Gives us the following equation: ln(c/t) = + ln A
Or ln t = +ln e – ln A
As both ln c and in ln A are contants, this is the equation of a straight line. Experiment data can thus be used to generate this straight line and use it to calculate activation energy.
Hypothesis: As the temperature increases (with the concentration kept at a constant) the rate of the reaction increases, as the temperature decreases (with the concentration kept at a constant) the rate of the reaction decreases.
Procedure: This experiment was done in pairs. First 10 cm3 of 0.01 mol dm-3 of a bromide/bromated (V) solution was measured with a measuring cylinder and then poured into a boiling tube. Then 4 drops of methyl red were added to the boiling tube with the bromide/bromated (V) solution. Another boiling tube was taken and filled with 5 cm3 of 0.5 mol dm-3 of sulphuric acid (H2SO4). Several water baths were made, with temperatures ranging from 0°C-65°C. The boiling tubes were then placed in one of these water baths. Once the contents of the boiling tube were equilibrated to the temperate of the water, the contents of the boiling tubes were mixed together very quickly. As one partner mixed the two solutions together, the other started a timer simultaneously. The timer was stopped once the colour of the methyl red disappeared. This experiment was done in baths of 0°C, 15°C, 20.5°C(room temperature), 35°C, and 65°C.
Results:
The following results were obtained from the experiment stated above:
Table 1: Results of time taken for reaction to reach end point at different temperatures and additional observations
If one wishes to obtain the activation energy of this reaction graphically, more data is required. This data is summarized in the following table.
Table 2: Data needed for calculation of activation energy
With the data above, the following graph can be made to calculate the activation energy of the reaction.
Graph 1: 1/Absolute temperature vs. Natural log of rate of reaction
Data processing: In the above graph the experimental data is plotted as well as a best fit line. In order to calculate the reaction’s activation energy, the gradient must be calculated, a gradient for the best fit line is already calculated, however I shall also calculate the gradient for the experimental data as well.
Gradient = or
Gradient = = -9585 or -8045 (best fit line)
R = 8.31 −1 −1
- EA = gradient R
= -9585 (or -8045) 8.31
= -79651.35 (or -66853.95)
EA = 79651.35 (or 66853.95) J moles-1
EA = 79.65135 (or 66.85395) kJ moles-1→79.65 (or 66.85) kJ moles-1
Analysis: The reaction that took place in this experiment was between bromate and bromide ions in the presence of an acid, this reaction is summarized by the following equation:
KBrO3 + 5KBr + 3H2SO4 3K2SO4 + 3H2O + 3Br2
In this reaction, the potassium and sulphate ions are not affected and therefore are called “spectator” ions. The ionic reaction is summarized by the following ionic equation:
5Br− + BrO3− + 6H+ 3Br2 + 3H2O
The rate of this reaction is measured by measuring the rate at which bromine is produced. This is done by adding a limited amount of phenol and the dye methyl red to the reaction mixture, the bromine reacts very rapidly with the phenol to form tribromophenol. This is expressed in the following equation:
Once all the phenol has reacted, the excess of Br2 is released by the reaction. The Br2 then oxidises the methyl red causing the red colour of the mixture to disappear. Thus, if the time taken (t) for the red colour to disappear is measured from the start of the reaction then this will closely correspond to the amount of time taken for the reaction to produce enough bromine to react with a known quantity of phenol.
Since the concentrations of the reactants and the quantity of phenol added are set at particular values, the rate of reaction solely depends on the temperature of the solutions. Thus the value of the rate constant at a given temperature is proportional to the reciprocal value of time taken for the reaction to reach “end point” also known as the rate of reaction (t-1). Thus by measuring t at various temperatures, a value for the activation energy (Ea) for the reaction can be measured.
The reason why the rate of reaction of reaction increases as temperature increases is because for a reaction to take place, molecules must collide with other molecules with sufficient energy for the reaction to take place (collision theory). These molecules will only react if they have enough energy. When the reactants are heated, the energy levels of the molecules of these reactants are increased as well, enabling the molecules to move faster (kinetic theory). This can be observed in the Maxwell-Botlzmann curve.
Fig 1: Maxwell-Boltzmann distribution curves for particles at 273 and 283 K.
The diagram above shows that at higher temperatures, more particles have higher values for kinetic energy and the peak of the curve shifts to the right. At higher temperatures there is an increase in collision frequency due to the higher energy levels, and there is an increase in the number of collisions involving particles with the necessary kinetic energy to overcome the threshold value of the activation energy.
Conclusion:
It can be concluded that as the temperature increases the rate of reaction is increased. This is due to more kinetic energy in the particles and more successful collisions. We also see that when the temperature is increased from 293.5 K to 306.5 K, almost a 10 K difference the time taken for the reaction goes from 196 seconds to 71 seconds respectively. This shows the reaction is nearly doubled for approximately every 10 K, this is seen in the following calculations:
A raise in 13 K gives a percentage increase of 276%.
It can also be concluded that the activation energy for this experiment is ≈79.65 kJ moles-1
Evaluation:
This experiment included several uncertainties. A few of these errors are described below along with some possible solutions: