Activation energy FIELDS OF STUDY. Physical Chemistry; Inorganic Chemistry; Biochemistry SUMMARY

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1 A Ativation energy FIELDS OF STUDY Physial Chemistry; Inorgani Chemistry; Biohemistry SUMMARY The ativation energy of a proess is defined, and its importane in hemial proesses is elaborated. Ativation energy is a widely variable quantity in different reations but is nevertheless harateristi of any speifi reation proess. PRINCIPAL TERMS Arrhenius equation: a mathematial funtion that relates the rate of a reation to the energy required to initiate the reation and the absolute temperature at whih it is arried out. atalyst: a hemial speies that initiates or speeds up a hemial reation but is not itself onsumed in the reation. hemial reation: a proess in whih the moleules of two or more hemial speies interat with eah other in a way that auses the eletrons in the bonds between atoms to be rearranged, resulting: in hanges to the hemial identities of the materials. reation rate: how muh of a partiular reation or reation step ours per unit time. transition state: an unstable struture formed during a hemial reation at the peak of its potential energy that annot be isolated and ultimately breaks down, either forming the produts of the reation or reverting bak to the original reatants. Ativation Energy in Chemial Reations Ativation energy an be thought of as a barrier that the reatants in a hemial reation must overome if the reation is to proeed to the formation of produts. The moleules that are involved must rearrange to form either a transition state or an intermediate that is higher in energy than the starting materials. An intermediate is a stable hemial struture formed during a reation proess that an often be aptured and isolated by hemial means. One this struture is formed, the reation proess an either progress to form produts or revert bak to the original reatants. Ativation energy is the energy required for a speifi hemial reation to our. In a reation, two reatant moleules ontat eah other with the energy of their ambient states.(the ambient state of a material an be thought of as its default state the state it takes at one atmosphere of pressure and what is ommonly onsidered to be room temperature.) In the ase of a spontaneous reation, the energy of the ollision is suffiient to initiate the formation of the transition state or intermediate. In a nonspontaneous reation, the energy of the moleular ollision is not suffiient, and the two moleules will not interat. The input of some additional energy is required to drive the two moleules together so that the transition state or intermediate is formed and the reation an proeed. The energy released in the transformation of reatants into produts is generally suffiient to drive the reations of other moleules in the reation mixture. Another way to look at ativation energy is to think of it as the minimum amount of energy that two interating moleules must gain in order to weaken bonds between atoms in both moleules so that those bonds an be rearranged. Sine hemial reations are essentially proesses of breaking and making bonds, having suffiient energy to overome the strength of the appropriate bonds is essential if there is to be any reation between the two moleules. Ativation Energy and Reation Rates Reation rates an be related diretly to their ativation energies. This relationship is defined by the Arrhenius equation, formulated in 884 by the Swedish sientist Svante Arrhenius (859 97), who reeived the Nobel Prize in Chemistry in 903.The

2 Ativation energy Priniples of Biology Potential Energy Arrhenius equation relates the rate onstant of a reation to its ativation energy and the absolute temperature and has the form A+B ACTIVATION ENERGY DIAGRAM Reation Progress k = Ae E/RT where k is the rate onstant for the reation or proess; A is the pre-exponential fator, also known in some ases as the frequeny fator; E (or E a ) is the ativation energy for the reation or proess; R is the gas onstant; T is the absolute temperature; and the mathematial onstant e is the base of the natural logarithm, so that the natural logarithm (ln) of e is equal to.the Arrhenius equation has been found to apply not only to hemial reations but to physial proesses as well. T he relationship an be most learly seen by plotting experimentally determined logarithmi values of k against the inverse of the absolute temperature, /T. This results in a straight line plot, from whih the ativation energy of the reation or proess an be alulated. The pre-exponential fator A is identified as the value that the speifi rate onstant k would have if the