Rate Law and Activation Energy Essay

implantation garmentIn this experiment we ar analyzing the relationship between answer roams at different dumbnesss and temperatures to restrain the genuine localize aeonian, energizing energy, chemical answer secerns, and half-life of a reaction. The reaction of interest is the addition of a hydroxyl group to the nucleus of crystallisation purple. watch crystal purple, or hexamethylparaosaniline chloride for short, is a pixilatedly colored proud dye with the chemical formula C25H30N3Cl and disassociates completely in consequence. The relevant structure for this compound can be seen in pre embark 1Figure 1The base that is being used for the reaction is the strong base Sodium Hydroxide, or NaOH. This molecule also completely disassociates in water. Because measuring the concentrations of reactants is knockout in a simple lab setting, the reaction between Crystal Violet and Sodium Hydroxide go away be measured finished light absorbance. As the reaction between t he chemicals takes place and the Crystal Violet receives the hydroxide the overall intensity of the purple color will decrease thus affecting the absorbance. The absorbance of the issue will be measured with a colorimeter as the reaction takes place and will be interpreted as a direct representation of concentration of Crystal Violet.After the reaction has interpreted place, through analysis of graphs plotting absorption vs. time, the natural log of absorption vs. time, and the inverse of absorption vs. time the reaction will be determined to be either zeroth, head start, or second order with watch to crystallizing violet. From here the a impostor rate constant can be determined, and using comparisons of different constants at different concentrations of NaOH solvent and different temperatures, the reaction order with esteem to hydroxide, the lusty rate constant for the reaction, and the activation energy for the reaction can all be determined with the following compariso ns respectively.equating 1Where k2 is the pseudo rate constant of the reaction using twice the initial OH- concentration as is used in the k1 reaction and n is equal to the reaction order with respect to OH-. equation 2Where k is a pseudo rate constant based off of absorption and n is the reaction order with respect to OH- determined by equation 1.equation 3Where k1 is the reaction constant at temperature T1, a is a constant that can be ignored due to the way the equation will be utilized, R is that gas constant, and Ea is the activation energy.ProcedureThe following materials were needed for the experiment4 100mL beakers250mL beaker2.510-5M Crystal Violet straining solution0.10M NaOH Stock solutionDistilled Water10 dry plastic cuvettes and capsStirring rod vernier Colorimeter50mL volumetric pipet100L syringe2 10mL vialsLogger Pro computer softwareVernier computer interfaceHot plateVernier temperature probe1. First, 100mL of 0.10M NaOH solution was obtained using a 50mL volumetric pipet, and 0.05M was prepared using a the pipet, the stock 0.10M NaOH solution, and distilled water. 2. The Logger Pro software was engaged and both the Vernier colorimeter and temperature probe were plugged into the appropriate channels. The temperature of the room was measured and the colorimeter was calibrated by setting the 0% light and 100% light conditions.3. The colorimeter was set to 565nm and 1mL of 2.510-5M Crystal Violet solution was flux with 1mL of 0.05M NaOH solution and quickly added to the colorimeter. Data correlating time, temperature, transmittance, and absorbance was wherefore recorded for seven minutes as the reaction between the dickens solutions took place, and this data was saved.4. This previous step was repeated two additional times with the 0.05M NaOH solution, and then three times with the 0.10M NaOH solution. 5. Last, two 10mL-vials of 0.05M NaOH and 2.510-5M Crystal Violet solution were prepared in a loosen up bath solution on the hot plate. Once t he temperature reached 35C and was recorded, steps BLANK through BLANK were repeated once again twice with the heated solutions of Crystal Violet and 0.05M NaOH. All of the data that was still was saved and distributed between the two lab partners and all excess solutions were disposed of properly under the feel hood.ResultsThe following are the graphs obtained from the absorption and time recordings of the third run for the reaction between 1mL of 0.05M NaOH and 1mL of and 2.510-5M Crystal Violet carried off at 22.62C. figure 2figure 3figure 4These plots show that the reaction order with respect to crystal violet is clearly 1st order due to the great r2 rate of the linear trend line. Since our pseudo rate constant based off of absorption is equal to the proscribe slope of our linear plot, our k in for the reaction of 1mL of 0.05M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 22.62C is 0.1894.These next three plots are the graphs obtained from the absorption and t ime recordings of the prototypic run for the reaction between 1mL of 0.10M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 22.50C. figure 5figure 6figure 7As expected, these results still indicate a reaction order of 1 with respect to crystal violet as demonstrated by the linear plot on the figure 6. Our k in for the reaction of 1mL of 0.10M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 22.50C is 0.2993. Now that we have two pseudo reaction constants in which the OH- concentration differs by a factor of 2, we can use equation 1 to obtain the reaction order with respect to OH-.Since the reaction order mustiness be an integer we can see that the n must be 1. It is now know that for the reaction, the reaction orders with respect to both reactants are 1. At this point, the