Determining Rate Constant

12 Key excerpts on "Determining Rate Constant"

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  Engineering Chemistry

  Fundamentals and Applications

  • Shikha Agarwal(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  Characteristics of rate constant 1. Rate constant is a measure of the reaction rate. Larger the value of k, faster is the reaction. Similarly, smaller value of k indicates slow reaction. 2. At a particular temperature, the rate constant of a particular reaction is fixed. Rate constant varies with the temperature of the reaction. 3. For a specific reaction, the rate constant does not depend on the concentration of the reacting species. Table 11.1 Difference between rate of reaction and rate constant Rate of reaction Rate constant 1. It measures speed of the reaction and can be defined as the rate of change of concentration of either reactants or products with time. 2. Initial concentration of the reactants affects the rate of the reaction 3. Its units are moles/litre/time Rate constant is equal to the rate of the reaction when the concentration of each of the reactants is unity. It is independent of the initial concentration of the reactants The units of rate constant depend on the order of the reaction 536 Engineering Chemistry: Fundamentals and Applications Units of rate constant Consider a general reaction aA + bB+ ………… → Products. Rate of reaction, dx/dt = k[A] a [B] b (1) Unit of rate of reaction = moles/L/sec (2) and [A] and [B] are moles/L (3) Substituting (2) and (3) in (1), we get 1 moles moles moles sec litre litre litre a b k −     × = × ×…         or ( ) ( ) 1 1 moles sec litre a b k − + +… −     = ×           ( ) ( ) 1 ( .....) 1 1 moles litre sec a b − + + − − = × ( ) ( ) ( ) 1 1 1 moles litres sec n n − − − = (4) (a + b + … = n) n = order of the reaction 11.6 Factors Influencing Reaction Rate The principal factors affecting the rate of the reactions are as follows: 1. Concentration of reactants 2. Nature of reactants and products 3. Temperature 4. Catalyst 5. Surface area 6. Effect of radiations 1. Concentration of reactants Rate of reaction is directly proportional to the concentration of the reactants at a particular time.

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  Laboratory Manual for Principles of General Chemistry

  • J. A. Beran, Mark Lassiter(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  In Parts A–D of this experiment, the rate law for a reaction is determined by mea- suring how reaction rates change with changes in reactant concentrations at room tem- perature. In Part E, the reaction rate is determined at different temperatures, allowing us to use the data to calculate the activation energy for the reaction. To assist in understanding the relationship between reactant concentration and re- action rate, consider the general reaction, A 2 + 2 B 2 → 2 AB 2 . The rate of this reaction is related, by some exponential power, to the initial concentration of each reactant. For this reaction, we can write the relationship as rate = k [A 2 ] p [B 2 ] q (15.1) This expression is called the rate law for the reaction. The value of k, the reaction rate constant, varies with temperature but is independent of reactant concentrations. The superscripts p and q designate the order with respect to each reactant and are always determined experimentally. For example, if tripling the molar concentration of A 2 while holding the B 2 concentration constant increases the reaction rate by a fac- tor of 9, then p = 2. In practice, when the B 2 concentration is in large excess relative to the A 2 concentration, the B 2 concentration remains essentially constant during the course of the reaction; therefore, the change in the reaction rate results from the more significant change in the smaller amount of A 2 in the reaction. An experimental study of the kinetics of any reaction involves determining the values of k, p, and q. Rate constant: a proportionality constant relating the rate of a reaction to the initial concentrations of the reactants Order: the exponential factor by which the concentration of a substance affects reaction rate Figure 15.1 The rate of thermal decomposition of calcium carbonate is determined by measuring the volume of evolved carbon dioxide gas versus time.

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  Experimental Methods in Kinetic Studies

  • Bohdan Wojciechowski, Norman Rice(Authors)
  • 2003(Publication Date)
  • Elsevier Science

    (Publisher)