ativation energy E were zero (a spontaneous reation).in that speial ase, the exponent E/RT would also be equal to zero, making e E/RT equal and thus ausing the value of k to be equal to A. For different speifi reations, the value of A ranges over several orders of magnitude, but Ativation Energy (E a ) C+D the rate onstant k is determined almost solely by the value of e E/ RT, whih an range over several hundred orders of magnitude, depending on the relative values of E and T. The ourse of a reation depends on the relative differene between the energy of the reatants and that of the produts. The greater this differene is, the more impetus there is for the reation to proeed to the formation of produts. This is typially illustrated in a plot of energy versus the reation oordinate, a symboli representation of the progress of a reation. In the plot, the energy level of the reatants, on the left, is either higher or lower than that of the produts, on the right. In between, a urved line rises from the energy level of the reatants to a maximum value before falling to the energy level of the produts. The differene between the energy level of the reatants and this peak energy value represents the ativation energy for the reation, while the differene between the energy levels of the reatants and the produts represents the energy released in the reation, also alled its enthalpy. The speifi rate of any individual reation is determined by its ativation energy. However, in mass quantities, the energy differenes between reatants and produts in the system also play a role. This an be understood by onsidering the Boltzmann fration e E/RT, whih desribes the fration of moleules in the system having energy greater than E. As energy is released from several reations, the fration of moleules present at any given time with suffiient energy to reat inreases, and more reations an our in any given time period. Eah reation requires the same ativation energy, and the amount of energy that is available in the system to permit reations to our may be anything from barely enough to exessive. The ativation energy of a reation an be greatly redued by the inlusion of a atalyst, a material that takes part in the reation mehanism but is not onsumed in the reation. Catalysts funtion by forming an ativated omplex with the reatants, typially

3 Priniples of Biology Ativation energy Unatalyzed Ativation Energy Unatalyzed Reation Catalyzed Reation (E a ) Potential Energy A+B CATALYZED ACTIVATION ENERGY Reation Progress onstraining the reatant moleules in an orientation that they would otherwise have to ahieve through ollision with eah other. This redues the energy neessary to ahieve that partiular orientation that is, the ativation energy so that the reation an proeed. When the reatant moleules are onstrained in the ativated omplex with the atalyst, bonds between ertain atoms are weakened and the orientations of atomi and moleular orbitals that must interat are often brought into the proper alignment, or trajetory, for the new bonds to form between atoms. Ativation Energy in Ation The ativation energy of a reation an range from exeedingly small to very large. Two examples serve to illustrate this point. For the first, onsider the addition of two parts hydrogen gas (H ) to one part oxygen gas (O ).This is an explosive mixture of gases, yet the two mixed gases are quite happy to oexist quietly in the same ontainer, no matter how muh is present. The introdution of an initiator suh as an eletrial spark, however, results in an almost instantaneous reation to form water (H O), aompanied by the release of a great deal of energy. The ativation energy of the reation between hydrogen and oxygen is very low, and the amount of energy released by one reation is more than Z (Ea) Catalyzed Ativation Energy C+D suffiient to drive many instanes of the reation in the gas mixture, with eah subsequent ourrene releasing an equal amount of energy as the enthalpy of reation. The seond example is the soalled thermite reation, in whih iron oxide and aluminum metal reat to produe aluminum oxide and iron metal. This is a spetaular reation often demonstrated for hemistry exhibitions. Beause the ativation energy of the thermite reation is very high, the reation is very diffiult to initiate and must typially be ignited by a burning piee of magnesium metal; one it has begun, however, it is essentially impossible to stop it due to the amount of energy that is released. Typially, the iron metal falls out of the reation mixture as a white-hot liquid. Ativation Energy in Biologial Systems Ativation energy applies to biohemial proesses as well as to physial proesses. The