results in a lower final pressure provided the vapor pressure of the diluent is relatively low. 

The heat balance for a batch reactor, where Qin is zero, shows that heat accumulation is the difference between heat production and heat removal, from Equation (3-1), leading to Equation (3-7)  

The heat removal depends linearly on the difference between the reactor temperature and the coolant temperature since qm = UAS(T - Tm), where the subscript m refers to the cooling medium. The heat removal is represented by straight lines on the figure. The heat flow is zero if no heat is removed, which is the case if the coolant temperature is equal to the temperature of the system. Thus, the intersection of a heat removal line with the Y-axis (e.g., Tm,i) 

FIGURE 3.7. Stability as a Function of Heat Production and Heat Removal. 

A stable situation is represented by the heat removal line (1), provided the temperature of the system is lower than the temperature Tc, which here is equal to the temperature of no return (Tnr). Under these conditions, the cooling capacity of the system exceeds the heat that is generated and the system temperature will invariably drop to the point of intersection SI. 

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Selectivity for series reactions of the types given in Eqs. (2.7) to (2.9) is increased by low concentrations of reactants involved in the secondary reactions. In the preceding example, this means reactor operation with a low concentration of PRODUCT—in other words, with low conversion. For series reactions, a significant reduction in selectivity is likely as the conversion increases. 

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

A transfer rate constant can be obtained by applying a Boltzmann distribution, and by writing the concentration of reactant present as... 

Krypton clathrates have been prepared with hydroquinone and phenol. 85Kr has found recent application in chemical analysis. By imbedding the isotope in various solids, kryptonates are formed. The activity of these kryptonates is sensitive to chemical reactions at the surface. Estimates of the concentration of reactants are therefore made possible. Krypton is used in certain photographic flash lamps for high-speed photography. Uses thus far have been limited because of its high cost. Krypton gas presently costs about 30/1. 

Reducing the temperature or increasing the concentration of reactants, particularly of dinitrogen pentoxide, advanced the onset and increased the intensity of the autocatalysis. Added nitric acid and, to a greater extent sulphuric acid, made the effect more prominent. 

The expression template reaction indicates mostly a reaction in which a complexed me) ion holds reactive groups in the correct orientation to allow selective multi-step reactions. T1 template effect of the metal is twofold (i) polymerization reactions are suppressed, since th local concentration of reactants around the metal ion is very high (ii) multi-step reactions are possible, since the metal holds the reactants together. In the following one-step synthesis eleven molecules (three ethylenediamine — en , six formaldehyde, and two ammonia molecules) react with each other to form one single compound in a reported yield of 95%. It is ob vious that such a reaction is dictated by the organizing power of the metal ion (I.I. Creasei 1977),... 

A system is at equilibrium when the concentrations of reactants and products remain constant. 

As a system moves from a nonequilibrium to an equilibrium position, AG must change from its initial value to zero. At the same time, the species involved in the reaction undergo a change in their concentrations. The Gibb s free energy, therefore, must be a function of the concentrations of reactants and products. 

The relationship between electrochemical potential and the concentrations of reactants and products can be determined by substituting equation 6.23 into equation 6.3... 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

The rate, or velocity, at which this reaction approaches its equilibrium position can be determined by following the change in concentration of a reactant or a product as a function of time. For example, if we monitor the concentration of reactant A, we express the rate as... 

The Initial Conditions One of two very different strategies are used in kinetic measurements to produce the initial, nonequilibrium concentrations of reactants. Either the separate reagents are mixed or a system previously at equiUbrium is perturbed. Each of these basic strategies has many variations. 

The solution of the simultaneous differential equations implied by the mechanism can be expressed to give the time-varying concentrations of reactants, products, and intermediates in terms of increasing and decreasing exponential functions (8). Expressions for each component become comphcated very rapidly and thus approximations are built in at the level of the differential equations so that these may be treated at various limiting cases. In equations 2222 and 2323, the first reaction may reach equiUbrium for [i] much more rapidly than I is converted to P. This is described as a case of pre-equihbrium. At equihbrium, / y[A][S] = k [I]. Hence,... 