  41 3. Using Kinetic Data in Reaction Studies Uninterpreted data is a neglected gem. Uncut and unpolished by the expertise of a craftsman, it is nothing but a stone devoid of bnlliance or significance. The Rate Expression The rate of a reaction is governed by reactant concentrations and by physical parameters such as pressure and temperature, but how it is governed by these conditions depends on the mechanism of the reaction. It is the mechanism that lies behind the kinetic rate ex- pression. Understanding the mechanism and its rate expression allows us to engineer the reaction by influencing elementary steps in the overall conversion process. We note from the beginning that the mechanism of a reaction does not usually change with reaction conditions; it is a fundamental property ofthe reaction. This is also true for catalytic reactions on a homologous series of catalysts at similar reaction condi- tions. In a given setting, the rates of the elementary steps of a mechanism depend solely on the concentrations of the reactants (and active sites in the case of a catalyst) and the reaction temperature. Of these, temperature affects the rate parameters only. The behav- iour of these is well understood from thermodynamic considerations and well described by the Arrhenius equation containing: 9 a pre-exponential, temperature-independent term A, multiplied by 9 an exponential term containing an energy term E. This dependence is so important that we will examine it more closely later. The concentration dependence of the rate expression has a more varied effect on the behaviour of the kinetics since it dictates the algebraic form of the rate expression. Identification of a rate expression that fits the experimental rate data and agrees with a plausible reaction mechanism for the reaction requires an extensive experimental inves- tigation of reaction rates, and much thought.

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  General Chemistry

  • Linus Pauling(Author)
  • 2014(Publication Date)
  • Dover Publications

    (Publisher)

  thermostat, which is held at a fixed temperature. The quantitative theory of reaction rate, discussed below, has special interest because of its relation to the theory of chemical equilibrium, which is treated in the following chapter.

  16-2. The Rate of a First-order Reaction at Constant Temperature

  If a molecule, which we represent by the general symbol A, has a tendency to decompose spontaneously into smaller molecules

  at a rate that is not influenced by the presence of other molecules, we expect that the number of molecules that decompose by such a unimolecular process in unit time will be proportional to the number present. If the volume of the system remains constant, the concentration of A will decrease at a rate proportional to this concentration. The symbol [A] represents the concentration of A (in moles per liter). The rate of decrease in concentration with time is—d [A]/dt. For a unimolecular decomposition we accordingly may write the equation

  as the differential equation determining the rate of the reaction. The factor k is called the first-order rate constant. A reaction of this kind is called a first-order reaction ; the order of a reaction is the sum of the powers of the concentration factors in the rate expression (on the right side of the rate equation).

       For example, the rate constant k may have the value 0.001, with the time t measured in seconds. The equation would then state that during each second 1/1000 of the molecules present would decompose. Suppose that at the time t = 0 there were 1,000,000,000 molecules per milliliter in the reaction vessel. During the first second 0.1% of these molecules would decompose, and there would remain at t = 1 second only 999,000,000 molecules undecomposed. During the next second 999,000 molecules would decompose, and there would remain 998,001,000 molecules.*

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  An Introduction to Chemical Metallurgy

  International Series on Materials Science and Technology

  • R. H. Parker, D. W. Hopkins(Authors)
  • 2016(Publication Date)
  • Pergamon

    (Publisher)

  Rates vary between the extremes of the almost instantaneous neutralization of a strong acid by a strong base, and the virtually undetectable combustion of a gaseous fuel in air at room temperature, and the subject of chemical kinetics includes the study of the influence of 121 122 AN INTRODUCTION TO CHEMICAL METALLURGY variables such as temperature and concentration on reaction rates. It would be fair to say that experimental work on the kin-etics of reaction —particularly in metallurgical processes —lags far behind that on thermodynamics, but it must be remembered that the experimental difficulties are much more formidable in the former field than in the latter. Methods used to follow the rate of a reaction involve the determination of the amount of reactants remaining or products present after a given time. If possible, the method of measure-ment used should be applied continuously without involving a delay in the process or in the measurement, and, in this respect, physical methods (such as a continuous measurement of the conductance of an electrolyte) are to be preferred to chemical methods which involve the removal of samples for analysis. Techniques of continuous analysis of metal and slag in steel-making processes by electrochemical methods, which are in the experimental stage, could make available a much more comprehensive volume of data on rates of reactions in these processes than has hitherto been produced. Continuous tem-perature measurement will also be necessary as temperature influences reaction rates considerably, and it is encouraging to hear that techniques of continuous pyrometry are being de-veloped at the same time as continuous analysis for reactions in liquid phases at temperatures as high as 1600°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)

  In addition to spectrophotometric or spectroscopic measurements, there are a number of other optical measurements that can be used to monitor the course of various reactions. Among the optical properties that can be used for these studies are optical rotation, refractive indices, fluorescence, and colorimetry. There also are several electrical measurements that may be used for analysis of solutions under in situ conditions. Among the properties that may be measured are dielectric constants, electrical conductivity or resistivity, and the redox potential of solutions. These properties are easily measured with instrumentation that is readily interfaced to a computer for data acquisition and manipulation for analysis. However, most of these techniques should be used only after careful calibration and do not give better than 1% accuracy without unusual care in the experimental work.

