Arrhenius equation
The Arrhenius equation is a fundamental mathematical formula in physical chemistry that describes the relationship between temperature and the rate of chemical reactions. Developed by Swedish chemist Svante Arrhenius in the late 19th century, the equation helps to predict how quickly a reaction will occur based on the activation energy required and the temperature of the substances involved. Essentially, as temperature increases, so does the kinetic constant, leading to faster reaction rates. This principle has practical applications in various industries, including food preparation and pharmaceuticals, where understanding the effects of temperature can significantly influence product safety and quality.
For instance, the Arrhenius equation is indirectly applied by home cooks and chefs when they adjust cooking times and temperatures to achieve desired food textures and flavors. In commercial settings, it allows food manufacturers to determine shelf life and appropriate storage conditions, while pharmaceutical companies use it to ensure that drugs remain effective within their labeled expiration dates. Overall, the Arrhenius equation provides a scientific basis for the effects of temperature on chemical reactions, enabling better control and predictability in both everyday cooking and industrial processes.
Arrhenius equation
The Arrhenius equation is a mathematical formula used to determine the relationship between temperature and how quickly a chemical reaction occurs. It is one of the most significant equations in the science of physical chemistry. The equation is useful because it can determine how fast an object or substance will break down based on the temperature around it; if the effect of temperature on an object or substance is known, the equation provides a way to determine how quickly it will change at various temperatures.
Calculating the speed of a reaction relative to temperature has many applications in industry, particularly in food preparation and storage and in pharmaceuticals. In addition, while home cooks and chefs do not generally use the equation itself, the concept and calculations behind it are the reasons food is refrigerated to prevent spoiling and heated in various ways and for certain lengths of time to change texture, taste, etc.
Origins
The equation was proposed at the end of the nineteenth century by Swedish chemist Svante Arrhenius (1859 – 1927). Arrhenius is also credited with being the first scientist to ask if the temperature of the ground on Earth was affected by heat-absorbing gases in the atmosphere above the planet—the origins of the global climate change theory. The equation that bears his name was part of his early research into the effects of temperature on chemical reaction.
People had known for some time that temperature affected how things changed; for example, food spoiled more rapidly in warm temperatures, while cold temperatures affected some things to make them move more slowly, such as the difference between pouring warm or refrigerated maple syrup. In 1899, Arrhenius created a mathematical equation that allows the calculation of the rate constant by determining the activation energy required for the chemical reaction or change and the temperature involved in the reaction.
Explanation
Chemical reactions take place when two or more molecules come close enough to each other to interact. These interactions, called collisions, interrupt the bonds that hold the molecules together and allow new bonds to form. However, not all such collisions are equal in generating new bonds. Just as two cars colliding at slow speeds will cause less breakdown and change to the vehicles than a high-speed collision, so too does the speed of a molecular collision affect how the bonds break down and generate change. The energy required for a reaction is called activation energy. Heat is a catalyst and an accelerator, increasing the activation energy and causing the molecules to move faster and collide with more force. Therefore, reactions that take place at higher temperatures take place more quickly and with greater force.
Importance
Scientists in Arrhenius's time knew that heat could increase reactions. A 10 degree difference in temperature approximately doubles the speed with which reactions occur. Arrhenius's equation provides a way to accurately predict the speed with which reactions occur at different temperatures by calculating the effects an increase in activation energy has on the average kinetic energy, or the energy generated by the motion of an object or its molecules. It also allows for the effects of other factors, such as the rate at which the molecules involved move with sufficient force and direction to facilitate a collision.
The ability to quantify the effects of temperature on a chemical reaction also provides evidence that these reactions occur consistently and allows for them to be controlled through temperature adjustments. This is of great importance to anyone who prepares food. Preparing food by cooking is essentially accelerating spoilage in a controlled way. Recipes that provide information on the time and temperature at which food should be cooked are applying the concepts of the Arrhenius equation, which establish how long it will take for the chemical reactions that result in cooked or baked food to be completed. Likewise, cold temperatures generated by refrigeration and freezing slow the chemical reactions that lead to spoiling and allow for longer storage of foods.
Applications
Home cooks and chefs usually apply the principles behind the Arrhenius equation without actually doing the calculations. The equation is very important to commercial food producers, however, and is used in industrial settings to calculate the shelf life of food products. Food manufacturers are able to calculate the effect of heat and/or refrigeration on the chemical reactions that cause food to spoil or go stale. This enables them to determine the shelf life of a product after it is made and provide "use by" or "sell by" dates to guide consumers.
Pharmaceutical manufacturers use the equation to determine how long a drug will remain viable, or able to act in the body in the way it is intended. Temperatures at either extreme of heat and cold can affect the ability of a drug to work as it is expected to. The Arrhenius equation allows manufacturers to project how long a drug will remain effective at various temperatures. They can then predict the shelf life and provide an expiration date so consumers can have confidence that the product will perform as expected. The equation is also behind the safety information sometimes found on medications providing guidelines for storage. Arrhenius's equation can be used to determine whether extreme heat or cold will have such a significant and detrimental effect on the effectiveness of the product that it should be stored at a specific temperature.
Bibliography
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"Arrhenius Model: Believe It or Not, You Use It All the Time … and So Does Martha Stewart." Apex Ridge Reliability. Apex Ridge Reliability. 27 Jan. 2016. Web. 1 Feb. 2016. http://apexridge.com/arrhenius-model-believe-it-or-not-you-use-it-all-the-time-and-so-does-martha-stewart/
Del Mundo, Guenevieve, et al. "Arrhenius Equation." University of California–Davis Chemwiki. UC Davis ChemWiki. Web. 1 Feb. 2016. http://chemwiki.ucdavis.edu/Physical‗Chemistry/Kinetics/Modeling‗Reaction‗Kinetics/Temperature‗Dependence‗of‗Reaction‗Rates/The‗Arrhenius‗Law/Arrhenius‗Equation
Duncan, Michelle, PhD. and Irene Zaretsky, MS. "Do the Math for Shelf Life." Pharmaceutical Formulation & Quantity. Volume 13, Number 3. April/May 2011. PDF. 1 Feb. 2016. Available online at http://www.baxterbiopharmasolutions.com/pdf/920829-00-pfq-aprmay-2011-ep.pdf
Graham, Steve. "Svante Arrhenius (1859 – 1927)." Earth Observatory. NASA Goddard Space Flight Center. 18 Jan. 2000. Web. 1 Feb. 2016. http://earthobservatory.nasa.gov/Features/Arrhenius/