Rate Laws Concentration Changes over Time

4 INTEGRATED RATE LAWS CONCENTRATION CHANGES OVER TIME 

Notice that the rate laws we ve developed so far do not include time as a variable. They tell us the rate or concentration at a given instant, allowing us to answer a critical question, How fast is the reaction proceeding at the moment when y moles per liter of A are reacting with z moles per liter of B However, by employing different forms of the rate laws, called integrated rate laws, we can consider the time factor and answer other questions, such as How long will it take for x moles per liter of A to be used up and What is the concentration of A after y minutes of reaction  

Integrated Rate Lows for First-Order, Second-Order, and Zero-Order Reactions 

Setting these different expressions equal to each other gives 

Using calculus, this expression is integrated over time to obtain the integrated rate law for a first-order reaction  

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Integrated Rate Laws Concentration Changes Over Time... 

Integrated rate laws show how the concentration of a particular species changes over time, and they can be useful in deducing empirical rate laws and rate constants when it is difficult to measure initial rates. c( ) = for a first order reaction. 

So far, we have used only instantaneous data in the rate expression. These expressions allow us to answer questions concerning the speed of the reaction at a particular moment, but not questions like about how long it might take to use up a certain reactant. However, if we take into account changes in the concentration of reactants or products over time, as expressed in the integrated rate laws, we can answer these types of questions. 

Kinetics is the study of the speed of reactions. The speed of reaction is affected by the nature of the reactants, the temperature, the concentration of reactants, the physical state of the reactants, and catalysts. A rate law relates the speed of reaction to the reactant concentrations and the orders of reaction. Integrated rate laws relate the rate of reaction to a change in reactant or product concentration over time. We may use the Arrhenius equation to calculate the activation... 

One way to ensure that back reactions are not important is to measure initial rates. The initial rate is the limit of the reaction rate as time reaches zero. With an initial rate method, one plots the concentration of a reactant or product over a short reaction time period during which the concentrations of the reactants change so little that the instantaneous rate is hardly affected. Thus,by measuring initial rates, one can assume that only the forward reaction in Eq. (35) predominates. This would simplify the rate law to that given in Eq. (36) which as written would be a second-order reaction, first-order in reactant A and first-order in reactant B. Equation (35), under these conditions, would represent a second-order irreversible elementary reaction. 

Equation (21) is an excellent approximation to Equation (20) for moderate to high kj/kj ratios ( 10 and higher) for processes that occur by first-order kinetics. It is important to note, however, that a specific rate law does not appear anywhere in Equations (20) and (21), and they are equally valid for any reaction process where Xpejm) is small. Equation (21) illustrates that oxidation of Fe(II)a, to Fe(III)a, produces a markedly different isotopic mass balance than that associated with DIR. In cases where the product of DIR is Fe(II)aq, the concentration of this component is continually increasing, changing the relative mass balance among the exchangeable pools of Fe over time. 

Because we are looking at change in concentration over time, we need the first-order integrated rate law. Equation... 

Catalytic kinetics in the twentieth century were dominated by rate equations.Rate constants, were and are, extracted from rate equations obtained by fitting kinetic data, usually obtained by adjusting the process parameters to enable linearity. A catalytic cycle, however, is a nonlinear dynamic system. Even with a fixed set of paramefers, turn-over limiting states may change with time and extent of fumover. Thus, depending on the portion of the catalytic reaction under study, the rate law may be different. Therefore, can statements as to the kinetic order of the overall catalytic reaction with respect to either substrate(s) consumption or product production obtained by traditional concentration kinetics always be universally assumed to be correct Even if they are, different reaction mechanisms may predict the same overall reaction rate. 

We can now give precise definitions of some words and phrases that are often used loosely. A reaction rate is a rate of change of the concentration of some chemical species at a particular moment it is derived from a set of observations, in which the course of a reaction is monitored over a period of time. Such observations are the basic experimental data. By analysing the relation between these rates and the corresponding concentrations, one obtains a rate law that fits both the data and (often) some standard form (e.g., first-order, in which the rate is proportional to the concentration of one of the reactants). These rate laws, along with known structural data, may be given some interpretation in terms of reaction kinetics, one would describe a scheme of molecular motions that would explain the rate law. Often there are several alternative schemes that would be consistent with a particular set of data further experimentation would then be needed in order to choose between them. Such schemes in terms of chemical kinetics describe events on the microscopic scale, involving atoms and molecules, as distinct from rate laws which are expressed in terms of macromolecular quantities (time and concentration). The schemes may in turn be interpreted in terms of a reaction mechanism, which relates them to chemical dynamics, i.e., to theories of how molecules behave, in terms either of some particular model with limited scope (such as collison theory, or transition-state theory) or of the more fundamental body of theory based upon quantum mechanics. 

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