File Name: determination of the rate of a reaction its order and its activation energy .zip
- Chemical kinetics
- 2.10: Zero-Order Reactions
- Determination of kinetic mechanisms for reactions measured with thermoanalytical instruments
- Determination of kinetic mechanisms for reactions measured with thermoanalytical instruments
A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration.
The work considers the methods and techniques, allowing the assignment of the kinetic mechanisms to the chemical reactions evaluated from signals of thermoanalytical measurements. It describes which information about the kinetic mechanisms can be found from either model-free or model-based methods. The work considers the applicability of both methods and compares their results.
The work considers the methods and techniques, allowing the assignment of the kinetic mechanisms to the chemical reactions evaluated from signals of thermoanalytical measurements. It describes which information about the kinetic mechanisms can be found from either model-free or model-based methods. The work considers the applicability of both methods and compares their results. The multiple-step reactions with well-separated peaks can be equally analyzed by both methods, but for overlapping peaks or for simultaneously running parallel reactions the model-free methods provide irrelevant results.
Methods of kinetic analysis for thermoanalytical measurements depend on the application goal. The purpose of a kinetic analysis can have two directions:. Find the degree of conversion for given temperature conditions, if the chemical mechanism of reaction is unknown and not really important,. Determine and describe the kinetic mechanism if the chemical mechanism of reaction is unknown or partially unknown. The first task is a more technical task and usually could be solved experimentally if the measurement equipment allows to follow the desired temperature conditions.
If the measurements cannot be done exactly according to the temperature conditions, then extrapolation is done by kinetic methods without of the detailed description of the chemical mechanisms of the process. This study deals only with the second task, where the kinetic mechanism must be detected. The thermoanalytical measurements for kinetic analysis must have the measured signal as the function of the time and temperature and must include signal changes caused by the chemical processes in the sample.
There are two approaches to kinetic analysis of thermoanalytical data: model-free analysis and model-based analysis. Both approaches need several thermoanalytical measurements with different temperature conditions. Usually this is a set of measurements with different heating rates or a set of isothermal measurements with different temperatures. We will consider here the set of different heating rates, because it can be analyzed by all model-free methods.
Model-free analysis allows to find activation energy of the reaction process without the assumption of a kinetic model for the process. Usually the knowledge of the reaction type is also not necessary to find the activation energy by model-free methods. The second assumption for model - free analysis : the reaction rate at a constant value of conversion is only a function of temperature [ 1 , 2 ]. In model-free analysis the thermoanalytical signal is equal to the reaction rate 1 , multiplied by the total effect of reaction: total enthalpy for DSC or total mass loss for TG.
There are several different model-free methods including Friedman analysis [ 2 ], Ozawa—Flynn—Wall analysis. They are wide-used for various applications [ 3 — 8 ], but all of them are based on the above described assumptions.
The first assumption for the model - based method : the reaction consists of several elementary reaction steps, and the reaction rate of each step can be described by an own kinetic equation for this step, depending on the concentration of the initial reactant e j , the concentration of product p j , the pre-exponential factor A j and the activation energy E j , specific only for this step with number j [ 9 ].
The number of kinetic equations is equal to the number of the reaction steps, the concentration for each reactant increases by the reaction steps where this reactant is a product, and decreases by reaction steps, where this reactant is a starting substance.
For example, in the model of two consecutive steps the rate of the concentration for the intermediate product c int is calculated as the difference between the reaction rate of the first step and reaction rate of the second step:.
The second assumption for model - based analysis : all kinetic parameters like activation energy, pre-exponential factor, order of reaction, and reaction type are assumed constant during the reaction progress for every individual reaction step. The third assumption for model - based analysis : the thermoanalytical signal is the sum of the signals of the single reaction steps. The effect of each step is calculated as the reaction rate, multiplied by the effect of this step like enthalpy change or mass loss.
For single-step reactions, where the reaction mechanism does not change during the reaction [ 10 ], both, model-free and model-based approaches result in the same kinetic equation with the same kinetic parameters, which are constant or nearly constant during the reaction progress. Single-step reactions are well studied in the literature, and therefore are omitted here.
For complex reactions, where the kinetic mechanism changes during the reaction, there is big difference in interpretation of kinetic results, obtained by different approaches. For model-free approaches, the change of the kinetic mechanism is described by the continuous changing of the activation energy and the pre-exponential factor with the progress of the reaction. For model-based approaches, the change of the kinetic mechanism is described by appearing of several reaction steps with own activation energy and with own reaction type.
