Determining Rate Constant
The rate constant in chemistry is a proportionality constant that relates the rate of a chemical reaction to the concentrations of reactants. It is determined experimentally by measuring the reaction rate at different concentrations of reactants and using this data to calculate the rate constant. The rate constant is specific to a particular reaction at a given temperature.
8 Key excerpts on "Determining Rate Constant"
eBook - ePub- Kevin R. Reel(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...CHAPTER 7 Kinetics CHAPTER 7 KINETICS REACTION RATE • Kinetics determines the speed of a reaction, and is dependent on the mechanism by which reactants turn into products. • Reaction rate is based on the rate of appearance of a product or disappearance of a reactant, and is expressed as a change in concentration over time. • Reaction rates are determined experimentally by measuring concentrations. • Reaction rates increase by increasing concentration or by increasing the temperature. • Reaction rates may also increase by increasing the surface area of the reactant—which is the same as increasing the concentration of possible participants in the reaction, or by adding a catalyst. RATE LAW AND REACTION ORDER • The rate law describes the rate of the reaction as a function of a rate constant, which is dependent on the temperature and the concentrations of the reactants. • All rate laws take the form of rate = k [reactants] x, where k is the rate constant, [reactants] refers to the molar concentration of reactants, and the exponent, x, is the reaction order. • For all single-step reactions, the rate law for a particular step can be surmised from the balanced equation for that step because the rate of the forward reaction is proportional to the concentration of available reactants. Example: Total reaction (single. step): A → B + C rate = k [A] (first order) Or Total reaction (single step): A + A → B rate = k [A] 2 (second order) Or Total reaction (single step): A + B → C rate = k [A] [B] (second order overall) • It cannot be assumed that a reaction involves only a single step. Therefore, the rate law (and determination of the order of reaction with respect to each reactant) can only be determined experimentally. Example: Use the experimental data in the table to determine the rate law for the following reaction, A + B → C Solution: When doubling [B] between the first and second trial (holding [A] constant), the reaction rate also doubles...
- Kevin Reel, Derrick C. Wood, Scott A. Best(Authors)
- 2014(Publication Date)
- Research & Education Association(Publisher)
...Chapter 11 Chemical Kinetics Rates of Reaction Chemical kinetics involves the measurement of how fast a chemical reaction occurs. Many of the reactions that are performed in AP Chemistry classes happen at a relatively fast rate: the reactants are mixed together and seconds, maybe minutes later, the products are formed and the reaction is over. Some reactions are spontaneous but still occur at a slow rate, such as the reaction of diamond with air to form carbon dioxide—which takes thousands of years to occur. There are a variety of factors that affect the rate of a chemical reaction, including concentration, the nature of the reactants, temperature, surface area, and the presence of a catalyst. Measuring Reaction Rates The reaction rate of a chemical reaction is a measure of the change in concentration per unit of time. Reaction rate can be expressed in terms of either the appearance of a product or the disappearance of a reactant. For example, the rate of the reaction below can be expressed as follows. In the preceding equation, the negative sign indicates that the reactant is decreasing in concentration. The multiplicative factor ½ in front of the HCl is utilized for stoichiometric reasons since 2 moles of HCl react for every 1 mole of products formed. Effect of Concentration In general, increasing the concentration of a reactant will increase the rate of a chemical reaction. One way to study the effect of concentration on reaction rate is through studying the rate using initial concentrations of the reactants (method of initial rates). The overall dependence of concentration of reactants on rate can be expressed as an experimental rate law. For the following hypothetical reaction, the rate law has the form: where k is the rate constant, x and y are the orders of the individual reactants, and [A] and [B] are the concentrations of A and B, respectively...
eBook - ePub- Jeffrey Gaffney, Nancy Marley(Authors)
- 2017(Publication Date)
- Elsevier(Publisher)
...How these concentration changes affect the reaction rate is determined experimentally by measuring the reaction rates as the concentrations of the reactants are varied. The result is a proportionality between the reaction rate and the concentration of reactants. This proportionality is called a rate law or rate equation. A rate law is an experimentally determined equation that relates the reaction rate with the concentration of the reactants. The proportionality coefficient is called the rate constant (k). The rate law will usually fit an equation of the form; Reaction rate = − d A dt = k A m B n (2) The value of the rate constant is independent of concentration. However, it varies with temperature, usually increasing as temperature increases. It should also be emphasized that both the rate constant and the exponents “m” and “n” must be derived experimentally and that the rate law exponents have no relationship to the reaction's stoichiometric coefficients. The reaction order with respect to one particular reactant is equal to the value of the exponent of that reactant's concentration. In the general rate law (Eq. 2), the reaction order with respect to the reactant A is the value of “m” and the reaction order with respect to reactant B is the value of “n.” The overall reaction order is defined as the value of the sum of all exponents in the rate law or m + n for the general rate law (Eq. 2). In other words, the order of the reaction described by the rate Eq. (2) is m + n, while the reaction is m th order in reactant A and n th order in reactant B. The rate constant for a reaction of the order m + n has units of; mol 1 − m + n • L m + n – 1 • s − 1 The reaction order can be determined from measurements of reaction rate for different concentrations of reactants. But, since the reaction rate changes as the concentration of the reactants change, the reaction rate is not constant throughout a chemical reaction...