  3.3 Techniques for the Interpretation of Kinetic Data

  In Section 3.1 the mathematical expressions that result from integration of various reaction rate functions were discussed in some detail. Our present problem is the converse of that considered earlier (i.e., given data on the concentration of a reactant or product as a function of time, how does one proceed to determine the reaction rate expression?).

  Determination of the rate expression normally involves a two-step procedure. First, the concentration dependence is determined at a fixed temperature. Then the temperature dependence of the rate constants is evaluated to obtain a complete reaction rate expression. The form of this temperature dependence is given by equation (3.0.14), so our present problem reduces to that of determining the form of the concentration dependence and the value of the rate constant at the temperature of the experiment.

  Unfortunately, there is no completely general method of determining the reaction rate expression or even of determining the order of a reaction. Usually, one employs an iterative trial-and-error procedure based on intelligent guesses and past experience with similar systems. Very often the stoichiometry of the reaction and knowledge of whether the reaction is “reversible” or “irreversible” will suggest a form of the rate equation to try first. If this initial guess (hypothesis) is incorrect, the investigator may then try other forms that are suggested either by assumptions about the mechanism of the reaction or by the nature of the discrepancies between the data and the mathematical model employed in a previous trial. Each reaction presents a unique problem, and success in fitting a reaction rate expression to the experimental data depends on the ingenuity of the individual investigator.

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  Physical Chemistry for Engineering and Applied Sciences

  • Frank R. Foulkes(Author)
  • 2012(Publication Date)
  • CRC Press

    (Publisher)

  . . [4] Example 26-1 The rate of the reaction A + 2B A 3C + D was reported as 2.0 mol L –1 s –1 . State the rates of consumption or formation of each participant. 3 The introductory treatment of chemical kinetics given in this chapter deals mainly with constant volume batch processes in closed systems. CHEMICAL REACTION KINETICS 26-3 Solution The rate of the reaction is r = < 1 1 d[A] dt = < 1 2 d[B] dt = + 1 3 d[C] dt = + 1 1 d[D] dt = 2.0 mol L –1 s –1 For species A : r = < 1 1 d[A] dt ; therefore d dt [ ] A = – r = – 2.0 mol L –1 s –1 [ Ans .] For species B : r = < 1 2 d dt [ ] B ; therefore d dt [ ] B = – 2r = – 4.0 mol L –1 s –1 [ Ans .] For species C : r = + 1 3 d dt [ ] C ; therefore d dt [ ] C = + 3r = + 6.0 mol L –1 s –1 [ Ans .] For species D : r = + 1 1 d[D] dt ; therefore d dt [ ] D = + r = + 2.0 mol L –1 s –1 [ Ans .] 26.4 DIFFERENTIAL RATE LAWS It is usually possible to express the rate of a chemical reaction as a product of the reactant concentrations, each raised to some power: For example, for 3A + 2B A C + D we can put r = < 1 3 d dt [ ] A = < 1 2 d dt [ ] B = d dt [ ] C = d dt [ ] D = k [A] [B] m n where m and n are generally integers or half-integers. We say that m is the order of the reaction with respect to A , and n is the order of the reaction with respect to B . The overall order of the reaction is (m + n) . m and n must be determined experimentally ; they are sometimes––but not always––equal to the stoichiometric coefficients. Thus, for H 2 + I 2 A 2HI r = < d H dt [ ] 2 = k H I [ ][ ] 2 2 but for H 2 + Br 2 A 2HBr r = < d H dt [ ] 2 = v k [H ][Br ] 2 2 1/2 k and v k are called the rate constants for the reactions, and indicate whether the reactions are fast or slow. The greater the rate constant, the faster the reaction. Like the equilibrium constant, the rate constant is a function of temperature, but not of concentration.