The highest interest and complexity lies in the analysis of multi-step processes, because of the ambiguity of applying different approaches and interpretation of results. Usually for reactions with unknown reaction mechanism the number of reaction steps is also unknown.
Sometimes several chemical reactions could be proposed from the chemical point of view, but the kinetic parameters of the reaction steps are unknown. There are first questions which must be answered before a kinetic analysis: how many reaction steps are present in the measured process? How many steps can be analyzed? The answers to the first and second question can be quite different. Processes can chemically have several reaction steps, but corresponding to the thermoanalytical curve, can show only a single peak.
In this case only one step, responsible for this peak, can be analyzed, and only for this peak kinetic parameters can be found correctly. The analysis of these data provides the kinetic parameters like activation energy, pre-exponential factor and reaction order only for the first step, but the area of the DSC peak will have the meaning of the sum of enthalpies of both steps. The kinetic parameters for the first step can be found by both model-free and model-based methods.
But it is impossible to find parameters for the second step from such measured data by any method, because the experimental data do not contain any kinetic information about the second step. The kinetic parameters can be found only for those reaction steps, which are visible on the thermoanalytical curve as peaks or shoulders in DSC curves, or as steps in TG curves.
Kinetic parameters cannot be found from thermoanalytical data for individual steps taking place during a reaction, without showing the corresponding peaks or part of peaks on the thermoanalytical curve. The kinetic model for this process includes several-independent reaction parameters. The most common example is the process in the mixture of several materials, which react independently of each other.
Let us consider the simplest situation, the mixture of two materials, where Peak1 on DSC or DTG curve means the reaction in material1, and Peak2—reaction in material2. By the increasing of the heating rate the peaks are shifted to the higher temperatures, and the shift value is higher for lower activation energy. If the activation energies of two processes are not exactly the same, then by changing of heating rate, the distance between peaks is also changed. We apply here the model-free and model-based analyses to the different data sets for the same process of two independent reactions and compare the results.
Two independent single-step decompositions for the first and second substances for the set of the same heating rates are represented in Fig. It is seen that for lower heating rates the decomposition of the first substance takes place at much lower temperatures than the decomposition of the second substance. But for high heating rates there is another order: decomposition of the second substance happens earlier than that of the first one.
Again, for lower heating rates we have first step before the second step, and for high heating rates the second step is before the first step. In Fig. TGA data set for the mixture of two substances decomposing independently. TGA set for substance1 a and substance2 b. TGA set for a mixture, calculated as the sum of two independent sets a , model-free analysis for this set of data b.
The steps are well-separated for the low and for the high heating rates. Let us analyze separately the set of three curves at low heating rates, the set of three curves at high heating rates, and the total set of curves by the both model-free and model-based methods and then compare the results.
Here the steps are well separated. From model-free analysis, the activation energy for first part of reaction e. Formal concentration of reactants for decomposition of independent substances at the lowest heating rate a ; TGA signal b , and activation energy as the function of conversion from Friedman analysis c for the set of three low heating rates.
The predictions based on model-free results can be done only for much lower heating rates, where the steps remain well separated. For heating rates higher than the ones presented in this figure, the steps are overlapped and model-free prediction cannot be used because it cannot show the independent character of the steps.
It is impossible to get the curves shown in Fig. Formal concentration of reactants for decomposition of independent substances at the highest heating rate a ; TGA signal b , and activation energy as the function of conversion from Friedman analysis c for the set of three high heating rates. The steps are still slightly overlapping, but for very high heating rates the overlapping disappears and peaks will be well separated. The model-based analysis of the two independent steps provides the same results as for the set of low heating rates.
The results of model-free analysis are now not the same as the results for the set of low heating rates. Now the predictions based on model-free results can be done only for very high heating rates, where the steps are well separated. But for lower heating rates there is the overlapping of steps and model-free predictions cannot get a result showing the independent character of steps. The steps are separated only for low and high heating rates, but overlapped for the middle heating rates.
But the model-based analysis based on two independent steps provides here the same results as for the two previous sets of data. The comparison of the model-free results for the process with independent steps indicates different dependencies of the activation energy on the degree of conversion for the set of high heating rates, for the set of low heating rates and for the complete set of data.
