Study in Batch Reactor Kinetics Background A batch reactor is a type of reactor that is conducted in a stirred tank, in which the reactants are added batch-wise. These type of reactors are also used for small-scale operation and production; i.e. typically less than 1 million pounds/year. In addition, they are used for testing new processes that have not been fully developed, for the manufacture of expensive products, and for processes that are difficult to convert to continuous operations ( for example, fermentation of beer which can take many weeks of residence time). Batch reactors will typically range in size from 5 gallons (wastebasket) to as much as 8000 gallons (gasoline tanker) and cost anywhere from $25,000 to $250,000. Most batch reactors are glass lined and the prices listed above will generally include heating/cooling jacket, motor, mixer, and baffles. Batch reactors also have the ability to perform at a wide range of temperatures, ranging anywhere from 20 to 450 degrees F, and at high pressures (up to 100 psi). A typical simple batch homogenous reactor will contain hand holes for charging the reactor, a connection for the heating or cooling jacket and an agitator, and will look like Figure 1 on the following page. The advantage for using batch reactors includes a high conversion, which can be obtained by leaving the reactant in the reactor for long periods of time. On the other hand, the disadvantages may include high labor costs per batch and the difficulty of large-scale production. Another main aspect of batch reactors is that the data taken from them can be used to determine and subsequently analyze the kinetics for the given reaction. Hand holes for charging reactor Connection for heating or cooling jacket Agitator E-1 Figure 1 - Simple Batch Homogeneous Reactor Reaction Kinetics The rates of chemical reactions are a function of the concentrations of the reactions and of the temperature at which the reaction occurs. In this experiment, you will observe Chemical and Biomedical Engineering Department USF page 1 of 5
the reaction between crystal violet and sodium hydroxide in a batch reactor. equation for the reaction is as follows: The A simplified version of the equation is: CV + + OH - CVOH (crystal violet) (hydroxide) The large molecule on the left is a cation. Every carbon atom in the central part has a double bond to one of its neighboring carbons. This allows -electrons to move relatively long distances over the molecule, creating a large conjugated system. This process is what causes the ion to possess its intense violet color. The conjugation between benzene rings is disrupted when an OH - group attaches to the central carbon atom of the crystal violet molecule. As a result, the central carbon atom will no longer form a double bond with its neighbor, and the molecule will become colorless. The reaction of crystal violet with hydroxide ion can be observed by a device called a colorimeter, which measures the percentage transmittance, or the amount of light passing through a solution. This quantity can be converted to another unit of measurement called absorbance. The absorbance of crystal violet is directly proportional to its concentration. For this reason, its value is used in place of the actual concentration for the purpose of this experiment. The rate law for the crystal violet reaction is in the form: rate = k[cv + ] m [OH - ] n, where k is the rate constant for the reaction, m is the order with respect to crystal violet (CV + ), and n is the order with respect to the hydroxide ion. Activation Energy The determination of the activation energy, E a, for a chemical reaction is an integral part of kinetic analysis. The activation energy can be defined as the energy necessary to initiate an otherwise spontaneous chemical reaction so that it will continue to react without the need for additional energy. An example of activation energy is the Chemical and Biomedical Engineering Department USF page 2 of 5
combustion of paper. It is very easy to notice that paper does not require any additional energy to keep burning. On the other hand, the reaction of cellulose and oxygen is spontaneous, but you need to initiate the combustion by adding activation energy from a lit match. The molar concentration of the sodium hydroxide, NaOH, solution will be much greater than the concentration of crystal violet for this experiment. This ensures that the reaction, which is first order with respect to crystal violet, will be first order overall (with respect to both reactants) throughout the experiment. You will monitor the reaction at different temperatures, while keeping the initial concentrations of the reactants the same for each trial. Hence, you will be able to observe and measure the effect of temperature change on the rate of the reaction. From this information you will be able to calculate the activation energy, E a, for the reaction. Rate Law Determination Using a Batch Reactor Given the rate law expression for the reaction between crystal violet and hydroxide ions: rate = k[cv + ] m [OH - ] n in order to determine n, you will follow the disappearance of the crystal violet as a function of time in the presence of a large excess of hydroxide ion. Under these conditions, the concentration of hydroxide is