hirping of rikets, for example, is dependent on temperature in a manner that is in omplete aord with the Arrhenius equation. In biologial systems, the ativation energy of proesses is made a great deal lower by the atalyti ation of protein moleules alled enzymes. Enzymes have well-defined threedimensional strutural shapes that allow them to oordinate with other moleules in speifi ways, rather like the way a key works with a lok. The oordination normally alters the three-dimensional shape of the substrate moleule or otherwise interats with it so that speifi bonds are weakened and the moleular geometry is hanged suh that reation is highly favored. Rihard M. Renneboog, MS Further Reading Arnaut, Luís, Sebastião Formosinho, and Hugh Burrows. Chemial Kinetis: From Moleular Struture to Chemial Reativity. Oxford: Elsevier, 007. Print. Bell, erry A. Chemistry: A Projet of the Amerian Chemial Soiety. New York: Freeman, 005.Print. 3

4 Ative transport Priniples of Biology Lafferty, Peter, and ulian Rowe, eds. The Huthinson Ditionary of Siene. nd ed. Oxford: Helion, 998.Print. Masterton, William L., Ceile N. Hurley, and Edward Neth. Chemistry: Priniples and Reations. 7th ed. Belmont: Brooks, 0. Print. Raymond, Kenneth W. General, Organi, and Biologial Chemistry: An Integrated Approah. 4th ed. Hoboken: Wiley, 04.Print. Zumdahl, Steven S., and Susan Zumdahl. Chemistry. 9th ed. Belmont: Brooks Coles, 03. Print. ACTIVATION ENERGY SAMPLE PROBLEM Use the Arrhenius equation to determine the ativation energy at 0 C for a reation having a speifi rate onstant (k) of 0.03 moles per liter per seond and a pre-exponential fator (A) of,303 moles per liter per seond. Use the gas onstant. Answer: R = 8.34 mol K Convert the temperature from degrees Celsius to kelvins, given that K = C : K = = 73.5 The Arrhenius equation is k = Ae E/RT Rearrange the equation using natural logarithmi (ln) relationships: E/ RT ln k = ln A + ln(e ) E ln k = ln A RT E = ln A ln k RT E = RT (lna ln k) Substitute in the values of R (8.34 ), T mol K (temperature), A (pre-exponential fator), and k (rate onstant). Calulate, paying attention to the units throughout: E = RT( ln A ln k) E = ( K)(ln 303 ln 0.03) mol K E = ( K)[7.74 ( 3.77)] mol K E = m ol Ative transport FIELDS OF STUDY Biohemistry; Moleular Biology; Genetis SUMMARY The proess of ative transport is defined, and its importane in biohemial proesses is elaborated. Ative transport is an essential feature of the biohemistry of living systems and helps maintain the neessary onentrations of various biohemial omponents and eletrolytes for the proper funtioning of ellular metabolism. PRINCIPAL TERMS adenosine triphosphate (ATP): a moleule onsisting of adenine, ribose, and a triphosphate hain that is used to transfer the energy needed to arry out numerous ellular proesses. ell membrane: a biologial membrane that forms a semipermeable barrier separating the interior of a ell from the exterior. onentration gradient: the gradual hange in the onentration of solutes in a solution aross a speifi distane. 4

5 Priniples of Biology Ative transport ACTIVE TRANSPORT Outside of Cell ATP ADP +P Inside of Cell diffusion: the proess by whih different partiles, suh as atoms and moleules, gradually beome intermingled due to random motion aused by thermal energy. passive transport: the passage of materials through a membrane with no input of energy required. The Mehanis of Ative Transport In living ells, biohemial proesses transport materials neessary for a properly funtioning metabolism through ell membranes. Passive transport does not require an input of energy to move materials aross ell walls beause it operates in the same diretion as the onentration gradient, moving the materials from an area of high pressure to one of low pressure. Ative transport an be thought of as a shuttle servie for ions and other polar materials that annot pass through a ell membrane by diffusion, a kind of passive transport. Instead, those entities must be physially transported aross membranes by various mehanisms olletively termed pumps. A pump is a type of mediated transport system that funtions to ondut ions, amino aids, gluose, and other polar ompounds through the nonioni lipid bilayer, the highly nonpolar material that makes up the ell wall. Pumps always work against the onentration gradient to move materials out of regions of low onentration and into regions of higher onentration, using energy derived from biohemial reations. The transported material is subsequently used in other biohemial reations that return the energy used during transport. Cell Walls and Lipid Bilayers Long-hain fatty aids are organi moleules whose moleular struture onsists of a single hydroarbon hain terminated by a arboxyli aid 5

