How to Calculate Activation Energy

How to Calculate Activation Energy Activation energy is the amount of energy that needs to be supplied in order for a chemical reaction to proceed. The example problem below demonstrates how to determine the activation energy of a reaction from reaction rate constants at different temperatures. Activation Energy Problem A second-order reaction was observed. The  reaction rate constant at three degrees Celsius was found to be 8.9 x 10-3 L/mol and 7.1 x 10-2 L/mol at 35 degrees Celsius. What is the activation energy of this reaction? Solution The  activation energy can be determined using the equation:ln(k2/k1) Ea/R x (1/T1 - 1/T2)whereEa the activation energy of the reaction in J/molR the ideal  gas constant 8.3145 J/K ·molT1 and T2 absolute temperatures (in Kelvin)k1 and k2 the reaction rate constants at T1 and T2 Step 1: Convert temperatures from degrees Celsius to KelvinT degrees Celsius 273.15T1 3 273.15T1 276.15 KT2 35 273.15T2 308.15 Kelvin Step 2 - Find Ealn(k2/k1) Ea/R x (1/T1 - 1/T2)ln(7.1 x 10-2/8.9 x 10-3) Ea/8.3145 J/K ·mol x (1/276.15 K - 1/308.15 K)ln(7.98) Ea/8.3145 J/K ·mol x 3.76 x 10-4 K-12.077 Ea(4.52 x 10-5 mol/J)Ea 4.59 x 104 J/molor in kJ/mol, (divide by 1000)Ea 45.9 kJ/mol Answer: The activation energy for this reaction is 4.59 x 104 J/mol or 45.9 kJ/mol. How to Use a Graph to Find Activation Energy Another way to calculate the activation energy of a reaction is to graph ln k (the rate constant) versus 1/T (the inverse of the temperature in Kelvin). The plot will form a straight line expressed by the equation: m - Ea/R where m is the slope of the line, Ea is the activation energy, and R is the ideal gas constant of 8.314 J/mol-K. If you took temperature measurements in Celsius or Fahrenheit, remember to convert them to Kelvin before calculating 1/T and plotting the graph. If you were to make a plot of the energy of the reaction versus the reaction coordinate, the difference between the energy of the reactants and the products would be ΔH, while the excess energy (the part of the curve above that of the products) would be the activation energy. Keep in mind, while most reaction rates increase with temperature, there are some cases where the rate of reaction decreases with temperature. These reactions have negative activation energy. So, while you should expect activation energy to be a positive number, be aware that its possible for it to be negative as well. Who Discovered Activation Energy? Swedish scientist Svante Arrhenius proposed the term activation energy in 1880 to define the minimum energy needed for a set of chemical reactants to interact and form products. In a diagram, activation energy is graphed as the height of an energy barrier between two minimum points of potential energy. The minimum points are the energies of the stable reactants and products. Even exothermic reactions, such as burning a candle, require energy input. In the case of combustion, a lit match or extreme heat starts the reaction. From there, the heat evolved from the reaction supplies the energy to make it self-sustaining.

