Rate Law and Activation Energy Essay

IntroductionIn this prove we atomic number 18 analyzing the relationship amidst reply sites at incompatible c erstwhilentrations and temperatures to determine the on-key stray aeonian, activation push, response sites, and half life of a reception. The reception of interest is the addition of a hydroxyl group to the inwardness of watch crystal empurpled. crystallizing over-embellished, or hexamethylparaosaniline chloride for short, is a strongly colored majestic dye with the chemical formula C25H30N3Cl and disassociates completely in closure. The relevant expression for this compound shadower be seen in count 1 find out 1The trading floor that is being utilize for the reception is the strong base Sodium Hydroxide, or NaOH. This molecule also completely disassociates in water. Because bill the concentrations of reactants is difficult in a simple science laboratory setting, the chemical reaction between Crystal imperial and Sodium Hydroxide provideing be mensural through crystallize absorbance. As the reaction between the 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 resoluteness will be delibe prise with a tintometer as the reaction takes place and will be interpreted as a direct representation of concentration of Crystal Violet.After the reaction has taken place, through analysis of graphs plotting engrossment vs. time, the congenital log of absorption vs. time, and the inverse of absorption vs. time the reaction will be contumacious to be either zeroth, first, or second ordain with respectfulness to crystal violet. From here the a skulker rate eonian can be find out, and using comparisons of different eternals at different concentrations of NaOH theme and different temperatures, the reaction order with respect to hydroxide, the true rate constant for the reaction, and the activation ene rgy for the reaction can all be determined with the following equalitys respectively. equivalence 1Where k2 is the pseudo rate constant of the reaction using twice the initial OH- concentration as is utilize in the k1 reaction and n is equal to the reaction order with respect to OH-. equation 2Where k is a pseudo rate constant comprise 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 imputable 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 Stock solution0.10M NaOH Stock solutionDistilled Water10 juiceless plastic cuvettes and capsStirring rod vernier Colorimeter50mL volumetric pipet100L syringe2 10mL vialsLogger Pro softwargonVernier computer interfaceHot plateVernier tempera ture canvass1. First, 100mL of 0.10M NaOH solution was bring forthed 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 mixed with 1mL of 0.05M NaOH solution and quickly added to the colorimeter. Data correlating time, temperature, transmittance, and absorbance was then recorded for seven minutes as the reaction between the twain solutions took place, and this data was deliver.4. This previous step was recurrent 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 C rystal Violet solution were prepared in a hard bath solution on the hot plate. Once the temperature reached 35C and was recorded, steps BLANK through BLANK were repeated again twice with the heated solutions of Crystal Violet and 0.05M NaOH. All of the data that was collected was saved and distri neverthelessed between the two lab partners and all excess solutions were disposed of powerful under the fume hood.ResultsThe following are the graphs obtained from the absorption and time recordings of the leash put to work for the reaction between 1mL of 0.05M NaOH and 1mL of and 2.510-5M Crystal Violet carried out at 22.62C. inscribe 2 grade 3figure 4These plots portray that the reaction order with respect to crystal violet is clearly initiatory order due to the great r2 value of the li dependable trend line. Since our pseudo rate constant based off of absorption is equal to the damaging 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 undermentioned three plots are the graphs obtained from the absorption and time recordings of the first 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 contribute 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 must be an whole number we can see that the n must be 1. It is now sleep together 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 equa tion 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 obtained 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 plain from the three plots that the reaction is first order with respect to crystal violet. However, the motive we performed this last kinetic run was to obtain a value for k at a different temperature. This way we have two sets of value 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. nevertheless first k must again be figure for the reaction at the new temperature. Doing this the same way as done in count 2, we obtain a reaction constant of 4.964 a higher(prenominal) value, which is to be expected with the increa se in temperature. Now, manipulating equation 4 we obtain thatequation 4While plugging the proper values provideswhich by and bywards nigh arithmetic leads to a calculated Ea of 15,254.67J, or 15.25467kJ. The calculation for half-lives for the different conditions is simple, and undecomposed 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(prenominal) issues calculated and several sources of error to take into account. Error needs to be calculated for the rate constants k, for the half-lives, and for activation energy. The errors 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 const ant once must apply both the error in the pseudo rate constant and the error in the measurement 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 only 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 a fter the derivatives are solved is equal toequation 9And of job after the correct values for example the first kinetic run are plugged in providescalculation = .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 truly complex process follows. The same process as above was used but involving much more complicated 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 trued, and multiplied by the square of the respective variables uncertainty. These were added up and the square root was taken as in the abo ve methods. The end result was a calculated error of 2 KJ for the calculated activation energy of 15kJ.Figure 11Overall this lab was very successful in the use of absorption as a method of monitoring change in concentration. The calculated errors all have the appearance _or_ semblance to be about what one might expect. This lab was very analytical outside of one glaring hole. You can see in figure 9 a slight curve 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 agelong controlled as the reaction takes place for the following seven minutes.Thus, as the temperature fall 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. Aside from that, there is little room for error outside of pellucid blunders.ConclusionA reasonable value for activation energy was calculated from the data collected in this experiment. There were no major mistakes make in the laboratory, and the calculations all went smoothly. This experiment demonstrated that there are originative ways around difficult problems in the laboratory, such as measuring rod absorption in place of concentration to follow the progress of a reaction.References-Alberty, A. A. Silbey, R. J. Physical chemical science, 2nd ed. Wiley New York, 1997. Department of Chemistry. (2013, Spring). CHEMISTRY 441G PhysicalChemistry Laboratory Manual. Lexington University of Kentucky