true rate constant can be determined using equation 2, where n is 1, the initial concentration of OH- is 0.05, and the pseudo rate constant k is 0.1894.These next three plots are the graphs o btained from the absorption and time recordings of the first run for the reaction between 1mL of 0.05M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 36.09C.figure 8figure 9figure 10Once again it is apparent from the three plots that the reaction is first order with respect to crystal violet. However, the reason we performed this last kinetic run was to obtain a nurse for k at a different temperature. This way we have two sets of values for equation 3 with two temperatures, and two rate constants. With this information we can cut out the pre-exponential factor a and solve for the activation energy. But first k must again be cypher for the reaction at the naked as a jaybird temperature. Doing this the same way as done in calculation 2, we obtain a reaction constant of 4.964 a higher value, which is to be expected with the increase in temperature. Now, manipulating equation 4 we obtain thatequation 4While plugging the proper values provideswhich subsequently some arit hmetic leads to a calculated Ea of 15,254.67J, or 15.25467kJ. The calculation for half-lives for the different conditions is simple, and just requires the following equation.equation 5When using the rate constant found in calculation 1, t1/2 for the kinetic run for the reaction between 1mL of 0.05M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 22.62C is found to be 0.183 seconds.Error AnalysisIn this experiment there are several things calculated and several sources of fracture to take into account. Error needs to be calculated for the rate constants k, for the half-lives, and for activation energy. The faults for the pseudo-rate constants are obtained using the LLS method. Once these are obtained the next step is to calculate the error in the true rate constants.When calculating the error in true rate constant once must apply both the error in the pseudo rate constant and the error in the cadence of volume for the 100L syringe as it pertains to the concentration of hydroxide. The error in the syringe is 0.02mL, which for 0.05M NaOH solution leads to an error in concentration of approximately 110-3M and 210-3M for 0.10M NaOH. Equation 2 is manipulated to solve for the true rate constant. The following equation is used to solve for the error in the true rate constant. equation 6And when the derivatives are solved is equal toequation 7And when the numbers are plugged in for the first kinetic run looks like calculation =.08In other words, the rate constant for the first kinetic run came out to be 3.79.08. Now when calculating the error in the half-life the precisely thing that has to be taken into consideration is the error in the rate constant, which was just calculated above. using the same method, equation 5 is solved for half-life, and the error is calculated like so.equation 8Which after the derivatives are solved is equal toequation 9And of course after the correct values for precedent the first kinetic run are plugged in providescalculat ion = .004And last but nowhere near least, is the error analysis for the activation energy. With this the error for the true rate constant must again be taken into consideration, and the error for the temperature probe. The error for the true rate constant has already been calculated, while the error for the temperature probe is provided in the lab manual as being 0.03K. Taking these into consideration, a very multifactorial process follows. The same process as above was used but involving much more vary and lengthy derivatives. First equation 3 was manipulated to the following form.equation 10The derivative of this equation with respect to each variable (T1, T2, K1, and K2) was then taken squared, and multiplied by the square of the respective variables uncertainty. These were added up and the square root was taken as in the above methods. The end result was a calculated error of 2 KJ for the calculated activation energy of 15kJ.Figure 11Overall this lab was very happy in the u se of absorption as a method of monitoring change in concentration. The calculated errors all seem to be about what one might expect. This lab was very analytical exterior of one glaring hole. You can see in figure 9 a slight submit in the plot that isnt found on either figure 3 or figure 6. To me this seems to be because the reactants are heated up to a temperature around 35-36C, but once the chemicals are mixed and placed in the cuvette the temperature is no longer controlled as the reaction takes place for the following seven minutes.Thus, as the temperature falls the rate of the reaction slows, and the pseudo rate constant is lower than it should be. This of course leads to a rate constant lower than it should be, and then the activation energy is affected as well. If I were going to change one thing about the lab, I would try and do something to control the temperature as the reaction persisted. asunder from that, there is little room for error outside of obvious blunders.Co nclusionA reasonable value for activation energy was calculated from the data collected in this experiment. There were no major mistakes do in the laboratory, and the calculations all went smoothly. This experiment demonstrated that there are creative ways around difficult problems in the laboratory, such as measuring absorption in place of concentration to follow the pass on of a reaction.References-Alberty, A. A. Silbey, R. J. Physical Chemistry, 2nd ed. Wiley New York, 1997. Department of Chemistry. (2013, Spring). CHEMISTRY 441G PhysicalChemistry Laboratory Manual. Lexington University of Kentucky