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The aim of this experiment is to study the kinetics of an ionic reaction through investigating the order of reaction with respect to [H+], [Br-], [BrO3-] by calculating initial rate of reaction, so as to evaluate the rate constant of the reaction and to observe qualitatively the effect of changing ionic strength on the reaction rate.
Data Treatment and Analysis
In this experiment, ionic strength plays an important part. A sample calculation has shown to calculate for the ionic strength of each runs.
For reference solution (Run 1),
By varying the different amount of reactants used will allow to find the initial rate of the whole reaction. The different amount of reactants used for each reactant variation used in the experiment was tabulated into Table 1 found in Appendix 2.
The experimental data collected during the experiment can be found Table 2 in Appendix 3.
It is being considered that the volume of Na2S2O3 used is proportional to the concentration of I2 produced which is then proportional to the concentration of Br2 present from the reaction.
Therefore, with the amount of Br2, the rate of reaction to produce Br2 can be determined. NaHCO3 is acting as a base that quenches the reaction by reacting with the acidic [H+] ions that is present in the reaction mixture
The three graphs are plotted from the result above can be found in Figure 1 to 3 of Appendix 4.
The equation of the each plot was differentiated and tends reaction time to zero to calculate the initial rate with the coefficient of stoichiometry of each reactant as according to the average reaction rate equation shown here:
For Run 1,
= 1.016 x 10-5 M s-1
It is assumed that the volume of Na2S2O3 used is proportional to concentration of Br2 produced and hence, the initial rate is in M s-1.
Table 3 found in Appendix 5 shows the table of calculated initial rate, ln initial rate, concentration of reactants and ln concentration of reactants.
Using the Regression function in Excel 2010 with the Add-ins of data analysis function for Run 1 to Run 13, the order of reaction for [Br-], [BrO3-] and [H+] were found out to be 0.8091 (Â± 0.0313), 0.8962 (Â±0.0313), 1.7745 (Â±0.0313) which are rounded off to 1, 1, 2 respectively. The summary output of Regression Statistic can be found in Appendix 6.
The rounded off integers of the order of reaction number were substitute into to the rate law to find k, the rate constant:
Using the rate law, the rate constant, k, are calculated and tabulated into Table 7 found on Appendix 7.
The k is range from 3.568 M-3s-1 to 5.370M-3S-1 for Run 1 to Run 13.
Average k (from Run 1 to run 13) =
= 4.14 M-3S-1
Using the k from Run 1 to Run 13, the average of k was calculated to be 4.14 M-3S-1
Run 14 have k of 3.536 and Run 15 M-3S-1 has k of 3.120 M-3S-1.
Derivation of Rate Law
From the experimental result, the order of reaction of [H+], [Br-], [BrO3-] are determined to be 2, 1, and 1 respectively. The total order of reaction will be 4. Hence, the rate law of this ionic reaction can be written as:
Rate = k [Br-] [BrO3-] [H+] 2
Using the rate law, it can be assumed that the reaction happen in a single step that engage simultaneously all three species (termolecular reaction) and four particles. However, reaction with an overall order of 4 are challenging and are of low probability to occur successfully as it will need to require 4 molecules to collide at the same time with enough activation energy in order to commence the reaction. The activation energy for the molecules to collide with each other in the correct spatial orientation for bond breaking and bond forming is high for terrmolecular reaction which causes the reaction to be highly non-feasible. Moreover, in this experiment, both Br- and BrO3- are both negative charges in which the strong electron-electron repulsion will be present if ever the collision occurred between these ions and hence the collision will not be effective due to inter-electronic repulsion. Therefore, it is more favourable for this reaction to occur via more than one step. The proposed mechanism can be found in the later paragraph.
In addition to previous mentioned the equation of this reaction was given to be:
5Br- + BrO3- + 6H+ = 3H2O + 3Br2
The order of reaction is not similar to the coefficient of this reaction which can conclude that this reaction is not the elementary step and more than one step is required for this reaction to occur.
A possible mechanism of the reaction has been proposed below:
H+ + Br- Â® HBr (fast)
H+ + BrO3- Â® HBrO3 (fast)
HBr + HBrO3 Â® HBrO + HBrO2 (slow)
HBrO2 + HBr Â® 2HBrO (fast)
HBrO + HBr Â® H2O + Br2 (fast)
This proposed mechanism has a rate-determining step which agrees with the rate law where the concentration of the reactants in the rate determining step are exponential to the exponent with each of their respective individual stoichiometric coefficient appears in the rate law. Therefore, this is a possible mechanism of the reaction. It is also noted that water and sodium nitrate are not part of the proposed mechanism as both are in large excess in which the rate of change of sodium nitrate and water are relatively insignificant.
Effect of Ionic Strength on the Rate of Reaction
The rate constant, k, found for Run 14 is 3.536 M-3S-1. It is relatively lower than the range of 3.568 M-3s-1 to 5.370M-3S-1 for Run 1 to Run 13 and the average k of 4.14 M-3S-1 . With 50% more of HNO3 to create a more acidic environment show a decrease of rate of reaction. This trend can be explained by the obstructed interaction between the reacting particles. When ionic strength increases with the increase amount of HNO3 added, there will be greater number of spectator ions present in it. This will cause an increase in the columbic attraction between the spectator ions and reacting particles which will slow down and hinder the collision with the other reactants. Hence, the number and chances of effective collision will decrease which will cause the rate of reaction to decrease.