It means that the model-free result for overlapping independent steps depends on the heating rate and on the number of measured curves. But this fact is in conflict with the above mentioned second assumption of the model-free analysis, where the reaction rate at a constant conversion must be only a function of temperature.
If this assumption of the model-free analysis cannot be fulfilled, then the model-free analysis may not be used for the situation with overlapping independent steps. The reason for the different model-free results for the range of overlapping peaks can be found by the detailed consideration of applying this analysis to the total data set.
Three sets of data, a set with low heating rates, a set with high heating rates and a complete set of data were analyzed by model-free and by model-based analysis. The model-based results are the same for all three sets. The model-free results are different for all three sets. Model-free analysis Friedman analysis for the process of two independent steps is represented in Fig. The method calculates the activation energy as the slope of the straight line drawn through the points with the same conversion value.
In the plot, the curves with high heating rates are higher than the curves with the low heating rates. Each of two peaks on each curve corresponds to a reaction step. Iso-conversional lines are drawn separately for each step. It is seen that the independent steps go through each other. For low heating rates Step1 appears before Step2 graphic must be read from right to left because of the reciprocal temperature , and for high heating rate Step1 appears after Step2.
Stars mark the points with the same conversion value of 0. It is clearly seen that the stars with low heating rates belong to the Step2, and are placed on the straight line with slope, corresponding to Step2.
The stars with high heating rates belong to Step1 and are placed on the straight line with slope corresponding to Step1. Here the peaks go independently through each other. This fact could be used as the indicator of independent reaction steps. The dashed line represents the attempt to use the standard model-free analysis for the complete data set, where iso-conversion line must be drawn through all points with the same conversion value marked with stars.
But the points belong to different reactions and therefore are not placed on one line. By using linear regression, a straight dashed line results, which is far from the marked points stars , especially for the highest and for the lowest heating rates.
2.10: Zero-Order Reactions
Chemical kinetics , also known as reaction kinetics , is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with thermodynamics, which deals with the direction in which a process occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states , as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. In , Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action , which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances. Relatively simple rate laws exist for zero order reactions for which reaction rates are independent of concentration , first order reactions , and second order reactions , and can be derived for others. Elementary reactions follow the law of mass action , but the rate law of stepwise reactions has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, the rate-determining step often determines the kinetics.
Many chemical reactions, and almost all biochemical reactions do not occur spontaneously and must have an initial input of energy called the activation energy to get started. Activation energy must be considered when analyzing both endergonic and exergonic reactions. Exergonic reactions have a net release of energy, but they still require a small amount of energy input before they can proceed with their energy-releasing steps. This small amount of energy input necessary for all chemical reactions to occur is called the activation energy or free energy of activation and is abbreviated E A. Activation energy : Activation energy is the energy required for a reaction to proceed; it is lower if the reaction is catalyzed. The horizontal axis of this diagram describes the sequence of events in time. The reason lies in the steps that take place during a chemical reaction.
Reaction Rate: The change in the concentration of a reactant or a Determining Reaction Order: The Method of Initial Rates. 2NO(g) + 2H2(g) half its original value. o. [A]. [A]. 2 The Activation energy, Ea, is the minimum energy required to.
Determination of kinetic mechanisms for reactions measured with thermoanalytical instruments
In some reactions, the rate is apparently independent of the reactant concentration. The rates of these zero-order reactions do not vary with increasing nor decreasing reactants concentrations. This property differs from both first-order reactions and second-order reactions.
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time.
Determination of kinetic mechanisms for reactions measured with thermoanalytical instruments
Chemical Kinetics and Transport pp Cite as. Altering the constraints on a chemical system poses two distinct questions. What is the new equilibrium configuration? How rapidly does the system approach this new state? The first is a problem of applied thermodynamics; the second is the central problem of chemical kinetics.
State two quantities that must be measured to establish the rate of a chemical reaction and cite several factors that affect the rate of a chemical reaction. The rate of a reaction is defined as the change in concentration as a function of time. Thus, the two quantities that must be measured are the molarity of either a reactant or product and the time. The factors that affect a reaction rate include the temperature, the concentration of reactants, the surface area if solids are involved in the reaction, and the presence or absence of a catalyst. This means that the rate of consumption of NO is twice as fast as the rate of production of N 2. What plot of experimental data can be used to evaluate the activation energy, E a , of a reaction?