Week 8: Coordination Chemistry 4 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		Chemistry & Background Kinetic studies have established that the mechanism of the initial reaction is not a simple exchange of the H2O and NO2- ligands. The reactive species is not the aqua complex, but rather its conjugate base, [Co(NH3)5(OH)]2+. This reacts with N2O3 to form the nitrito isomer and nitrous acid, HNO2, as shown below. In this mechanism, the oxygen atom of the original water ligand is marked with a star to help you keep track of it. The structure with dotted lines is a transition state between reactants and products. In this structure, the dotted lines show the formation of new bonds, Note that the labeled oxygen atom bonded to the cobalt ion in the nitrito complex was originally part of the water ligand, rather than a nitrite ion. This mechanism was confirmed by kinetic studies on [Co(NH3)5(H2O)]3+ that contained 18O isotopes, so that the source of the oxygen atom in the final product could be traced. In the second step of the reaction, the NO2- ligand isomerizes. The nitro and nitrito linkage isomers exist in equilibrium. The equilibrium is shown below, with the two resonance structures of the nitro isomer shown explicitly: This equilibrium is the second step in the reaction and you will determine the overall rate constant for the change from the initial isomer, which is kinetically favored, to the final isomer, which is more thermodynamically stable. Last week you used absorbance measurements to monitor the concentration of [Co(NH3)5(H2O)]3+ with time. These measurements were conveniently made at 500 nm, since the absorbance of the reactant aqua complex was between that of the nitro and nitrito complexes. By looking at the change of absorbance at 500 nm, you could see which isomer formed first by observing whether the absorbance increased or decreased. This week, your goal is to determine the rate constant for the initial ligand exchange reaction and the subsequent ligand isomerization reaction. To do so, it is useful to observe the two reactions sequentially, at different wavelengths and different temperatures. To monitor the first reaction, you should monitor absorbance at a wavelength where the overall rate of disappearance of the starting reactant [Co(NH3)5(H2O)]3+ can be monitored. This can be done at a wavelength where the absorbance of the nitrito and nitro complex are equal, such as 415 nm. To monitor the second reaction, the ligand isomerization, it is important to wait until the initial reaction is complete. Then it is useful to monitor a wavelength that has a large difference between the nitro and nitrito isomer absorbance, such as 450 nm. The rate law for the initial ligand substitution reaction shown in the above mechanism has been found by experiment to be Rate = k [Co(NH3)5(OH)2+] [HNO2]2 This fits with the mechanism given above, since two HNO2 molecules and one [Co(NH3)5(OH)]2+ ion react before the rate limiting step. Taking into account the acid dissociation of [Co(NH3)5(H2O)]3+ and nitrous acid, this rate law can also be expressed as Rate = k [Co(NH3)5(H2O)3+] [NO2-] [HNO2] In other words, the reaction has been found by experiment to be first order in the aqua cobalt complex, nitrous acid, and nitrite ion. The reaction conditions can be manipulated to make it possible to determine reaction orders independently. For example, if the concentrations of NO2- and HNO2 are much greater that that of [Co(NH3)5(H2O)]3+, such that they remain nearly constant throughout the course of the reaction, the conditions will be pseudo first order, with a rate law of Rate = k' [Co(NH3)5(H2O)3+] where k' = k [NO2-] [HNO2] To determine the order of a reaction, experimenters can measure the rate of reaction at a variety of reactant concentrations to see how the rate changes. For example if the concentration of nitrite ion is doubled, while all other concentrations remain constant, the reaction rate will also double, since the nitrite dependence is first order. Likewise, the pseudo first order rate constant will also double if the nitrite ion concentration is doubled. Another way to determine the order of a reaction is to monitor concentration of a reactant as a function of time and compare to the predictions of the integrated rate law for various reaction orders. The concentration vs. time data can be plotted in the form of various integrated rate laws and the correct reaction order confirmed by a linear plot for the correct integrated rate equation, as you saw in the first week of Chem 6 lab. The integrated rate law for a zeroth order reaction predicts a linear change in concentration with time, as you saw in Weeks 1 and 2. In this case, a linear plot of concentration vs. time confirmed that the reaction was zeroth order. For a first order reaction, the integrated rate law gives a dependence of reactant concentration, c, with time of c = c0 e-kt or ln c / c0 = -kt where k is the rate constant, c0 is the initial reactant concentration, and t is time. Thus, for a reaction that is first order with respect to the reactant with concentration c, a plot of concentration vs. time will have an exponential decay. A plot of ln c / c0 vs. time will be linear with a slope of -k and an intercept of zero. The second step of the reaction, the isomerization from nitrito to nitro forms is also first order with respect to [Co(NH3)5(H2O)]3+. This experimental observation gave rise to the predicted mechanism given earlier: What reaction order with respect to NO2- and HNO2 would you predict for the ligand isomerization reaction, from this mechanism? In this week's experiments, you will determine the rate constants and confirm the reactions orders predicted by the proposed mechanism. To confirm the reaction order with respect to [Co(NH3)5(H2O)]3+ for both steps in the reaction, we will measure absorbance vs. time. We first need to relate the integrated rate law, in terms of concentrations, to the absorbance values measured. We will use the relationship between concentration and absorbance, Beer's Law: A = c L The absorbance of light at a given wavelength is the sum of the absorbance of the different complex ions in solution. By combining this sum with Beer's Law and the stoichiometry of the reaction, it can be shown that where A0 is the initial absorbance, at t zero time, and A is the final absorbance, at infinite time. For this experiment, c is the concentration of [Co(NH3)5(H2O)]3+ at time t and c0 is the initial concentration of [Co(NH3)5(H2O)]3+. Substituting this expression into the integrated rate law gives This equation gives us a way to use the absorbance vs. time data to determine the rate constant. A plot of ln [A - A / A0 - A] vs. time will give a straight line with slope -k, for a first order or pseudo first order reaction. To successfully determine the reaction rate constants, your measurements will need to include the initial absorbance, A0, and the final absorbance, A. If psuedo first order conditions are used, the pseudo first order rate constant k' can be determined from the plot. Then the rate constant k can be calculated using equation k' = k [NO2-] [HNO2].
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