ln k =

where

k = rate constant

A = Arrhenius constant

E = activation energy

R = Universal gas constant = 8.31 J k-1 mol-1

T = temperature in Kelvin

This logarithmic form of the Arrhenius equation resembles a linear function in the form y = mx + b. The corresponding parts can be summarized as follow:

y m x b

Since = m, the activation energy can be determined by multiplying the gradient of the linear line of best fit on the graph above by the universal gas constant and -1. This is shown as follows:

= -6368.5

-6368.5 8.31 -1 = 52900 Joules per mole (3sf)= 52.9 kilojoules per mole

Where the gradient is measured over the range of 0.00310~0.00330 K-1.

Uncertainties

As with any experiment, uncertainties existed throughout this investigation.

There are many sources of uncertainties. Firstly, the solutions used in this study were prepared by lab equipments such as measuring cylinders and mass balance, which all have degrees of accuracy associated with them (for example, a mass balance’s accuracy is g±0.001). The burette used for measuring the solution’s quantity also had an associated uncertainty, which was ml±0.05. Lastly, uncertainties could be found in data collection. This investigation required the experimenter to determine the time of colour change and to press the stopwatch. The uncertainties are in the experimenter’s subjective view of when the colour had changed and the time taken for the experimenter to press the stopwatch after he sees a colour change. However, it is assumed for this investigation that the uncertainty in time is ±1 second.

Assuming that uncertainties for the Universal Gas Constant, R, and Arrhenius’ Constant, A, are zero, and taking the values associated with the median temperature of 313Kelvin we are left with the following limits of accuracies:

Time = ±1

OR

To calculate the uncertainty of ln k, Time for the median temperature, 76 seconds, is taken.

Thus, it can be seen that the uncertainty for ln k is approximately ±0.01 or 0.231%

Calculating the overall uncertainty

The Arrhenius equation can be rearranged as follows:

Since R and ln A are assumed to have zero uncertainty, the overall uncertainty can be calculated as follows:

Uncertainty of T + uncertainty of ln k = 1.32% + 0.231% = 1.55%

Overall uncertainty =

Therefore, the activation energy is as follows:

52.9kJ mol-1±0.820

Conclusion

By using the experimental data and the Arrhenius equation, the activation energy for the reduction of peroxodisulphate ions, S2O82-(aq) by iodide ions, I-(aq) in a clock reaction is found to be approximately 52.9kJ mol-1±0.820. Since the R2 value is close to 1, it suggests that the calculated Ea value is fairly reliable.

The data also corresponds well to general literature values. Although literature data on this type of experiment could not be found, results from the following reaction:

2HI(g) H2(g) + I2(g)

can be used too^{}. The data is shown below:

By plotting 1/T against ln k, a similar graph to that of this experiment can be drawn:

By comparing Graph 1 and Graph 2 it can be observed that the data from this experiment corresponds closely to literature value in that the points in Graph 1 are almost collinear like those in Graph 2.

Thus, one can conclude by referring to the R2 and literature value that the activation energy found in this experiment is fairly accurate.

Evaluation

Although this experiment attempts to control the variables which may affect the results, the method leaves room for improvements. The clock was stopped when the observer could see a colour change in the mixture. However, this colour change was gradual, and this was especially true when the solutions were under lower temperatures such as 30℃ and 35℃. A way to improve the accuracy in data collection is to use greater concentrations of solutions so that the change in colour would be more instantaneous. However, for the purpose of this investigation the accuracy of the time recorded was assumed to be approximately ±1 second.

An improvement that can be made to the method is in the way the solutions are mixed together. In this experiment the two solutions are mixed manually. Although the way in which they were mixed was kept as constant as possible, a better method can be adopted to ensure that all the mixing is done uniformly. For example, a magnetic stirrer can be used in place of manual mixing – one can control the intensity and speed at which the solutions are mixed in this way.

One way to develop this experiment further is to investigate in the effect of catalysts such as Fe2+ and Fe3+. Catalysts generally lower the activation energy, so it would be interesting to investigate in how Fe2+ and Fe3+ affect this particular reaction.

Eileen Ramsden (2000). A-Level Chemistry. 4th ed. London: Nelson Thornes. 169.