approximately constant, so k[oh - ] n is also a constant, k. Therefore, the rate law becomes: rate = k [CV + ] m The constant, k, is called a pseudo rate constant, because it does not take into consideration the effects of hydroxide ion on the rate law expression. This equation can be integrated using calculus to give the following equations, depending on the value of m: For m = 0 (called zeroth order ): [cv + ] t = -k t + [cv + ] 0 For m = 1 (called first order ): ln[cv + ] t = -k t + ln[cv + ] 0 For m = 2 (called second order ): 1/[cv + ] t = k t + 1/[cv + ] 0 These equations all have the form of a straight line: y = mx + b In order to analyze the data collected, you must create the following three plots: [cv + ] t vs. time: A linear plot indicates a zero order reaction (k = -slope) ln [cv + ] t vs. time: A linear plot indicates a first order reaction (k = -slope) 1/[cv + ] t vs. time: A linear plot indicates a second order reaction (k = slope) The half-life for this reaction can be obtained from the following equation: t 1/2 = ln 2 / k Chemical and Biomedical Engineering Department USF page 3 of 5
where t 1/2 is the half-life for the reaction, or the time it takes for the concentration to decrease by half, and k is the rate constant for the given rate expression. An extension of this experiment is to determine the order with respect to [OH - ]. This is done by performing the same procedure using a different concentration of OH -. It is recommended to use 0.01 M NaOH (or half the concentration of the initial OH concentration used). Combine equal quantities of 2.0 x 10-5 M crystal violet solution and 0.01 M NaOH. The rate constant found in this extension will be different than the one found in the main experiment, due to the fact that these are pseudo rate constants. Once two different k values corresponding to two different OH - concentrations have been found, the order, n, for [OH - ] can be determined: k1 / k2 = ([OH - ] 1 / [OH - ] 2 ) n Rate Constant and Activation Energy from Initial Rate Data The activation energy, E a, for the chemical reaction between sodium hydroxide solution, NaOH, and crystal violet solution can be determined by using the Arrhenius equation: k = k 0 exp(-e a / RT) where E a is the activation energy of the reaction and k 0 is the pre-exponential factor. Instruments Used The Vernier Colorimeter (Figure 2) is designed to determine the concentration of a solution by analyzing its color intensity. The color of a solution may be inherent or derived by adding another reagent to it. The Colorimeter measures the amount of light transmitted through a sample at a user-selectable wavelength. Using the front panel knob, you may choose from four wavelengths: 430 nm, 470 nm, 565 nm, and 635 nm. Features such as automatic sensor identification and one-step calibration make this sensor easy to use. How the Colorimeter works The light from a LED passes through a cuvette containing a solution sample, as shown in Figure 1. Some of the incoming light is absorbed by the solution. As a result, light of a lower intensity strikes a photodiode. (Figure 3) Source Detector LED Transmitted Light Figure 2 -Vernier Colorimeter Figure 3 Internal Components Chemical and Biomedical Engineering Department USF page 4 of 5
The amount of light that passes through a solution is known as transmittance. Transmittance can be expressed as the ratio of the intensity of the transmitted light, I t, and the initial intensity of the light beam, I 0, as expressed by the formula: T = I t / I 0 The Colorimeter produces an output voltage which varies in a liner way with transmittance, allowing a computer, calculator, or handheld to monitor transmittance data for a solution. The reciprocal of transmittance of the sample varies logarithmically (base ten) with the product of three factors:, the molar absorptivity of the solution, b, the cell or cuvette width, and C, the molar concentration: Log(1/T) = bc (1) In addition, many experiments designed to use a Colorimeter require a related measurement, absorbance. At first glance, the relationship between transmittance and absorbance would appear to be a simple inverse relationship; that is, as the amount of light transmitted by a solution increases, the amount of light absorbed might be expected to decrease proportionally. But the true relationship between these two variables is inverse and logarithmic (base 10). It can be expressed as A = log(1/t) (2) Combining (1) and (2) gives the following expression A = bc (3) For a given solution contained in a cuvette with a constant cell width, one can assume and b to be constant. This leads to the equation: A = k * C (Beer s law) (4) where k is a proportionality constant and can be determined by obtaining the slope of an absorbance versus concentration plot. For the purpose of this experiment, the computer program used interprets the transmittance as percent transmittance or %T. Since T = %T/100, the formula can be rewritten as A = log(100/%t) or A = 2 log%t (5) Calibrating the Colorimeter The Colorimeter must be calibrated before experimental testing to ensure accurate results and to diminish chances for experimental error. This process is discussed further in the Experimental Procedure section below. Chemical and Biomedical Engineering Department USF page 5 of 5