The Change of Concentration with Time

7 Key excerpts on "The Change of Concentration with Time"

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  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  The dependence of the reaction rate on the concentration of each reactant can be found experimentally. The data is generated by measuring changes in reactant concentration as a function of time.

  Reaction rates are rates of concentration changes (concentration changes per unit time). Changes in a concentration of any specific reactant may or may not affect how fast the reaction occurs.

  Mathematical analysis of f{concentrations} vs. time can provide the exponent (order) for each reactant (the order may be zero, equivalent to no relationship) and a calculation for the rate constant, k.

  ZERO -ORDER REACTANTS

  The simplest case, possible for multistep reactions, is a rate that is independent of a specific reactant concentration. This does not mean that the reactant is unused, just that the specific molecule being analyzed has no role in the reaction steps that affect the rate of the overall (i.e. complete) reaction.

  The rate of the reaction is independent of [A]; the reaction rate expression for this specific reactant for any reaction would be:

  rate (r) = k [A]0

  This is equivalent to rate (r) = rate constant × 1 or rate (r) = k.

  (Any number to the zero power = 1.) The reaction is said to be zero order in this component and the rate remains constant with changing concentration of [A].

  Using the general letter A for any specific reactant, the plot of [A] vs. t (time) would be a straight line with a single (constant) slope. ([A] means “concentration of A”)

  Do not confuse rate with concentration. The concentration of “A” changes continuously with time, but the rate of change of the concentration remains the same (constant slope). The number of molecules of “A” consumed by reaction per unit time does not change as the concentration of “A” decreases.

  A kinetic analysis that yields a straight-line plot of reactant concentration vs. time ([reactant] vs. t), specifically characterizes that reactant as being zero order

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  Foundations for Nanoscience and Nanotechnology

  • Nils O. Petersen(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  This is possible in many systems and is the classical way to measure transport phenomena. We shall see later that it is also possible to measure the rates of diffusion or flow of molecules by measuring fluctuations of numbers of molecules in small volumes. 13.1.2 Reaction kinetics Chemical reactions will change the concentrations of the species involved in the reaction until an equilibrium is reached, but even at equilibrium, the concentrations will fluctuate. Recall that we describe reactions in terms of the order of reactions, which reflects the number of species involved in the rate limiting step of the reaction. We are generally interested in measuring the rate of a chemical reaction because it can be a clue to the mechanism of the reaction. In order to measure the rate, we would initiate the reaction with only the reactant(s) present and then measure its (their) disappearance or the appearance of the product(s). First order kinetics For a first order reaction A → k 1 B 1 the rate of disappearance of the reactant is (13.13) - d [ A ] d t = k 1 [ A ], which leads to (13.14) [ A ] = [ A ] 0 e - k 1 t, where [ A ] 0 is the initial concentration of the reactant. Correspondingly, the rate of appearance of the product (see problems assignment). is (13.15) [ B ] = [ A ] 0 ((1 - e - k 1 t). When the reaction is reversible, the reverse reaction B → k 2 A will become important as the product concentration increases and the reactant concentration decreases. At some point in time, the concentrations reach the equilibrium concentrations where the rate of the forward reaction equals that of the reverse reaction, and hence (13.16) - d [ A ] d t = k 1 [ A ] e q = d [ B ] d t = k 2 [ B ] e q, which tells us that the equilibrium constant K = [ B ] e q [ A ] e q = k 1 k 2. Parallel first order kinetics We shall later encounter parallel first order reactions, in which a single reactant can yield two or more products: A → k B B and A → k C C

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  Introduction to Chemical Engineering Kinetics and Reactor Design

  • Charles G. Hill, Thatcher W. Root(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  A may be determined), it is possible to use equation (3.1.47) or (3.1.50) to determine the fraction conversion of the limiting reagent at this time. Equation (3.1.51) may then be used to determine the reaction rate corresponding to this conversion:

  3.1.51

  Thus, for both variable and constant volume batch reactors, one can manipulate concentration versus time data to obtain values of the reaction rate as a function of time or as a function of the concentrations of the various species present in the reaction mixture. The task then becomes one of fitting these data to a reaction rate expression of the form of equation (3.0.13).