eBook - ePub- Gavin Whittaker, Andy Mount, Matthew Heal(Authors)
- 2000(Publication Date)
- Taylor & Francis(Publisher)
...Section F— Kinetics F1 EMPIRICAL APPROACHES TO KINETICS Key Notes Experimental methods Experimental methods in kinetics measure change in the composition of a reaction mixture with time, either continuously as the reaction progresses, or at fixed intervals after the reactants have come together. The techniques applied vary depending on the timescale of the reaction and the chemical species under study. Additional kinetic information is obtained by varying experimental parameters such as the initial concentration of reactant(s) or the temperature of the mixture. Rate of reaction The instantaneous rate of reaction for a species is the rate of change of concentration with time of that species at a particular instant during the reaction. Units of reaction rate always have dimensions of concentration time −1. Rate law The rate law is the empirically determined mathematical relationship describing the observed rate of reaction in terms of the concentrations of the species involved in the reaction. Rate laws do not necessarily fit the simple stoichiometry of a balanced chemical reaction but may be the consequence of a more complex underlying mechanism to the observed reaction. Rate constants Rate constants are the constants of proportionality within the empirical rate law linking rate of reaction and concentration of species involved in the reaction. The units of rate constants are particular to the rate law and can be derived by dimensional analysis. Rate constants usually vary with temperature. Order of reaction If the rate law for a reaction can be written in the form, rate ∝ [A] α [B] β then the reaction is classified as α -order in A, β -order in B,…and as (α+β+…) -order overall. The exponents do not have to be integers, and for complex rate laws, the order may not be a definable quantity. Molecularity The molecularity of a reaction is the number of molecules which come together to react and is independent of the order of a reaction...
eBook - ePub- Pieter Walstra(Author)
- 2002(Publication Date)
- CRC Press(Publisher)
...Also the rate constant is an empirical quantity to be experimentally determined, and it depends on the reaction order. The combined knowledge of the order, the rate constant, and the initial concentration of the reactant(s) allows calculation of changes occurring. An example is prediction of the extent to which a certain component is formed or degraded during long storage of a food. As is illustrated in Figure 4.2, it may need very precise determination of the time dependent concentration of a reaction product to establish the order, as long as the reaction has not proceeded very far. Another difference among the rates of reactions of various order is, of course, the dependence on the concentration of the reactant(s). As seen in Table 4.1, the rate is independent of concentration for zero-order, proportional to concentration for first-order, and proportional to concentration squared for second-order reactions. FIGURE 4.2 The change in concentration of reactant A with time for reactions of order 0, 1, and 2. k is the rate constant; t is time. Note Up till now, we have used concentrations in the rate equations, whereas we have learned in Chapter 2 that activities should be used. In many cases the difference is unimportant, not because it is small, but because we generally have no way of predicting the rate constant from first principles. Whether a reaction is slow because of a low activity coefficient or because of a low rate constant then would be a mere academic question. Nevertheless, there may be situations where it is important to know about activity coefficients, for instance when comparing the same reaction in different media or when the activity coefficient of one of the reactants varies in a different manner with conditions than that of another reactant. Question A food company pasteurizes a beverage for 15 s at 70°C in a heat exchanger, and it is then aseptically packaged in 1 liter cartons...
