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Chemical Kinetics
Kinetics is the study of rates of reactions, and the various parameters, which effect reaction rates. When an extensive kinetic study is performed, the rate law of the reaction can be determined, and a plausible reaction mechanism can be proposed.
rate law- a mathematical expression, which relates the rate of reaction to a rate constant times the concentration of reactants (and sometime products), raised to various powers. The exponents must be determined experimentally. They are referred to as the order with respect to each reactant. The sum of the exponents is known as the overall order of the reaction.
reaction mechanism - the step-by-step process by which reactants are converted to products.
The rate of a reaction (usually expressed in M/time) varies with concentration, temperature, solvent, etc. Therefore, it is important to define exactly what you mean by the rate of reaction. Since most reaction rates depend upon the concentration of reactants, as the reaction proceeds, these concentrations decrease, and the rate likewise decreases.
For a reaction such as: H2(g) + I2(g) ---> 2 HI(g), we can define the rate of reaction = rate of loss of hydrogen. Due to the stoichiometry of the reaction, the rate of reaction will also equal the rate of loss of iodine. Since two moles of HI are made for each more of hydrogen or iodine reacted, the rate of reaction will also equal 1/2 the rate of formation of HI.
where the square brackets represent concentration in moles/liter, and the negative sign indicates the disappearance of reactant. rate = rate of loss of H2 = rate of loss of I2 = 1/2 rate of formation of HI or
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Determining Rate LawsThe rate law of a reaction can only be determined experimentally. To determine the relationship between reaction rate and concentration(s), graphing is often used. One method involves the method of initial rates. In this method, the reaction is carried out several times. In each experiment, only the concentration of one reactant is varied while the concentration of the others are held constant. By comparing the initial rate (the initial slope of a graph of concentration versus time) for each experiment, you can determine the dependence of the rate on each reactant.
Problem: For the reaction below, use the data to determine the order of the reaction with respect to each reactant, and the value of the rate constant.
2 HgCl2(aq) + C2O42- ---> 2 Cl-(aq) + 2 CO2(g) + Hg2Cl2(s)
experiment [HgCl2] [C2O42-] initial rate M/s 1 .105 .15 1.8 x 10-5 2 .105 .30 7.1 x 10-5 3 .052 .30 3.5 x 10-5 4 .052 .15 8.9 X 10-6 Units of Rate Constants
The units of the rate constant, k, will vary with the reaction order. For first-order reactions, k has the units of inverse time. For second-order reactions, the units are M-1time-1, and for third-order reactions, the units are M-2time-1. Reactions, which are, zero order, or higher than third order are quite rare.
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Graphical Methods of Determining Rate LawsRate laws for first and second order reactions can be integrated and then obey linear equations. Experimentally, concentrations (or properties proportional to concentration such as color, pressure, volume, etc) are measured at various times. While graphs of concentration versus time are curved (except for zero order rxns), the integrated rate laws indicate that graphing ln(concentration) or 1/(concentration) will be linear if the reaction is first order or second order respectively.
First-order Reactions
The last equation, known as the integrated rate law for a first-order reaction, can be rearranged to linear form. ln[A] = kt + ln[A]o , where a graph of ln of concentration of A versus time will be linear (if the reaction is first-order with respect to A) with a slope of k.
The half-life of a reaction (t1/2) is the time required for half of the initial amount of reactant to react. First-order reactions have a constant half-life for the duration of the reaction. Using the integrated rate law, and substituting t1/2 for t and [A] at t1/2 = .5[A]o provides the following relationship for half-life. Note that the half like is constant for first-order reactions.
Problem: The shroud from a mummy has a 14C activity of 8.9 disintegrations/min/g of C compared to living organisms which have 15.2 dis/min/g C. Calculate the age of the shroud. The half-life of 14C is 5730 years.
Second-Order Reactions
A graph of 1/[A] versus time will be linear if the reaction is second-order with respect to A, with a slope = k.
The half-life of a second order reaction lengthens as the reaction proceeds.
Note that the half-life changes because the concentration of A at the beginning of each interval changes. Each half-life is double the one that preceded it.
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Determining Rate Laws for Reactions with Several Reactants Either use the method of initial rates, or perform rate measurements in which the dependence of one reactant is being studied, and the other reactants are in at least a 10 fold excess. In this way, the concentration of the other reactants remains relatively constant during the course of the reaction. You can thus isolate the reactant being studied and determine the order of the reaction with respect to this reactant using the graphing techniques described above.
Relationship between Rate Laws and Reaction Mechanisms
mechanism - a series of elementary reactions or steps by which reactants become products.
elementary reactions - steps of a mechanism. Rate laws for elementary reactions can be written without experimental study because they represent the collision of molecules and/or the rearrangement of bonds which occur in a single step. The number of molecules which react or collide in an elementary reaction is called the molecularity of the step. Note that termolecular (3-way collisions) elementary steps are extremely rate.
reaction intermediate - a species which is formed and consumed during the course of the reaction.
rate determining step - the slowest in a series of elementary reactions which comprise the reaction mechanism. The rate of reaction can be no faster than its slowest step.For a Proposed Mechanism to be Valid
1. The sum of the elementary steps must yield the overall balanced equation for the reaction.
2. The observed rate law must be in agreement with the rate law derived from the mechanism.
3. The proposed mechanism must be consistent with all other kinetic data. Problem: For the decomposition of H2O2: 2 H2O2 --> 2 H2O + O2
The rate law is: rate = k[H2O2]. Is the following mechanism possible? What (if any) are the reaction intermediates?Proposed mechanism:
H2O2 --> 2 OH (slow)
H2O2 + OH --> H2O + HO2
HO2 + OH --> H2O + O2Return to Class Schedule
Energy and Reaction Rates For a reaction to occur:
1. Molecules must collide.
2. They must collide with sufficient energy to produce products.
3. They must collide with proper spatial orientation to produce products.All reactions require a minimum amount of energy in order to proceed to product formation. This energy is called the activation energy Ea. The relationship between collision frequency, energy, and rate constant was developed by Arrhenius. Note that all rate constants are temperature dependent.
where A is the pre-exponential factor, R = 8.314 J/mol-K, T is temperature in Kelvins, and k is the rate constant.
The ln of the above equation provides a graphical way to obtain the activation energy without determining the pre-exponential factor. The rate constant is determined at several temperatures.
A graph of ln k versus 1/T gives a straight line with the slope = to -Ea/R.
If the rate constant is determined at only two temperatures, the equation can be rearranged to the form:catalysts- increase reaction rates by providing a lower energy pathway. They are not consumed during the reaction. Biological catalysts are called enzymes.
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Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell. You may freely edit these pages for use in a non-profit, educational setting. Please include this copyright notice on all pages.