  Since data are almost invariably taken under isothermal conditions to eliminate the temperature dependence of reaction rate constants, one is concerned primarily with determining the concentration dependence of the rate expression φ(C

  i

  ) and the rate constant at the temperature in question. Next we consider two differential methods that can be used in the analysis of rate data.

  3.3.1.1 Differentiation of Data Obtained in the Course of a Single Experimental Run

  If one has experimental results in the form of concentration versus time data, the following general differential procedure may be used to determine φ(C

  i

  ) and the rate constant at the temperature in question:

  1. Set forth a hypothesis as to the form of the concentration dependent portion of the rate function, φ(C
     i
     ).
  2. From the experimental concentration versus time data, determine reaction rates corresponding to various times.
  3. At the selected times, prepare a table listing the reaction rate and the concentrations of the various species present in the reaction mixture. Calculate φ(C
     i
     ) at each of these points.
  4. Prepare a plot of the reaction rate versus φ(C
     i
     ). If the plot is linear and passes through the origin, the form of φ(C
     i

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  Molecular Kinetics in Condensed Phases

  Theory, Simulation, and Analysis

  • Ron Elber, Dmitrii E. Makarov, Henri Orland(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  8 The Rate of Conformational Change: Definition and Computation

  8.1 First‐order Chemical Kinetics

  Chemistry studies how molecules interconvert between their different forms. The description of this process usually takes the form of phenomenological rate equations describing the time evolution of concentrations (or populations) of chemical species, which is determined by rate coefficients (also referred to as “rate constants” or even simply “rates”). Such coefficients have already been introduced here: Section 4.1 introduced rate matrices, whose elements describe interconversion rates between pairs of discrete states, and Section 6.2 discussed the escape rate from a metastable state. Because the concept of rate is cental to chemical kinetics, this Chapter discusses how to define the rate precisely, how to relate the rate to the underlying microscopic dynamics, and how to compute the rate efficiently, both exactly and with simple approximations.

  Consider the simple example of chair‐boat isomerization (Figure. 8.1 ), where the chemical identity of the molecule remains unchanged, but the geometry is altered. Chemists describe this reaction by the following scheme:

  (8.1)

  Figure 8.1 Chair‐boat isomerization as an example of a reversible unimolecular reaction.

  Many other examples described by Eq. (8.1 ) exist, both in chemistry and outside it. Importantly, unless A and B denote specific quantum states of the same molecule, they do not provide precise information about its state. In some cases (such as in Figure. 8.1 ), the molecular forms A and B describe specific molecular geometries, to within relatively small fluctuations caused by thermal motion or quantum effects. But in other cases, A and B may represent ensembles involving diverse structures. For example, when the scheme of Eq. (8.1

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  College Chemistry

  • Steven Boone, Drew H. Wolfe(Authors)
  • 2011(Publication Date)
  • Collins Reference

    (Publisher)

  CHAPTER 14

  Rates of Chemical Reactions

  C hemical kinetics , also called reaction kinetics , is the study of the rates of chemical reactions and the underlying mechanisms by which reactants change to products. An important outcome for studying the rates of chemical reactions is to develop an understanding of how chemical reactions take place. Chemists attempt to identify the molecular events that occur as reactants change to products. The series of steps that take place in a reaction is termed the reaction mechanism .

  14.1 RATES OF CHEMICAL REACTIONS

  The enthalpy and entropy change in a chemical reaction is used to predict the spontaneity of the reaction (see Chapter 18), however, it provides no information regarding how long the reaction will take to reach completion, which is kinetics.

  Reaction Rates

  A rate refers to a change that occurs over a time interval. Chemical reaction rates may be monitored by measuring the change in concentration or pressure of a reactant or product over a time interval. Recall that the Greek letter delta, Δ, is used to represent a change. Therefore, this expression may be represented as follows.

  Exercise 14.1

  Consider the rate of the gas-phase reaction when nitrosyl fluoride, ONF, forms from F2 and NO.