The Permian-Triassic Extinction Event

The Permian-Triassic Extinction Event The Cretaceous-Tertiary (K/T) Extinctionthe global cataclysm that killed the dinosaurs 65 million years agogets all the press, but the fact is that the mother of all global extinctions was the Permian-Triassic (P/T) Event that transpired about 250 million years ago, at the end of the Permian period. Within the space of a million years or so, over 90 percent of the earths marine organisms were rendered extinct, along with more than 70 percent of their terrestrial counterparts. In fact, as far as we know, the P/T Extinction was as close as life has ever come to being completely wiped off the planet, and it had a profound effect on the plants and animals that survived into the ensuing Triassic period. (See a list of the Earths 10 Biggest Mass Extinctions.) Before getting to the causes of the Permian-Triassic Extinction, its worth examining its effects in closer detail. The hardest-hit organisms were marine invertebrates possessing calcified shells, including corals, crinoids and ammonoids, as well as various orders of land-dwelling insects (the only time we know of that insects, usually the hardiest of survivors, have ever succumbed to a mass extinction). Granted, this may not seem very dramatic compared to the 10-ton and 100-ton  dinosaurs that went defunct after the K/T Extinction, but these invertebrates dwelt close to the bottom of the food chain, with disastrous effects for vertebrates higher up the evolutionary ladder. Terrestrial organisms (other than insects) were spared the full brunt of the Permian-Triassic Extinction, only losing two-thirds of their numbers, by species and genera. The end of the Permian period witnessed the extinction of most plus-sized amphibians and sauropsid reptiles (i.e., lizards), as well as the majority of the therapsids, or mammal-like reptiles (the scattered survivors of this group evolved into the first mammals during the ensuing Triassic period). Most anapsid reptiles also disappeared, with the exception of the ancient ancestors of modern turtles and tortoises, like Procolophon. Its uncertain how much of an effect the P/T Extinction had on diapsid reptiles, the family from which crocodiles, pterosaurs and dinosaurs evolved, but clearly a sufficient number of diapsids survived to spawn these three major reptile families millions of years later. The Permian-Triassic Extinction Was a Long, Drawn-Out Event The severity of the Permian-Triassic Extinction stands in stark contrast to the leisurely pace at which it unfolded. We know that the later K/T Extinction was precipitated by the impact of an asteroid on Mexicos Yucatan Peninsula, which spewed millions of tons of dust and ash into the air and led, within a couple of hundred (or couple of thousand) years, to the extinction of dinosaurs, pterosaurs and marine reptiles worldwide. By contrast, the P/T Extinction was much less dramatic; by some estimates, this event actually spanned as much as five million years during the late Permian period. Further complicating our assessment of the P/T Extinction, many types of animals were already on the decline before this cataclysm started in earnest. For example, pelycosaursthe family of prehistoric reptiles best represented by Dimetrodonhad mostly disappeared off the face of the earth by the early Permian period, with a few straggling survivors succumbing millions of years later. The important thing to realize is that not all extinctions at this time can be directly attributed to the P/T Event; the evidence either way is constrained by which animals happen to be preserved in the fossil record. Another important clue, the importance of which has yet to be fully adduced, is that it took an unusually long time for the earth to replenish its previous diversity: for the first couple of million years of the Triassic period, the earth was an arid wasteland, practically devoid of life! What Caused the Permian-Triassic Extinction? Now we come to the million-dollar question: what was the proximate cause of the Great Dying, as the Permian-Triassic Extinction is called by some paleontologists? The slow pace with which the process unfolded points to a variety of interrelated factors, rather than a single, global catastrophe. Scientists have proposed everything from a series of major asteroid strikes (the evidence for which would have been erased by over 200 million years of erosion) to a calamitous change in ocean chemistry, perhaps caused by the sudden release of huge methane deposits (created by decaying microorganisms) from the bottom of the sea floor. The bulk of the recent evidence points to yet another possible culprita series of gigantic volcanic eruptions in the region of Pangea that today corresponds to modern-day eastern Russia (i.e., Siberia) and northern China. According to this theory, these eruptions released a huge amount of carbon dioxide into the earths atmosphere, which gradually leached down into the oceans. The disastrous effects were threefold: acidification of the water, global warming, and (most important of all) a drastic reduction in atmospheric and marine oxygen levels, which resulted in the slow asphyxiation of most marine organisms and many terrestrial ones. Could a disaster on the scale of the Permian-Triassic Extinction ever happen again? It may well be happening right now, but in super-slow-motion: the levels of carbon dioxide in the earths atmosphere are indisputably increasing, thanks partly to our burning of fossil fuels, and life in the oceans is beginning to be affected as well (as witness the crises facing coral reef communities around the world). Its unlikely that global warming will cause human beings to go extinct anytime soon, but the prospects are less sanguine for the rest of the plants and animals with which we share the planet!