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  This is rather like the situation in a crowded supermarket with only a single checkout lane open. It doesn’t matter how many people join the line; the line will move at the same rate no matter how many people are standing in it. An example of a zero- order chemical reaction is the elimination of ethyl alcohol in the body, by the liver. Regardless of the blood alcohol level, the rate of alcohol removal by the body is constant, because the number of available catalyst molecules present in the liver is constant. Another zero-order reaction is the decomposition of gaseous ammonia into H 2 and N 2 on a hot platinum surface. The rate at which ammonia decomposes is the same, regardless of its concentration in the gas. The rate law for a zero-order reaction is simply rate = k where the rate constant k has units of mol L −1 s −1 . The rate constant depends on the amount, quality, and available surface area of the catalyst. For example, forcing the ammonia through hot platinum powder (with a high surface area) would cause it to decompose faster than simply passing it over a hot platinum surface. In all of the rate laws, the rate constant, k, indicates how fast a reac- tion proceeds. If the value for k is large, the reaction proceeds rapidly, and if k is small, the reaction is slow. The units for k must be such that the rate calculated from the rate law has units of mol L −1 s −1 . A list of units for k, as it depends on the overall order of the reaction, is given in Table 13.2. NOTE When an exponent in an equation is found to be 1, it is usually omitted. 1 The reason for describing the order of a reaction is to take advantage of a great convenience—namely, the mathematics involved in the treatment of the data is the same for all reactions having the same order. We will not go into this very deeply, but you should be familiar with this terminology; it’s often used to describe the effects of concentration on reaction rates.

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  Chemistry

  The Molecular Nature of Matter

  • James E. Brady, Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Experiments yielded the following results: Initial Concentrations (mol L -1 ) Initial Rate of Formation of C (mol L -1 s -1 ) [A] [B] 0.40 0.30 1.00 Ž 10 -4 0.60 0.30 2.25 Ž 10 -4 0.80 0.60 1.60 Ž 10 -3 (a) What is the rate law for the reaction? (b) What is the value of the rate constant? (c) What are the units for the rate constant? (d) What is the overall order of this reaction? (Hint: Solve for the exponent of [A], then use it to solve for the exponent of [B].) 13.4 | Integrated Rate Laws The rate law tells us how the speed of a reaction varies with the concentrations of the reac- tants. Often, however, we are more interested in how the concentrations change over time. For instance, if we were preparing some compound, we might want to know how long it will take for the reactant concentrations to drop to some particular value, so we can decide when to isolate the products. The relationship between the concentration of a reactant and time can be derived from a rate law using calculus. By summing or “integrating” the instantaneous rates of a reaction from the start of the reaction until some specified time, t, we can obtain integrated rate laws that quantitatively give concentration as a function of time. The form of the integrated rate law depends on the order of the reaction. The mathematical expressions that relate concentra- tion and time in complex reactions can be complicated, so we will concentrate on using integrated rate laws for a few simple first- and second-order reactions with only one reactant. First-Order Reactions A first-order reaction is a reaction that has a rate law of the type rate = k 3 A 4 Practice Exercise 13.13 Practice Exercise 13.14 644 Chapter 13 | Chemical Kinetics Using calculus, 2 the following equation can be derived that relates the concentration of A and time: ln 3 A 4 0 3 A 4 t = kt (13.5) The symbol “ln” means natural logarithm.

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  Physical Chemistry and Its Biological Applications

  • Wallace Brey(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  There is an equilibrium between normal and activated molecules, the latter denoted by A*: A ^ A* (10-95) An equilibrium constant is defined by the equation K = [A*]/[A], from which the concentration of activated molecules is equal to K multi-plied by the concentration of normal molecules, or K[A]. The rate of reaction is proportional to the concentration of activated molecules, 10-7 TRANSITION-STATE THEORY 359 with a constant of proportionality k ' which is independent of tem-perature: rate = k'[A*] = k'K[A] (10-96) Since the fraction of molecules in the activated form at any one time is very small, the concentration of normal molecules is the same as the bulk concentration of the reactant. From Equation (10-96), we can write k = k'K (10-97) Differentiation of the logarithmic form of this equation with respect to temperature yields d i n k d i n k ' d In K -mr = -ir + -w-<10 -98) The first term on the right is zero, since all the temperature dependence of the rate constant is carried by the equilibrium constant K. The usual equation relating the temperature variation of the equilibrium con-stant to the energy change for the process in question can be substi-tuted for the second term on the right side of the equation: d i n k d l n K A E a — = — = ^ (10-99) dT dT RT 2 J It is well to point out that, if A E a is understood to be a change in inter-nal energy, this equation should strictly speaking contain an equilib-rium constant K c for molar concentrations. If the rate and equilibrium constants are given in terms of pressures, then it is the enthalpy of activation AH a that should determine the temperature dependence of the rate constant. However, in practice the difference between A E a and AH a is at or below the limits of accuracy of most kinetic experiments, and so the quantity is often simply called energy of activation whether it is an enthalpy or an internal energy quantity.

