## Graphing Example 4

This is a plot of the rate constant for the thermal degradation of ascorbic acid (vitamin C) as a function of temperature. The concept of a rate constant is typically taught in General Chemistry II or in Calculus II. But regardless of whether fitting a line to the data and getting the slope makes sense, it can still be done. The data does appear to be linear and you can press the “Best-Fit Line" button to verify that it is linear.

But what does the slope mean? Yes, it states the relationship between the x and y data which means the relationship between the rate constant and the temperature. If you look back at the first graphing example, you may notice that the slope of the best-fit line is equal to the density of the solution (water, in that case). Is there any other information that we can get from this data?

 Temperature (°C) Rate Constant (min-1) 70 0.00762 80 0.00875 90 0.01198 95 0.01313

Karhan, M., Aksu, M., Tetik, N., Turhan, I., "Kinetic Modeling of Anaerobic Thermal Degradation of Ascorbic Acid in Rose Hip (Rosa Canina L) Pulp", Journal of Food Quality, 2004, 27, p311.

Uses the JSXGraph JavaScript libraries.

Without going into the reasons for the data transformations (see the Arrhenius equation), I’ll take the reciprocal of the absolute temperature and the natural logarithm of the rate constant and again graph the data. The slope can then be used to calculate the activation energy for this reaction.

Now this is a more advanced graphing concept than the previous examples and at this level of instruction you won’t be expected to "magically" come up with some transformation unless we’ve discussed it.

 1/Temperature (K-1) ln(Rate Constant) 0.002914 -4.877 0.002832 -4.739 0.002754 -4.425 0.002716 -4.333
Uses the JSXGraph JavaScript libraries.