# Reaction Rate Dependence on Temperature and Moisture During Storage

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For chemical reactions and many biological processes in stored dried foods, the reaction rates depend on both the temperature and water activity, the latter determined by the moisture content. This dependence can be visualized in a 3D plot of rate constant-temperature-moisture content values, with their relationship generated with a nested model. It is assumed that the temperature dependence of the isothermal rate constant follows the exponential model, a simpler alternative to the Arrhenius equation, for which the two parameters for moisture dependence follow a similar type of exponential dependence.

Contributed by: Mark D. Normand and Micha Peleg (July 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: rate constant-temperature-moisture content relationship of a hypothetical reaction having low sensitivity to moisture content in the pertinent range

Snapshot 2: rate constant-temperature-moisture content relationship of a hypothetical reaction having high sensitivity to moisture content in the pertinent range

Snapshot 3: rate constant-temperature-moisture content relationship of a hypothetical reaction having low sensitivity to temperature in the pertinent range

Snapshot 4: rate constant-temperature-moisture content relationship of a hypothetical reaction having high sensitivity to temperature in the pertinent range

The temperature effect on the rate of chemical reactions and biological processes in dried foods has been described primarily using the Arrhenius equation, but also by several alternative models [1]. It has been shown that when the rate constant’s temperature dependence follows the Arrhenius equation, it can also be described by the simpler exponential model

,

where

is the temperature in °C,

is the rate at a chosen reference temperature , also in °C and

is a constant having units [2].

Reported isothermal moisture-dependence relationships versus show that within the range pertinent to dried food storage, they resemble those of the temperature [3, 4], in which case they can be described by a similar exponential model, at least as a first-order approximation.

Assuming that the moisture-dependence of the model's temperature parameters and both follow the exponential model, albeit having different parameters, they can be described by

and

,

where

is the moisture content on dry or wet basis,

is a reference moisture content on the same basis as and

, , and are constants characteristic of the food being considered.

Inserting the and terms so defined into the equation produces the four-parameter nested model of the rate constant-temperature-moisture relationship:

.

This Demonstration generates and displays rate constant versus temperature and moisture relationships in the form of 3D plots using the given equation as a model, with the reference temperature and moisture , as well as the , , and parameters and axes ranges entered by sliders. We also calculate and display the numerical value of for and values selected with sliders.

The primary purpose of this Demonstration is to visualize the nested model, not to match that of any specific reaction in a particular food. Therefore, not all the parameter-combinations allowed by the controls necessarily represent real-life scenarios. However, if the model's parameters , , and have been obtained from experimental data by regression, then the Demonstration can be used as a calculator for new and combinations in an appropriate temperature-moisture range.

References

[1] C. S. Barsa, M. D. Normand and M. Peleg, "On Models of the Temperature Effect on the Rate of Chemical Reactions and Biological Processes in Foods," *Food Engineering Reviews*, 4(4), 2012 pp. 191–202. doi:10.1007/s12393-012-9056-x.

[2] M. Peleg, M. D. Normand and M. G. Corradini, "The Arrhenius Equation Revisited," *Critical Reviews in Foods Science and Nutrition*, 52(9), 2012 pp. 830–851. doi:10.1080/10408398.2012.667460.

[3] K. Di Scala and G. Crapiste, "Drying Kinetics and Quality Changes During Drying of Red Peppers," *LWT - Food Science and Technology*, 41(5), 2008 pp. 789–795. doi:10.1016/j.lwt.2007.06.007.

[4] J. Qiu, J.-E. Vuist, R. M. Boom and M. A. I. Schutyser, "Formation and Degradation Kinetics of Organic Acids During Heating and Drying of Concentrated Tomato Juice," *LWT - Food Science and Technology,* 87(1), 2018 pp. 112–121. doi:10.1016/j.lwt.2017.08.081.

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