Calculating activation energy of the bromide-bromate reactionRaw dataTemperature (0.5C)Time (1s)Observations

25.0920Solution went from clear red color to a cloudy pink

35.0370

45.0140

55.059

65.041

75.020

Table 1: Temperature and time taken for reaction to go to completionAnalysisThe experiment can be represented by the following reaction mechanism:1. H2SO4 -> H+ + SO42-2. BrO3- + 5Br- + 6H+ -> 3Br2 + 3H2O3. C6H5OH + Br2 -> C6H2Br3OH + HBrSulphuric acid dissociates into H+ and SO42- in solution (reaction 1); when added to the bromide/bromate solution, the solution then dissociated into BrO3- and Br-, which reacted to form bromine and water (reaction 2).Bromine usually acts as a strong oxidizing agent and reacts with methyl red, very quickly bleaching its color. However, in this experiment, the reaction was slowed by the presence of phenol, which reacts more readily with bromine to produce tribromophenol (reaction 3). Essentially, the phenol served to lengthen the time taken for the bromine to react with the indicator. Otherwise, the bromine-bromate reaction, which I am calculating the activation energy for, would complete too quickly to be measured.Bromine is in excess in this reaction, so when all the phenol has reacted, the remaining bromine reacts very quickly with methyl red; the solution turns colorless, indicating the endpoint of the reactions.Finding the rate constantSubstanceConcentration(mol dm-3)Volume (cm3 1)

C6H5OH0.0110

Bromide/bromate mixture110

H2SO40.55

Table 2: Concentrations and volumes of reagentsThe activation energy of a reaction can be determined using the Arrhenius equation: K is the rate constant, A is the pre-exponential factor (representing frequency of particle collisions), Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. A is almost completely independent of temperature, so it is assumed that A is the same for each reaction regardless of temperature.The rate constant can be derived from the rate expression, which in turn is derived from the chemical equation. The chemical equation and rate equation for the reaction between bromide and bromate are as follows:BrO3- + 5Br- + 6H+ -> 3Br2 + 3H2OThe order of the bromide-bromate reaction are first order with respect to bromate, first order with respect to bromide, and second order with respect to H+ (Capriola, 2015). Thus, the rate expression can be written:Rate of reaction = k [BrO3-] [Br-] [H+]2

Rate = 1/time taken, so:Temperature (C 1)Time (s 1)Rate of reaction(s-1 )

259190.001088

353690.002710

451440.006944

55590.016949

65410.024390

75200.050000

Table 3: Time and rate of reaction at each temperatureThe rate constant of a reaction is dependent on temperature, so k will be different at every temperature. k is calculated in Table 4 using the aforementioned rate expression.Temperature(C 1)Rate of reaction(s-1 )kmol-3 dm-9 s-1

250.0010880.001088 0.00435

350.0027100.002710 0.01084

450.0069440.006944 0.02778

550.0169490.016949 0.06780

650.0243900.024390 0.09756

750.0500000.050000 0.20000

Table 4: Rate of reaction, temperature, and kTemperature(C 1)1/T (temperature)(1/K)Rate constant (k)(mol-3 dm-9 s-1)ln k(mol-3 dm-9 s-1)

251 (25 + 273) = 0.003360.001088 0.00435-5.43758

351 (35 + 273) = 0.003250.002710 0.01084-4.52451

451 (45 + 273) = 0.003140.006944 0.02778-3.58344

551 (55 + 273) = 0.003050.016949 0.06780-2.69119

651 (65 + 273) = 0.002960.024390 0.09756-2.32729

751 (75 + 273) = 0.002870.050000 0.20000-1.60944

Table 5: Calculating 1/T and ln kThe Arrhenius equation can be re-arranged to give the following:

R is a constant, and A is assumed to be temperature independent. Thus, graphing ln k against 1/T should give a linear plot.

The gradient of the line should be , and can be calculated using two points on the graph, (x1, y1) and (x2, y2):

DiscussionThe literature value for the activation energy of this reaction was found to be 52.4 kJ mol-1. Thus, the percentage error in the calculated value is:

An error of 26.1% is quite large, which means it is unlikely to be caused merely by random errors. It is more likely that systematic errors in the experimental methodology resulted in the large percentage error. This will be discussed in the evaluation section.In the analysis, a graph of ln k against 1/T had a linear line of best fit with a negative gradient. The correlation coefficient was calculated to be 0.9911, which is very close to 1, showing a very strong correlation. Mathematically, this trend shows that the rate constant increases with temperature.This is in accordance with kinetic molecular theory, which states that Kelvin temperature of a substance is proportional to the average kinetic energy of particles in the substance. If particles have greater average kinetic energy, a greater proportion of particles will have the energy necessary to initiate the reaction (overcome the activation energy barrier), so a greater proportion of particles will exceed the activation energy, increasing the rate of reaction. This is in line with the negative gradient of the graph of ln k against 1/T.EvaluationLimitationEffectImprovement

Plot of ln k against 1/T was not completely linear due to random errors in recorded data.The calculation of the gradient may not be accurate, leading to an inaccurate Ea valueUse technology to plot a line of best fit, and use its gradient to calculate activation energy.

Assumed that rate of reaction of bromination of phenol is independent of temperature even though it is also part of the rate expressionBromide/bromate rate of reaction values less accurate, calculation of the gradient and Ea value affectedConduct experiments at same temperatures, but repeat for varying concentration of reagents and average the results to reduce the significance of any errors

Difficult to determine when endpoint of reactionRecorded time taken for each reaction to complete may be shorter or longer than it should have been, affecting the calculated rate of reaction, gradient, and thus Ea valueRun a trial ahead of time and allow sufficient time for it to react completely. Use color of solution as baseline to determine endpoint for other reactions.

Lids of water baths had to be kept open while monitoring the reaction in the flasks.The temperature of the water baths and thus the solutions may have been lower than recorded, making 1/T values bigger than expected. This would make the calculated Ea value bigger than it should have beenInsulate the solution flasks to reduce heat loss.

ConclusionThe aim of this experiment was to calculate a value for the activation energy of the bromide-bromate reaction. This was successfully done using empirical data to determine the time taken for the reaction to complete at different temperatures and then calculating rate of reaction to determine the rate constant, which was in turn used to calculate the activation energy. Using the Arrhenius equation, the activation energy was determined to be approximately 66.1 kJ mol-1, which was 26.1% away from the literature value of 52.4 kJ mol-1.http://adamcap.com/schoolwork/the-kinetics-of-the-bromate-bromide-reaction/