6 Ative transport Priniples of Biology funtional group ( COOH). The arboxyl group is highly polar and hydrophili, while the hydroarbon moiety, or portion, of the moleule is very nonpolar and hydrophobi. Carboxyli aids are onverted to esters by enzyme-mediated reations with alohols. In an ester, the arboxyl funtional group retains the highly polar harater that it had in its free arboxyli aid form, giving the longhain esters, alled lipids, a polar-nonpolar struture similar to that of the free arboxyli aids. When arboxyli aids are esterified with glyerol, whih has three hydroxyl ( OH) funtional groups, the resulting triesters are alled triglyerides. Lipids and triglyerides are the prinipal forms in whih long-hain fatty aids are found in biologial systems. The hydroarbon hains and the arboxylbased portions of fatty aids and their esters do not interat with eah other due to their different hydrophiliities that is, the degrees to whih they attrat and interat with water and other polar moleules but they are quite apable of interating with the orresponding portions of other moleules. The hydroarbon hains assoiate preferentially with eah other, as do the arboxyl portions. The basi struture of the lipid bilayer results from the hydroarbon portions of the aids of two layers of suh moleules intermingling and essentially dissolving eah other. The arboxyl funtions on the other ends of the one on either side of the very hydrophobi interior layer. The resulting struture is a lipid bilayer. The walls of all animal ells are formed of lipid bilayers, allowing them to interat with water-based fluids while isolating the sensitive materials and proesses that take plae within eah ell. The fluid inside of eah ell is also water based, whih neessitates some means of transporting vital polar materials from the exterior of the ell to the interior and moving extraneous materials and metabolites in the opposite diretion for elimination. This movement is aomplished by ative transport. Funtions of Ative-Transport Systems Ative-transport systems serve a variety of funtions in the biohemistry of living systems. Their prinipal funtion is to allow the organism to extrat fuels and other essential materials for use in the metaboli funtions that our within ells. This is a very important funtion, and the nature of ative transport allows ells to retain a relatively high onentration of suh materials even when their onentrations outside of the ell are quite low. A seond important funtion of ative-transport systems is to regulate and maintain the organism s metaboli steady state, a balaned state in whih the material and energy that the organism removes from its environment through living funtions is equal to the energy and materials that it returns to the environment through those same funtions. The biohemial proesses of metabolism use energy and materials taken from the environment. Anaboli proesses remove materials from the environment and use energy from reations involving those materials to build and support the life of the organism. Cataboli proesses remove used materials from the organism and return them to the environment, releasing the energy stored in those materials. Ative transport maintains a onstant optimal amount of various inorgani elements within the living ells of an organism. Potassium ions, for example, are essential to the proper funtioning of many intraellular proesses. An ative-transport system produes potassium-ion hannels in ell walls of nerves and musles, inluding the ardia musles. Potassium ions are delivered into the ytoplasm of the ell via these hannels to replae ejeted sodium ions, thus maintaining a onstant ioni onentration within the ell. The system maintains a relatively high onentration of potassium ions in most aerobi ells, between 00 and 50 millimolars (mm), whether they are plant, animal, or mirobial in nature and regardless of the onentration outside of the ells. (A mm solution has a onentration of 0.00 moles per liter.) The potassium ions that are pumped into the ell also serve to maintain the eletri potential aross the ell membrane, a fator that affets the free-energy hange in reations involved in ative-transport systems. Ative Transport in Ation The transfer of ions aross a membrane or against a onentration gradient by ative transport is aompanied by a free-energy hange (ΔG) that an 6