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  Chemistry, 5th Edition

  • Allan Blackman, Steven E. Bottle, Siegbert Schmid, Mauro Mocerino, Uta Wille(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  (c) Which step is the rate-determining step? Explain. 15.124 Which of the five factors that affect the rate of a reaction is illustrated in each of the following? LO2 (a) Food is sometimes frozen before it is used. (b) Small sticks of wood are often used to start a fire. (c) In hospitals, the speed of the healing process is often increased in an oxygen tent. 15.125 Why would you expect the rate of the reaction: LO2 Ag + (aq) + Br − (aq) → AgBr(s) at room temperature to be much faster than the rate of the reaction: CH 4 (g) + 2O 2 (g) → CO 2 (g) + 2H 2 O(l) at room temperature? 15.126 Consider the reaction Zn(s) + 2HCl(aq) → ZnCl 2 (aq) + H 2 (g). What would be the effect on the rate of reaction if each of the following was done? LO6 (a) powdered zinc was used instead of a solid piece of zinc metal (b) the concentration of HCl(aq) was halved (c) the temperature was lowered Pdf_Folio:794 794 Chemistry MATHS FOR CHEMISTRY In chemistry, we often study particular aspects of a chemical reaction over a period of time, or as we change the temperature. For example, we might be interested in how the concentration of a reactant in a chemical reaction changes with time, or how the rate of a chemical reaction changes as the temperature is increased. One of the best ways of displaying trends in these data is to plot them on a graph. Generally, we do this in two dimensions, by plotting a graph of y (called the dependent variable) versus x (called the independent variable). Consider the following set of (x,y) data. (0, 2), (1, 4), (2, 6), (3, 8), (4, 10), (5, 12), (6, 14), (7, 16), (8, 18), (9, 20), (10, 22) Plotting these on an (x,y) graph gives the following. y-axis x-axis 0 0 2 4 6 8 10 12 5 10 15 20 25 It is immediately obvious that a straight line can be drawn through the data points, and we say that there is therefore a linear relationship between x and y.

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  Engineering Chemistry

  Fundamentals and Applications

  • Shikha Agarwal(Author)
  • 2019(Publication Date)
  • Cambridge University Press

    (Publisher)

  13.13 Variation of Reaction Rates with Temperature – Arrhenius Equation The rate of a chemical reaction increases with the rise in temperature and it has been found that it becomes almost double for every 10 °C rise in temperature. This is known as the temperature coefficient, which may be defined as the ratio of rate constants of the reaction at two temperatures differing by 10 °C. Thus, Temperature coefficient = Rate constant ( 10 C) Rate constant at C T T + ° ° Figure 13.8 Variation of reaction rate with temperature The curve shows that at higher temperature the curve is shifted towards the right indicating that at higher temperatures the molecules have higher energies. Since the rate of reaction depends on effective collisions, that is, collisions with sufficient energy and proper orientation (to be discussed in collision theory of reaction rates); hence, as seen from the graph the number of effective collision doubles on increasing the temperature by 10 °C; therefore, the rate of reaction also doubles. Arrhenius equation and calculation of activation energy Swedish chemist Arrhenius in 1889 gave a method for expressing the influence of temperature on reaction velocity. He proposed a quantitative relationship between rate constant and temperature: / Ea RT k Ae − = (1) where k is the rate constant, A is the pre-exponential factor which is related to the frequency of collision, E a is the activation energy or the energy barrier which the reactants must cross to form products, R is the gas constant and T is the temperature in K. Chemical Kinetics 723 Taking logarithm of both sides, ln ln a E k A RT = − (2) Converting to the base 10 ( 10 ln 2.303 log x x = ), we get 2.303 log 2.303 log a E k A RT = − log log 2.303 a E k A RT = − (3) The above equation shows that the value of k decreases as activation energy increases; hence, the rate of reaction decreases with the rise in activation energy.

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