Chemical Kinetics 1 Overview Getting Started Techniques Procedure FAQ Full Lab Manual Introduction & Goals Chemistry & Background Key Questions Prelab Problems Safety Procedure In Your Write-up Experiments Index ChemLab Home		Functional Groups While there is some truth in the statement that every molecule has different chemical properties, the major task of chemistry is to search for generalizations about chemical behavior. One of the most successful of these unifying concepts is the recognition that certain fixed groupings of atoms recur in many molecules; these recurring structural features are called  functional groupsand they can have a profound effect on the physical and chemical properties of molecules. Organic chemistry, in particular, uses the functional group concept, and most organic compounds can be classified systematically according to the functional groups present in the molecule. Examples of some functional groups are Many generalizations can be made about the chemistry of individual functional groups, and you will learn many of these if you proceed to study organic chemistry. This experiment will introduce you to some chemistry associated with the carbonyl group in organic compounds called ketones. Ketones The carbonyl or keto group, is an important example of an organic functional group. Simple mono-functional ketones contain only the carbonyl group, with the remainder of the molecule made up of carbon-carbon and carbon-hydrogen single bonds. Some frequently encountered examples are given below with their common names (systematic names are provided in parentheses): acetone methylethylketone cyclohexanone (2-propanone) (2-butanone) For ketones containing a carbon atom adjacent to the carbonyl group with hydrogen atoms attached to it, there is a second structural form, called an enol. The two forms exist in equilibrium as shown below for cyclohexanone: keto form enol form Normally the equilibrium lies well to the left hand side, and only traces of the enol form are present. Molecules which have the same formula, but different spatial arrangement of atoms, like this example, are called isomers. Note that when the enol forms, the carbonyl or keto group is no longer present and two new functional groups appear. These are an alkeneand an alcohol; the name enolis a composite of these two functional group names. The Halogenation of Ketones One of the characteristic reactions of ketones is the substitution of a halogen for one of the hydrogens adjacent to the keto group. The net reaction is: This reaction has been studied extensively and occurs for a wide variety of ketones. A four-step mechanism proposed for the reaction involves prior enolization to the ketone under acidic conditions: (1) (2) (3) (4) The main evidence for any mechanism is provided by kinetic studies to determine an experimental rate law. Your experiments will allow you to evaluate this possible mechanism and the relative rates of the four reactions in the proposed mechanism. Iodine Chemistry Elemental iodine is a violet-black solid at room temperature. It is quite volatile, readily subliming to give I2(g). The solid's solubility in water is quite small; a saturated solution contains an I2(aq) concentration of about 1.2 x 10-3 M. The solubility of I2 is greatly increased in a solution containing iodide ion (I-) since the iodine-triiodide (I3-) equilibrium keeps the free I2(aq) concentration relatively small. The equilibrium is: I2(aq) + I-(aq) I3-(aq) K = 710 The stock solution provided in this experiment has been prepared by dissolving about 4 x 10-2 moles of I2(s) and 0.4 moles of KI in one liter of water. The solution, therefore, is approximately 4 x 10-2 M in I3- with a ten-fold excess of I- present and only a small I2(aq) concentration. Note that the exact concentration, which will be given in the laboratory, may differ from this value. Both I2(aq) and I3-(aq) are effective iodinating agents in step (3) of the proposed mechanism. What we require, therefore, is a method of monitoring the rate of change of [I2] + [I3-] with time; this in turn is a measure of the rate of production of the reaction product. Fortunately, both I2 and I3- absorb visible light and therefore appear colored. Thus, the rate of reaction can be monitored by observing the disappearance of the characteristic color of I2 and I3-. The relationship between color or absorbance of light and the concentration of a substance is given by Beer's Law, described in the following section. Colorimetry and Beer's Law Colorimetry involves the measurement of the amount of light absorbed by a colored sample. Its use in chemical analysis stems from the familiar observation that the higher the concentration of a colored substance in a solution, the more light it absorbs. In simplest form, a colorimetric analysis involves visually comparing an unknown sample with a series of standards and estimating its concentration on the basis of the best match of color intensities. Much more powerful applications of light absorption are possible using an instrument which quantitatively measures the fraction of an incident light beam's energy which is absorbed by a sample. The design and interpretation of experiments carried out with such instruments, called colorimeters or spectrophotometers, requires a precise understanding of the factors which determine the light absorption properties of a colored sample. The fundamental law governing light absorption, known as Beer's law, is: A = c L (5) where A = absorbance of the sample (also defined below in terms of light intensity) c = concentration of the absorbing species (mol/liter) L = path length traveled by the light beam through the sample (cm) e = molar extinction coefficient of the absorbing species (L·mol-1·cm-1) Beer's law states that the absorbance of light is proportional to the product