Introduction
Every chemical reaction has a certain degree of complexity: while the kinetic parameters of some can be described relatively quickly using fundamental equations of the first or second order, more complex reactions, most often of biochemical nature, cannot be interpreted as easily. The experiment will monitor the reduction of Cr(VI) by glutathione, record the results, and investigate the reaction’s double-exponential dependency. The reaction’s rate equation and rate constants will be determined using exponential stripping and computer-assisted nonlinear regression analysis. Numerous biological processes and their rates cannot be readily explained using first or 2nd order kinetics. Numerous processes are very complicated, including several stages, reversible reactions, and intermediates; descriptions of such processes often assume the form of complex equations, necessitating the use of computers in data analysis and algorithms to understand the gathered experimental data.
Discussion
The current study intended to calculate the rate constants of Cr (VI) reaction with glutathione at near-neutral pH. The first trial results revealed that k1 = 0.00300 ????-1, k2 = 0.000510 ????-1, and k-1 = 0.00189 ????-1. On the other hand, during the second trial the obtained results were k1 = 0.00275 ????-1, k2 = 0.000684 ????-1, and k-1 = 0.00167 ????-1. It implies that the concentration of Cr(VI) in Cr(VI) -> Cr(VI) – GSH (thioester) reaction reduces by 0.00300 ????-1 (0.00275 ????-1) per second, and increases by 0.00189 ????-1 (0.00167 ????-1) during the reverse reaction Cr(VI)-GSH -> Cr(VI). In a similar vein, during the reaction thioester + GSH -> GSSG + Cr(III) the concentration of Cr(VI) reduces by 0.000510 ????-1 (0.000684 ????-1) per second. Consequently, these results can be used to determine a chemical reaction rate based on a rate law, where rate = k[R]n[I]m, which, however, is out of the scope of this research.
To achieve these results, the double-exponential dependence was investigated. In this regard, using this method helped to break one non-linear function into two linear ones and analyze each one separately. Firstly, the dependency between absorbance and time when t > t’ was calculated. As a result of two trials the following regression formulas were received: y = – 0.0003x – 1.4774 and y = – 0.0004x – 1.5206, where 0.0003 and 0.0004 are ????1 and -1.4774 and -1.5206 are c1. Applying similar logic to find the dependency between absorbance and time when t < t’ it was found that ????2 equals 0.0047 and 0.0041 for the first and the second trials accordingly, while c2 equals -1.2475 and -1.3305. Based on these values, amplitude ratio (A) was determined to be 1.258 in the first and 1.209 in the second trial.
Next, the optimized values for all the aforementioned values were determined. As such it was found that ????1 = 0.0003 (0.0004), ????2 = 0.0051 (0.0047), c1 = -1.4589 (-1.4818), c2 = -1.2050 (-1.2916), and A = 1.289 (1.209). Here it is important to mention that there were some differences between trials, although not significant, which indicates the greater reliability of the results. On the other hand, most of the time, the small differences in the trials are inevitable due to a number of external and internal reasons. Finally, using the optimized values of ????1, ????2, and A, the values of k1, k2, and k3 were calculated.
Conclusion
The experiment investigated the time dependency of glutathione reduction of Cr(VI) in an aqueous solution. The absorption of the oxidant and intermediate was used to calculate the rate constants. Nonlinear regression was used to examine the data. This reaction’s reactant was continually eaten while the reaction’s intermediate was created and devoured. It links two GSH units and oxidizes these to glutathione disulfide. The oxidation decreases the chromium ion’s oxidation state from +6 to +3. The thioester intermediate is anticipated to be formed by Cr(VI). In this case, the thioester intermediate joins with another GSH molecule. Because simple kinetic models cannot capture real-life rate processes, reversible multi-step sequential reaction mechanisms arise. This experiment’s reaction mechanism proposes that the reactant generates an intermediate and reverts to the reactant to form the product. This was occurring in the responses mentioned above. The blue line represents the outcome, the mediator’s black line, and the demarcation dot the intermediate. Since the concentration curve climbs and lowers towards the end, the intermediate is generated, and the reactant is continually consumed.
Reference
Experiment 6: Kinetics of a Reversible, First-Order, Consecutive Reaction: Reduction of Cr(VI) by Glutathione