A R R H E N I U S
C A L C U L A T I O N

A Java applet that performs an Arrhenius calculation. Using rate constants at several temperatures as input, the activation energy and entropy is calculated. Also calculates predicted rate and percent loss at a given temperature and time.

Directions
Enter the temperatures (in degrees Kelvin) and the corresponding rate constants in the cells at the top. [In some browsers, you may need to put a non-numeric character (such as the letter 'a') in the first blank cell after the data to get the browser to recognize the right number of data points.] The rate constants may be in any units. If you are using a time unit other than seconds, then you can enter a conversion factor in the Time Conversion cell. For instance, if your rates are in terms of hours instead of seconds, then enter 3600 in the Time Conversion cell. This is only necessary if you are interested in the Activation Entropy result; it has no bearing on the Activation Energy result.

Press the first Calculate button. The program fits the data to the following equation as a straight line with y values of ln k and x values of 1/T:

ln k = A + E / RT

A is listed as the pre-exponential factor, and E/R is listed as the slope. The slope is then multiplied by the gas constant (R = 8.314 J/mol K) to give the activation energy, -E. Typical values for the activation energy run from 20 to 150 kJ/mol. Low values are often observed for oxidation reactions, while higher values are seen for hydrolyses. Higher values of the activation energy also indicate a greater temperature dependence of the reaction rate.

In the Java Console and the status display the correlation coefficient is shown. The closer the absolute value of the coefficient is to 1, the better the fit.

The pre-exponential factor, A, is used to calculate the activation entropy, S, from the following equation:

A = e^S/R k_B T e / h

where k_B is the Boltzmann constant (1.38 x 10^-23 J/K), h is Planck's constant (6.626 x 10^-34 J s) and T is the average temperature of the data.

After the above calculation is done, the reaction rate at a specified temperature may be calculated, along with extent of reaction at a specified time. Enter the New Temperature (in degrees Kelvin) and New Time (in the same units as were used for the kinetics data), and then press the second calculate button.

The reaction rate, k, is calculated from the first equation above. The extent of reaction is calculated from the following equation, assuming a first-order reaction:

C = e^-kt

In the cell the extent of reaction is given as the loss relative to the initial concentration. The amount remaining (as a fractional value) is given in the Java console.

An example, taken from The Physical Basis of Organic Chemistry, Howard Maskill, Oxford University Press (1985), p. 232, for the first-order gas-phase isomerization of bicyclo[4.2.0]oct-7-ene:

	T (K)	k (s-1)
1	508.7	0.376 E-4
2	529.1	1.93 E-4
3	558.1	16.6 E-4

The slope is calculated to be -21,800 and the pre-exponential factor is 1.4 x 10¹⁴. The activation energy is given as 181 kJ/mol, while the activation entropy is 13 J/K mol. For the three points, the correlation coefficient is 0.99999.

At 540.3 K, the rate constant is 4.6 x 10^-4, and at 100 seconds, 4.5% of the starting product has been converted.

The Source Code
The Class Code