of the concentration, c, and the path length, L. The proportionality constant is , the molar extinction coefficient. Normally L is measured in centimeters and c in moles per liter therefore the molar extinction coefficient has units of reciprocal centimeters times reciprocal moles per liter. A = c L unitless = (M) (cm) (M-1cm-1) The absorbance (A) can be defined as the negative logarithm of the transmittance (T). The transmittance, in turn, is simply the ratio of the intensity of the transmitted beam to that of the incident beam. A = -log T = -log10 (I/Io) = absorbance (unitless) where                T = transmittance (unitless)                I = intensity of transmitted beam of light                Io = intensity of incident beam of light Note that absorbance increases as the transmittance, or fraction of light energy transmitted, decreases. A completely transparent sample, which transmits all visible light (I/Io = 1), has zero absorbance. A fully opaque sample, which absorbs all incident light (I/Io = 0), has infinite absorbance:         transparent sample    A = -log(1) = 0         opaque sample         A = -log(0) = Because the absorbance is logarithmically dependent on the transmittance, a sample which transmits 1% of the light (I/Io = 0.01; A = 2) has an absorbance only twice that of one which transmits 10% of the light (I/Io = 0.1; A = 1). An important property of absorbance is the additivity of absorbances in solutions which contain several colored components. A generalization of equation (5) for solutions containing several colored components is given by equation (6). A = Ai = L cii (6)         A = total absorbance of the solution         Ai = absorbance due to the ith component         L = the path length of light in cm         ci = concentration of the ith component         i = molar extinction coefficient of the ith component Since we are interested in the concentration of both I2(aq) and I3-(aq), we will use Equation (6) to consider the absorbance due to both species, at a given wavelength. The sum of the I2(aq) and I3-(aq) solution concentrations can be determined if we measure the absorbance A and use Beer's Law: A = L I2 [I2] + L I3- [I3-] Since we are only interested in determining changes in [I2] + [I3-] we select a wavelength ( = 565 nm) at which I2 = I3- = and the Beer's Law expression becomes A = L { [I2] + [I3-] } where L is the path length of the cell and is the extinction coefficient of both I2 and I3- at 565 nm. For this wavelength, is a constant. To relate the change in absorbance to the reaction rate, we can also write where dA and dt represent infinitesimally small changes in the absorbance and time, respectively. We will not measure infinitesimal (or even very small) changes in concentrations or time, and thus our rates are more correctly represented as finite changes: A/t for the absorbance rate of change and -([I2] + [I3-])/t for the reaction rate itself, expressed in terms of change of iodine concentration with time. Note that the change in absorbance at a give wavelength with time is proportional to the change in total iodine concentration with time. You will make use of this simple relationship when you explore how the reaction rate depends on the concentration of the reactants. The Experimental Approach A general expression for the rate law for the iodination of cyclohexanone can be written where k is the experimental rate constant for the overall reaction and a, b, and c are the orders of the reaction with respect to each of the three reactants. In order to measure the reaction rate, the change in concentration of one of the reactants or products must be monitored over time. In this experiment, the reaction rate is measured by determining the rate of disappearance of iodine, using a colorimeter to measure the change in I2 and I3- absorbance with time. To simplify the interpretation of your results, we will use the experimental technique called "flooding." Individual experiments will be carried out with cyclohexanone and hydrogen ion concentrations that are very high compared to the iodine concentration. Therefore, the cyclohexanone and hydrogen ion will remain at nearly constant concentrations during a given kinetic run and I2 and I3- will be the limiting reagent. Different experiments will be done at different initial values of these two concentrations to assess their effect on the rate, but the concentrations will always remain essentially constant during the course of a particular run. For this special case, with large and constant concentrations of H+ and cyclohexanone, the rate law can be written where [H+]0 and [cyclohexanone]0 are the initial concentrations of acid and cyclohexanone, which will remain nearly constant during the reaction. Thus, k' is also a constant, called the effective rate constant, for these "flooded" conditions. Using these special "flooded" reaction conditions, we can determine c, the reaction order with respect to I2 and I3-. If we integrate the differential rate law, for different possible values of c, we observe different behavior for the I2 + I3- concentration vs. time. For c=0, or zeroth order with respect to I2 + I3-, the dependence of the reaction rate on the I2 + I3- concentration becomes {[I3-] + [I2]}0, which equals 1. The rate law then reduces to (zeroth order) For the zero order case, the reaction rate does not depend on the concentration of I2 and I3-. For our special "flooded" conditions, with large and constant concentrations of acid and ketone, the rate of a given experimental run does not appear to depend on the concentration of any reactant. Reactions which show no dependence on concentration, even though the rate law contains at least one concentration term, are called pseudo zeroth order. In this situation, the rate of the reaction will be a constant, k' = k [H+]a0 [cyclohexanone]b0. For this zero order case, the integrated rate law is {[I3-] + [I2]}0 - {[I3-] + [I2]}t = k' t (zeroth order) This integrated rate law can be rewritten as {[I3-] + [I2]}t = - k' t + {[I3-] + [I2]}0 This equation has the form of a straight line, y = mx + constant. Thus, a plot of [I2] + [I3-] vs. time will be a straight line with a slope of - k' and y-intercept of this initial concentration, {[I3-] + [I2]}0. The concentration decreases linearly with time. For the case of c=1, the reaction would be first order with respect to I2 + I3-. In this case, the rate of reaction depends on the concentration of I2 + I3-, raised to the first power. For this case, the integrated rate law is ln{[I3-] + [I2]}0 - ln{[I3-] + [I2]}t = k' t (first order) We can again arrange this equation in a more obvious linear form, ln{[I3-] + [I2]}t = - k' t + ln{[I3-] + [I2]}0 If the reaction is first order with respect to to I2 + I3-, a plot of ln {[I3-] + [I2]} vs. t would be a straight line, with a slope - k' and y-intercept ln{[I3-] + [I2]}0. For first order, the natural log of concentration decreases linearly with time. Finally, if c=2 and the reaction is second order with respect to I2 + I3-, the integrated rate law predicts a linear relationship between the inverse of concentration and time. The integrated rate law is (second order) Rearranging gives Here a plot of the inverse of the total iodine concentration vs. time is a straight line with slope k' and y-intercept of the inverse of the initial concentration. For second order, the inverse of concentration increases linearly with time. These three cases illustrate the possible observations for zero, first, and second order reaction with respect to I2 + I3-. By plotting these three functions of the concentration of I2 + I3- vs. time for a single reaction observation, you would be able to determine the reaction order with respect to I2 + I3-. A zero order reaction would give a linear plot of I2 + I3- concentration vs. time. A first order reaction would result in a linear plot of ln {[I2] + [I3-]} vs. time. A second order reaction would result in a linear plot of 1/ {[I2] + [I3-]} vs. time. For each case, the slope of the linear graph will be related to k', the effective rate constant for our "flooded" conditions. Since Beer's Law tells us that the absorbance is directly proportional to the concentration of I2 + I3- at our chosen wavelength, we can plot absorbance vs. time, natural log of absorbance vs. time, and the inverse of absorbance vs. time, rather than these functions of concentration. We will observe the same functional form for each reaction order, when absorbance is used in place of concentration. When absorbance is plotted, the slopes for each of the three cases will be proportional to k', with Beer's Law giving us the different proportionality constants. In addition to determining the reaction order with respect to I2 + I3-, you will modify the reaction conditions to determine the reaction order with respect to acid and cyclohexanone. To find the reaction order with respect to acid, you will run the reaction more than once, with the same initial concentration of cyclohexanone, and different the concentrations of acid. These different runs will yield different values of the effective rate constant, k', For any of the three possible reaction orders with respect to total iodine, linear plots with slope proportional to k' will be obtained for each reaction run at different [H+]o. Each run will have a different slope and the variation of the slope with acid concentration, from run to run, will depend upon the value of a. Let's consider an example, to make this clearer. Example Absorbance vs. time was measured for two different trials of the reaction with two different concentrations of acid and the same concentration of cyclohexanone. The reaction order with respect to iodine and triiodide was determined and appropriate linear plots were obtained with the following slopes Run [H+]0 [cyclohexanone]0 slope of linear plot vi 0.1 M 0.09 M - 4.5 x 10-4 s-1 vii 0.2 M 0.09 M - 1.8 x 10-3 s-1 Solution To determine the reaction order with respect to acid, we will compare the slopes and concentrations for the two runs. For the correct reaction order with respect to I2 + I3- , when cyclohexanone and acid are present in great excess, the slope of the appropriate plot will be proportional to k'. Thus we can compare the ratio of the slopes for the two runs to the ratio of the two different concentrations of H+. Since [cyclohexanone]o and k are constant for the two runs, these terms will cancel, reducing our equation to For the example data, Taking the ratio of acid concentrations for the two runs gives The ratio of concentrations is 1/2 and the ratio of slopes is 1/4. This means that a must equal 2, or the reaction is second order with respect to H+. Similarly, you can determine the value of b, or the order of reaction with respect to cyclohexanone, by varying the initial concentration of cyclohexanone for constant concentrations of acid. Again, a comparison of the slopes of linear plots for different runs with varying cyclohexanone concentrations will allow you to find b, the reaction order with respect to cyclohexanone. Once you have determined a, b, and c, you will know the experimental differential rate law of the reaction. Then you can evaluate a possible mechanism, given in the introduction. You should examine each step of the mechanism, in light of your experimentally determined rate law, to decide which steps are fast or slow and which could be the rate-limiting step of the reaction. Remember, a basic principle of kinetics is that only the concentrations of reagents which enter the mechanism before or in the rate-determining step will affect the overall reaction rate.
Trustees of Dartmouth College, Copyright 1997–2004