The reaction of dextrose with a nitrogen-containing compound, eg, amino acids or proteins, yields a series of intermediates which form pigments of varied molecular weight (Maikard reaction). The type of pigments produced is dependent on reaction conditions such as pH, temperature, and concentration of reactants. 

Fig. 7. Crack velocity as a function of the applied stress intensity, Kj. Water and other corrosive species reduce the Kj required to propagate a crack at a given velocity. Increasing concentrations of reactant species shifts curve upward. Regions I, II, and III are discussed in text.

A thermal oxidizer is a chemical reactor in which the reaction is activated by heat and is characterized by a specific rate of reactant consumption. There are at least two chemical reactants, an oxidizing agent and a reducing agent. The rate of reaction is related both to the nature and to the concentration of reactants, and to the conditions of activation, ie, the temperature (activation), turbulence (mixing of reactants), and time of interaction. 

At the other extreme, when the ratio ki /mkc is much smaller than unity, the interfacial concentration of reactant A may be approximated by the equihbrium relation Xi = y/m, and the specific absorption rate expression is... 

Kinetic mles of oxidation of MDASA and TPASA by periodate ions in the weak-acidic medium at the presence of mthenium (VI), iridium (IV), rhodium (III) and their mixtures are investigated by spectrophotometric method. The influence of high temperature treatment with mineral acids of catalysts, concentration of reactants, interfering ions, temperature and ionic strength of solutions on the rate of reactions was investigated. Optimal conditions of indicator reactions, rate constants and energy of activation for arylamine oxidation reactions at the presence of individual catalysts are determined. 

Poor distribution Implement appropriate procedures and training of solids or liquid charge. Potential for excessive reaction rates due to localized over-concentrations of reactants. CCPS G-22... 

The basic chemical description of rare events can be written in terms of a set of phenomenological equations of motion for the time dependence of the populations of the reactant and product species [6-9]. Suppose that we are interested in the dynamics of a conformational rearrangement in a small peptide. The concentration of reactant states at time t is N-n(t), and the concentration of product states is N-pU). We assume that we can define the reactants and products as distinct macrostates that are separated by a transition state dividing surface. The transition state surface is typically the location of a significant energy barrier (see Fig. 1). 

Chemical engineering inherited the definition for the reaction rate from chemical kinetics. The definition is for closed systems, like batch reactors, in which most of the classical kinetic studies were done. Inside a batch reactor little else besides chemical reaction can change the concentration of reactant A. In a closed system, for the reaction of... 

The goal of a kinetic study is to establish the quantitative relationship between the concentration of reactants and catalysts and the rate of the reaction. Typically, such a study involves rate measurements at enough different concentrations of each reactant so that the kinetic order with respect to each reactant can be assessed. A complete investigation allows the reaction to be described by a rate law, which is an algebraic expression containing one or more rate constants as well as the concentrations of all reactants that are involved in the rate-determining step and steps prior to the rate-determining step. Each concentration has an exponent, which is the order of the reaction with respect to that component. The overall kinetic order of the reaction is the sum of all the exponents in the... 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

Can hazards from the reaction be reduced by changing the relative concentration of reactants or other operating conditions Can side reactions produce toxic or explosive material, or cause dangerous fouling ... 

Figure 3-9. Overaii order of reaction from a series of haif-iife experiments each at different initiai concentration of reactant.

The graphs of each of the species concentrations are plotted as a function of position along the tube z and time t. At the edges of the graphs for the concentrations of A and B we see the boundary and initial conditions. All values are unit or zero concentration as we had specified. As we move through time, we see the concentrations of both species drop monotonically at any position. Furthermore, if we take anytime slice, we see that the concentrations of reactants drop exponentially with position—as we know they should. At the longer times the profiles of... 

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