Chemistry
Rate Constant
The rate constant is a proportionality constant that relates the rate of a chemical reaction to the concentrations of reactants. It is specific to a particular reaction at a given temperature and is used in the rate law equation to express the relationship between reactant concentrations and reaction rate. The value of the rate constant is influenced by temperature and the specific reaction mechanism.
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11 Key excerpts on "Rate Constant"
eBook - PDFEngineering Chemistry
Fundamentals and Applications
- Shikha Agarwal(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
Therefore, the rate law is Rate = k[N 2 O 5 ] In the above example, a and b are not equal to p and q. 13.5 Velocity Constant or Rate Constant Consider a reaction A + B → products. The rate of the reaction is given by Rate a [A][B] Rate = k [A][B] Here k is the proportionality constant known as the velocity constant or the specific reaction rate of a reaction at a given temperature. If [A] = [B] = 1 then in the above equation, Rate = k Hence, velocity constant of a reaction at a given temperature can be defined as the rate of the reaction when the concentration of each of the reactants is unity. 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 13.1 Difference between rate of reaction and Rate Constant Rate of reaction Rate Constant 1. It measures the 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 unit is mol/L/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 unit of Rate Constant depends on the order of the reaction Chemical Kinetics 677 Units of Rate Constant Consider a general reaction aA + bB+ ………… → Products.
eBook - PDFEngineering 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.
- A. Kayode Coker(Author)
- 2001(Publication Date)
- Gulf Professional Publishing(Publisher)
The concentration dependent term is found by guessing the rate equation, and seeing whether or not it fits the data. Boudart [1] expressed the many variables that have influenced reaction rates as: 1. The rate of a chemical reaction depends on temperature, pressure, and composition of the system under investigation. 2. Certain species that do not appear in the stoichiometric equation for the reaction can affect the reaction rate even when they are present in only trace amounts. These materials are known as catalysts or inhibitors, depending on whether they increase or decrease the reaction rate. 3. At a constant temperature, the rate of reaction decreases with time or extent of the reaction. 4. Reactions that occur in systems that are far removed from equilibrium give the rate expressions in the form: Figure 3-2. Temperature dependency of the reaction rate. Reaction Rate Expression 113 Figure 3-3. Reaction rate as a function of concentration. r = kf(C Ai ) (3-6) where f(C Ai ) is a function that depends on the concentration (C A ) of the various species present in the system, such as reactants, products, catalysts, and inhibitors. The function f(C Ai ) may also depend on the temperature. The coefficient k is the reaction constant. It does not depend on the composition of the system and is also independent of time in an isothermal system. 5. The Rate Constant k varies with the absolute temperature T of the system according to the Arrhenius law: k = k o e –E/RT . 6. The function f(C Ai ) in Equation 3-6 is temperature independent and can be approximated as: f C C Ai i i i ( ) = ∏ β (3-7) where the product ∏ is taken over all components of the system. The exponents β i are the orders of the reaction with respect to each of the species present in the system. The algebraic sum of the exponents is called the total order or overall order of the reaction.
- 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.
eBook - PDFFoundations of Chemistry
An Introductory Course for Science Students
- Philippa B. Cranwell, Elizabeth M. Page(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Chemists and chemical engineers must be able to control reaction conditions in order to obtain maximum yields by optimising factors such as temperature and pressure. Equally important is the time required to produce products. Fast reaction times reduce costs and energy requirements. Reaction times are critical when designing drugs and in drug deliv-ery. To be effective a drug must be sufficiently inert that it reaches its target before breaking down but must then react quickly and produce waste products that are readily removed from the body. The area of chemistry concerned with studying and controlling the rates of chemical reactions is known as chemical kinetics . Chemists study the rates at which chemical reactions occur so they can control them. The series of molecular processes that occur when a chemical reaction takes place is called the mechanism of the reaction, and understanding the mechanism helps chemists control the rate of reaction . 8.2 The rate of reaction 8.2.1 Defining the rate of a chemical reaction The rate of a chemical reaction is defined as the increase in concentration of one of the products of reaction divided by the time taken. Alternatively, it can be defined as the decrease in concentration of one of the reactants divided by the time: Rate of reaction = change in concentration of reactant or product time taken for the change A plot of concentration against time is given in Figure 8.1 for the hypothetical reaction of reactant A being converted to product B, as represented by the equa-tion A B. The rate can be expressed as: Rate of reaction = change in concentration of B time or Δ B Δ t 256 Chemical kinetics – the rates of chemical reactions The symbol Δ (Greek letter delta) means ‘ a change ’ , so Δ [B] represents a change in concentration of B and Δ t is the time taken for this change to occur. The units for reaction rate are therefore units of concentration divided by time: typically, mol dm -3 s -1 .