  F2 (g) + 2NO(g) → 2ONF(g)

  (a) Write an expression that shows the rate of formation of ONF. (b) What are the units of reaction rate? (c) Write an expression that shows the rate of disappearance of NO. (d) Write an expression that shows the relationship between the rate of formation of ONF and rate of disappearance of NO. (e) Write an expression that shows the relationship between the rates of disappearance of F2

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  Principles of Water Treatment

  • Kerry J. Howe, David W. Hand, John C. Crittenden, R. Rhodes Trussell, George Tchobanoglous(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Chemical kinetics is the study of the rate at which chemical reactions take place, that is, the speed at which reactants are consumed and products are formed. The rate is not constant but normally depends on the chemical activity of the reacting species. Generally, the higher the concentration (and, therefore, the activity) of the reacting species, the faster the reaction will occur. Mechanistically, the reason for this trend is that reactions result from the collision of molecules; the more molecules present, the more often they come in contact with each other and the faster the reaction proceeds.

  The rate of a reaction is expressed as the amount of reactants consumed or products generated by the reaction per unit of volume and per unit time. In equation form, this can be expressed as

  4.25

  where

  rA = reaction rate, mol/L·s

  n = amount of reactant consumed or product generated, mol

  V = volume of reactor, L

  t = time, s

  The reaction rate will have a negative value for reactants that are being consumed and a positive value for products that are being generated.

  Reaction rates are often expressed as a change in concentration over time, but the concentration of species depends on other factors in a reactor. In a reactor with no inputs, outputs, or other reactions, the rate of a reaction will indeed be equal to the change in concentration over time, that is, rA  = dC/dt. In other systems, reactants continually enter a reactor and a reaction consumes them at the same rate that they are entering; thus the concentration of reactants in the reactor is constant even though a reaction is taking place. These and other types of reactors will be introduced later in this chapter.

  Rate Equations and Reaction Order

  The dependence of reaction rates on the activity of the chemical species present leads to the development of rate equations to describe the relationship between the reacting species and the reaction rate. The simplest form is for that of an irreversible elementary reaction. An elementary reaction is a reaction in which the species react directly to form products in a single reaction step and with a single transition state. In this case, the collision of reactant molecules leads directly to the formation of product molecules. The kinetics of such a reaction are such that the rate will be directly proportional to the activity of each reactant participating in the reaction. A general reaction for an irreversible elementary reaction can be written as

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  Water Quality Engineering

  Physical / Chemical Treatment Processes

  • Mark M. Benjamin, Desmond F. Lawler(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Once the dependence of the reaction rate on reactant concentrations is established, the effects of other factors on the reaction rates might be explored. The most important of these factors is usually temperature. The rest of this chapter describes approaches for carrying out each of the analytical components described earlier. The discussion is presented in four sections. The first three sections focus on the effects of concentration on reaction progress for irreversible, reversible, and sequential reactions, respectively; the final section then focuses on the effects of temperature on reaction rates.

  The Mass Balance for Batch Reactors with Irreversible Reactions

  Generally, the information available for analysis of a rate expression includes the stoichiometry of the overall reaction and some experimental data describing the concentration versus time profiles for one or more species that participate in the reaction. The experiments used to generate the data may be conducted in any type of reactor. However, the simplest and most common approach is to characterize the rate at which the substances of interest are generated or destroyed in a well-mixed, batch (no flow) reactor. The analysis of such a reactor involves writing one or more mass balances in which the control volume includes all the fluid in the system, such as the following.

  Since there is no flow into or out of the reactor, the advective term is zero, and since the aqueous phase ends at the boundaries of the control volume, the diffusive term is zero as well. Applying these ideas and dividing through by V , the mass balance can be simplified to the following expression:

  (3-14)

  where .10

  The overall reaction rate, r i , has dimensions of mass per volume per time and may be either positive (if the reaction forms the substance under consideration) or negative (if the reaction destroys it). Unfortunately, the simplicity of Equation 3-14 leads to a common error whereby the term dc i /dt is substituted for the reaction rate (r i

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