eBook - ePub- Adrian Dingle, Derrick C. Wood(Authors)
- 2014(Publication Date)
- Research & Education Association(Publisher)
...PART V RATES OF REACTION Chapter 14 Factors Affecting Rates of Reaction Note: It is likely that you will have been taught the contents of Chapter 15 before the contents of Chapter 14, and that makes sense. This book is compiled in the order of the Big Ideas and Enduring Understandings outlined in the College Board course and exam description. I. Kinetics A. Concept of Rate of Reaction 1. Rate of a chemical reaction is a measure of the change in concentration of reactants or products over time. 2. Can be measured as the decrease of the reactant concentration per unit time. 3. Can be measured as the increase of the product concentration per unit time. 4. One important method employed to measure rate is using Beer’s law to determine the concentration of a colored solution as a reaction proceeds. B. Conditions That Can Affect Rate 1. Increasing the surface area of a solid reactant can increase the rate by increasing the number of collisions between the reactant particles (see Chapter 15). 2. Catalyst increases the rate by lowering the activation energy of a reaction (see Chapter 17). 3. Increasing the temperature results in a faster reaction. The rate constant is temperature dependent and a rise in temperature will increase the rate constant (see below). 4. Concentration of reactants increases the amount of reactants colliding with each other, thus yielding product (see Chapter 15). C. Use of Experimental (Concentration) Data and Graphical Analysis to Determine Reactant Order, Rate Laws, and Rate Constants 1. General formula for rate equation. For the generic reaction Rate of reaction = k [ A ] x [ B ] y [ C ] z where k is the rate constant and x, y, z are the orders with respect to A, B, and C, respectively, but are not necessarily the stoichiometric coefficients of A, B, and C. 2. Orders i. The order with respect to a reactant is the exponent of the concentration term in the rate equation (a.k.a...
eBook - ePub- Mark E. Davis, Robert J. Davis(Authors)
- 2013(Publication Date)
- Dover Publications(Publisher)
...The Arrhenius form of the reaction rate constant is an empirical relationship. However, transition-state theory provides a justification for the Arrhenius formulation, as will be shown below. Note that the Arrhenius law (Equation 2.2.1) gives a linear relationship between ln k and T −1. EXAMPLE 2.2.1 The decomposition reaction: can proceed at temperatures below 100°C and the temperature dependence of the first-order rate constant has been measured. The data are: Suggest an experimental approach to obtain these rate constant data and calculate the activation energy and pre-exponential factor. (Adapted from C. G. Hill, An Introduction to Chemical Engineering Kinetics & Reactor Design, Wiley, New York, 1977.) Answer Note that the rate constants are for a first-order reaction. The material balance for a closed system at constant temperature is: where is the number of moles of N 2 O 5. If the system is at constant volume (a closed vessel), then as the reaction proceeds the pressure will rise because there is a positive mole change with reaction. That is to say that the pressure will increase as N 2 O 5 is reacted because the molar expansion factor is equal to 0.5. An expression for the total moles in the closed system can be written as: where n is the total number of moles in the system. The material balance on the closed system can be formulated in terms of the fractional conversion and integrated (see Example 1.5.2) to give: Since the closed system is at constant T and V (PV = nR g T): and the pressure can therefore be written as: If the pressure rise in the closed system is monitored as a function of time, it is clear from the above expression how the rate constant can be obtained at each temperature. In order to determine the pre-exponential factor and the activation energy, the ln k is plotted against T −1 as shown below: From a linear regression analysis of the data, the slope and intercept can be obtained, and they are 1.21 × 10 4 and 30.4, respectively...
eBook - ePub- Paul F. Cook, W. W. Cleland(Authors)
- 2007(Publication Date)
- Garland Science(Publisher)
...reactions involve the reaction of two molecules whose concentrations differ by several orders of magnitude. Then the concentration of the one present at a higher level is essentially constant during the reaction and the kinetics will appear first-order. The apparent first-order rate constant is the product of the true second-order rate constant and the concentration of the reactant in excess. This is normally the case for substrates combining with enzymes (see below), since the concentration of the enzyme is much lower than that of the substrate. Saturation Kinetics When a reactant is adsorbed on a surface or combines with a catalyst that is not used up and then reacts by a first-order process, the rate is v = − d A d t = k A K d + A (2-16) where k is the first-order rate constant for reaction of the adsorbed reactant or the complex with the catalyst and K d is the dissociation constant of the reactant. A plot of v versus A gives a rectangular hyperbola with a horizontal asymptote at high A of k and an initial slope of k / K d. The kinetics at low A are first-order with k / K d as the apparent rate constant, while at very high A the kinetics are zero-order (that is, the rate does not vary with A). In between these extremes, the kinetics are of mixed order. Equation 2-16 can be linearized in several ways, but the simplest is to invert both sides as shown in equation 2-17 : 1 v = (K d k) (1 A) + 1 k (2-17) A plot of 1/ v versus 1/ A determines 1/ k from the vertical intercept and K d from the ratio of slope and vertical intercept. Temperature Dependence of Kinetic Parameters The basic equation for the temperature dependence of a unimolecular rate constant is k = (k T h) e − (Δ G ‡ R T) (2-18) where k and h are Boltzmann’s and Planck’s constants, k is the rate constant in seconds −1, and T is the temperature in...