eBook - PDF- George W. Roberts(Author)
- 2015(Publication Date)
- Wiley(Publisher)
Chapter 2 Reaction Rates—Some Generalizations LEARNING OBJECTIVES After completing this chapter, you should be able to 1. use the Arrhenius relationship to calculate how reaction rate depends on temperature; 2. use the concept of reaction order to express the dependence of reaction rate on the individual species concentrations; 3. calculate the frequency of bimolecular and trimolecular collisions; 4. determine whether the rate equations for the forward and reverse rates of a reversible reaction are thermodynamically consistent; 5. calculate heats of reaction and equilibrium constants at various temperatures (review of thermodynamics). In order to design a new reactor, or analyze the behavior of an existing one, we need to know the rates of all the reactions that take place. In particular, we must know how the rates vary with temperature, and how they depend on the concentrations of the various species in the reactor. This is the field of chemical kinetics. This chapter presents an overview of chemical kinetics and introduces some of the molecular phenomena that provide a foundation for the field. The relationship between kinetics and chemical thermodynamics is also treated. The information in this chapter is sufficient to allow us to solve some problems in reactor design and analysis, which is the subject of Chapters 3 and 4. In Chapter 5, we will return to the subject of chemical kinetics and treat it more fundamentally and in greater depth. 2.1 RATE EQUATIONS A ‘‘rate equation’’ is used to describe the rate of a reaction quantitatively, and to express the functional dependence of the rate on temperature and on the species concentrations. In symbolic form, r A ¼ r A ðT , all C i Þ where T is the temperature. The term ‘‘all C i ’’ is present to remind us that the reaction rate can be affected by the concentrations of the reactant(s), the product(s), and any other compounds that are present, even if they do not participate in the reaction.
eBook - PDFChemistry
Principles and Reactions
- William Masterton, Cecile Hurley(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
▼ 274 ▼ Rate of Reaction 11 The rate at which the speeding train is traveling can be expressed in km/h. Similarly, the rate of a reaction can be expressed in M /h. Not every collision, not every punctilious trajectory by which billiard-ball complexes arrive at their calculable meeting places leads to reaction. Men (and women) are not as different from molecules as they think. —ROALD HOFFMANN Excerpt from Men and Molecules Chapter Outline 11-1 Meaning of Reaction Rate 11-2 Reaction Rate and Concentration 11-3 Reactant Concentration and Time 11-4 Models for Reaction Rate 11-5 Reaction Rate and Temperature 11-6 Catalysis 11-7 Reaction Mechanisms ▼ F or a chemical reaction to be feasible, it must occur at a reasonable rate. Conse-quently, it is important to be able to control the rate of reaction. Most often, this means making it occur more rapidly. When you carry out a reaction in the gen-eral chemistry laboratory, you want it to take place quickly. A research chemist trying to synthesize a new drug has the same objective. Sometimes, though, it is desirable to reduce the rate of reaction. The aging process, a complex series of biological oxida-tions, believed to involve “free radicals” with unpaired electrons such as O } H and O } O 2 is one we would all like to slow down. This chapter sets forth the principles of chemical kinetics , the study of reaction rates. The main emphasis is on those factors that influence rate. These include ■ ■ the concentrations of reactants (Sections 11-2 and 11-3). ■ ■ the process by which the reaction takes place (Section 11-4). ■ ■ the temperature (Section 11-5). ■ ■ the presence of a catalyst (Section 11-6). ■ ■ the reaction mechanism (Section 11-7). 11-1 Meaning of Reaction Rate To discuss reaction rate meaningfully, it must be defined precisely. The rate of reac-tion is a positive quantity that expresses how the concentration of a reactant or product changes with time.
eBook - PDFChemistry
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.
eBook - PDFChemistry
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.
- 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.
eBook - PDF- Youxue Zhang(Author)
- 2021(Publication Date)
- Princeton University Press(Publisher)
of concentration (in M) per unit time (in s), or M s 1 . Hence, the units of k are M s 1 for zeroth-order reactions, s 1 for first-order reactions, M 1 s 1 (or L mol 1 s 1 ) for second-order reactions, etc. For reactions in silicate melt or mineral, the concentration may be given by mole fractions that are dimension-less; then the unit of k would always be s 1 . Table 1-1 lists the values of k for some reactions. For overall reactions, the reaction rate law cannot be written down by simply looking at the reaction, but has to be determined from experimental studies. (Whether a reaction is elementary must be determined experimentally, which means that reaction rate laws for all chemical reactions must be experimentally determined.) The reaction rate law may take complicated forms, which might mean that the order of the reaction is not defined. Table 1-1a Reaction rate coefficients for some chemical reactions in aqueous solutions Reaction T (K) Order k f k b K Ref. H 2 O Ð H þ þ OH 298 0; 2 10 2.85 10 11.15 10 14.00 1 D 2 O Ð D þ þ OD 298 0; 2 10 3.79 10 10.92 10 14.71 2 H 3 O þ þ NH 3 ! NH þ 4 þ H 2 O 293 2; 1 10 10.63 10 1.37 10 9.26 2 CO 2 þ H 2 O Ð H 2 CO 3 298 1; 1 0.043 15 10 2.54 3 CO 2 þ H 2 O Ð H 2 CO 3 273 1; 1 0.002 4 H 2 CO 3 Ð H þ þ HCO 3 298 1; 2 10 6.9 10 10.67 10 3.77 3, 5 HCO 3 Ð CO 2 þ OH 298 1; 2 10 4.00 10 3.65 10 7.65 3, 5 HCO 3 Ð H þ þ CO 2 3 298 1; 2 10 10.33 5 HCO 3 þ OH Ð CO 2 3 þ H 2 O 293 2; 1 10 9.8 10 6.1 10 3.67 3 H 2 CO 3 þ OH Ð HCO 3 þ H 2 O 298 2; 1 10 10.23 56 Fe 2 þ þ 55 Fe 3 þ ? 56 Fe 3 þ þ 55 Fe 2 þ 2; 2 0.87 0.87 1.000 x 4 56 Fe 2 þ þ 55 FeCl 2 þ ? 56 FeCl 2 þ þ 55 Fe 2 þ 2; 2 5.4 5.4 1.000 x 4 Note . Units of k and K are customary with concentrations in M and time in s. In the ‘‘Order’’ column the first number indicates the reaction order of the forward reaction, and the second number for the backward reaction.
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