Effect of Replaced Na2SO4 for NaNO3
It can be observed from the result, that the Run 15 have a significant decrease in its rate constant which shows dramatic decrease of the rate of reaction as compared to the range of 3.568 M-3s-1 to 5.370M-3S-1 for Run 1 to Run 13 or the average k of 4.14 M-3S-1. Changing of Na2SO4 to NaNO3 has shown a decreased in rate of reaction. This can be explained by which SO42- have higher number of charge than NO3- for which SO42- will show stronger columbic attractions with spectator ions. Also, there are two times more amounts of sodium ions that contribute to the hindering of collision of the reacting particles. The spectator ions will thus be slow down and hindered which resulted in decrease of rate of reaction.
From the two changes in Run 14 and Run 15, both changing of the ionic strength and replacing the type of ions present will greatly affect the rate of reaction.
Debye-Hückel Theory and Transition State Theory
By combining the Debye-Hückel theory and The Transition State Theory, the effect of changing the ionic strength of the reaction on the rate constant of reaction between two ionic species between A and B:
From the equation above, the log kactivity\ can be calculated as according to the sample calculation below:
For Run 1,
The k activity was calculated and tabulated into Table 8 found in Appendix 8.
The rate constant of activity describe the effective concentration ions in the solution that is free for participating in the reactions and not the spectator ions. The average k activity is calculated to be 2.046 M-3S-1. This shows that the participating ions are lesser than expected of k concentration. Form the data calculated, it is observed that the activity is low when the ionic strength is 50% higher. The difference between the reference Run 1 and Run 14 for k concentration is (3.614 M-3S-1 - 3.536 M-3S-1) 0.077 M-3S-1 which the different between the reference Run 1 and Run 14 for k activity is (1.786 M-3S-1 - 1.571 M-3S-1) 0.214 M-3S-1. This result clearly shows that the rate constant based on activities of the 2 runs differ significantly. This coincides with the explanation mentioned in the previous paragraph where the effect of increasing the ionic strength decreases the value of the rate constant. A slower reaction rate is hence obtained. The result have shown that the number of free participating ions have been lower in Run 14 than in Run 1 which agree that that the increasing of ionic strength increase the amount of spectator ion which hinder the collision between the participating ions and thus result in lower activity of the ions and slower reaction rate obtained.
Temperature-Dependency of Rate Constant
The rate constant, K, can be affected by temperature as shown by the Arrhenius Equation:
A: Collision frequency factor; Ea: Activation energy; T: Temperature; R: energy gas constant
The Arrhenius equation shows that the rate constant is governed by the temperature which a change in temperature will result in change of the rate constant K. The slight change of temperature in the laboratory may cause the rate constant of each run to fluctuate and thus, giving a range of k of 3.568 M-3s-1 to 5.370M-3S-1 for Run 1 to 13 instead of a constant value. By keeping the temperature as constant as possible in a temperature-controlled environment can reduce such fluctuation and inaccuracy to the result.
However, this fluctuating of temperature may not be the sole source of error. There may be error of late addition of the aliquots to the quenching solution that causes more reaction between Br- and BrO3- and produced more Br2 which result in higher amount of Na2S2O3 used during titration. This results in inaccuracy of the initial rate of reaction. More limitation and sources of errors will be discussed.
Possible limitations and sources of errors in experiment
In this experiment, there are some limitations and possible sources of errors in experiment.
The major source of error will be from the titration with sodium thiosulfate (Na2S2O3) where there must be cautious in adding the Na2S2O3 to the solution to turn light yellowish brown before addition of starch. If the amount of starch is added too early, it will cause complexation and precipitation with iodine and also due to the poor solubility of the iodine. Hence, it will affect the endpoint of titration if poor judging of the shade of light yellowish brown before addition of the starch solution.
This shows that titration is not an effective method in determining the initial of reaction where it is prone to systematic errors that affect the accuracy of the result. There is only one titration performed for each runs at each time interval which reduce the accuracy and consistency of the result. Also, the precision of the method can be problematic due to different gauging of the colour change of purple to colourless to determine to be the endpoint. The consistency will also be affected. However, this error can be reduce but not eliminate with repeating the runs several time.
Another possible source of error is atmospheric carbon dioxide dissolve into the water used to form carbonic acid which can dissociate to form H+ and CO32- ions that will increase the acidic environment in the mixture which according to Le Chatelier's principle will cause REACTION NUMBER to shift forward and thus, more HBrO3 formed. This lead to more Br2 formed at inconsistent interval which will decrease accuracy of experiment. Using stopper can also help but not entirely eliminate such error.
To optimise consistency of the experiment, several precautions were taken to reduce random errors.
The starting of the stopwatch was always at the first drop of solution 2 added to the solution 1 during the preparation of the reaction mixture.
The amount of starch indicator was always consistent at two standard drops with constant swirling.
All of the glass wares were thoroughly washed with deionised water after each run to prevent inaccuracy due to left over solution from previous runs.
In conclusion, the orders of reactions of [H+], [Br-], [BrO3-] are determined to be 2, 1, and 1 respectively and the rate constant are from 3.568 M-3s-1 to 5.370M-3S-1 with an average rate constant of 4.14 M-3S-1. From this experiment, it can be concluded that the rate constant, k, will decrease with increasing ionic strength of the reaction.
 Atkins, P & dePaula, J. (2006). Atkins' Physical Chemistry (8th ed.). New York: Oxford University Press.
 G. D. Christian, J. E. O'Reilly, Instrumental Analysis, 2e, Allyn & Bacon, 1986.
 T. Engel and P. Reid, Physical Chemistry, 2nd ed.; Person Prentice Hall, 2010.
Appendix 2: Table of different amount of reactant used for each reactant variation used in the experiment
Table 1: Different amount of reactant used for each reactant variation used in the experiment
Amount of 1M of [KBr] used (ml)
Amount of 0.2 M of [KBrO3]
Amount of 1M of [NaNO3] used (ml)
Amount of 1M of [HNO3] used (ml)
Total Volume (ml)
Total Ionic strength