7 Priniples of Biology Ative transport be alulated by one of two equations. The first equation represents the free-energy hange for the transfer of neutral materials against a onentration gradient. This is desribed by the following equations: G = RT ln 8.34 mol K where R is the gas onstant and T is the absolute temperature in kelvins, ln is the natural logarithm funtion, and and are onentrations on either side of the membrane in molars, or moles per liter (M), with being greater than. The seond equation, whih represents the free-energy hange for the transfer of eletrially harged materials, needs to aount for the harge on the material being transported and the differene in eletri potential aross the membrane. The latter is determined by the neutral nature of the lipid bilayer, whih auses it to at as a apaitor, or energy-storage devie, and the presene of harge as maintained by the potassium ions in the ytosol. The free-energy expression for the transport of harged speies aross a ell membrane is given by the following equation: G = RT ln +ZF where Z is the harge on the ion, F is the Faraday onstant (96, oulombs per mole, the eletri harge on one mole of eletrons), and is the differene in eletri potential aross the membrane in volts. ATP and Ative Transport The energy used in ative-transport systems is obtained through enzyme-mediated reations of adenosine triphosphate (ATP). ATP moleules onsist of a moleule of the nuleobase adenine that is bonded to a moleule of ribose sugar, whih in turn is bonded to a triphosphate ion. A magnesium ion oordinates and stabilizes the seond and third segments of the triphosphate moiety. Energy is derived from the struture by the enzymati leavage of the third phosphate segment from the triphosphate moiety, transforming the moleule into adensosine diphosphate (ADP), and it is restored by onatenating, or joining, a third phosphate ion to ADP to re-form ATP. The funtion of musle ells depends on the ative transport of alium ions and sodium ions, a proess termed the alium ion pump or Ca + pump. The alium ion pump works in an organelle of musle ells alled the saroplasmi retiulum and is powered by ATP hydrolysis reations mediated by the enzyme alium adenosine triphosphatase. This proess is ritial to the ontration and relaxation of musle fibers, espeially heart musles. The saroplasmi retiulum is a ell struture that stores and releases alium ions to aid in this ontration and relaxation. In musle ells, the rapid release of alium ions from the saroplasmi retiulum into the ytosol, the ellular fluid outside of the organelles, triggers ontration of the musle, while rapid removal of alium ions from the ytosol and bak into the saroplasmi retiulum triggers relaxation of the musle. The normal onentration of free alium ions in the ytosol is between 0. and 0. miromolar (µm, or 0 6 moles per liter), inreasing when the musle ontrats and returning to the normal value when it relaxes. Rihard M. Renneboog, MS Further Reading Lafferty, Peter, and ulian Rowe, eds. The Huthinson Ditionary of Siene. nd ed. Oxford: Helion, 998. Print. Lehninger, Albert L. Biohemistry: The Moleular Basis of Cell Struture and Funtion. nd ed. New York: Worth, 975. Print. Lodish, Harvey, et al. Moleular Cell Biology. 7th ed. New York: Freeman, 03. Print. Pelzar, Mihael., r., E. C. S. Chan, and Noel R. Krieg. Mirobiology: Conepts and Appliations. New York: MGraw, 993. Print. Reee, ane B., et al. Campbell Biology. 0th ed. San Franiso: Cummings, 03. Print. 7

8 Aging Priniples of Biology ACTIVE TRANSPORT SAMPLE PROBLEM Use the free-energy equation for ative transport against a onentration gradient to determine the free energy assoiated with transporting neutral amino-aid moleules aross a membrane from a onentration of 0 μm to one of 43 μm. Assume normal body temperature of 37 C. Use. Answer: R = 8.34 mol K The materials being transported are eletrially neutral. Therefore, use the equation G = RT ln Convert the temperature from C to K: K = C K = = 30.5 Convert the onentration values from miromolars to molars: = 0 μm = M = M = 43 μm = M = M Substitute in the values of R, T,, and and alulate, paying attention to the units throughout: G = RT ln G = (8.34 )(30.5 K)ln mol K G = mol The free energy of ative transport of neutral amino aids aross a onentration gradient from 0 μm to 43 μm is joules per mole, or.9738 kilojoules per mole. Aging FIELDS OF STUDY Anatomy, ell biology, developmental biology, genetis, neurobiology, pathology, physiology SUMMARY Aging is the proess of progressive and irreversible hange ommon to all living organisms. There are striking similarities in the physial proess of aging among all animal speies. PRINCIPAL TERMS aging: a proess ommon to all living organisms, eventually resulting in death or onlusion of the life yle ognition: ability to pereive or understand death: the essation of all body and brain funtions funtion: ability, apaity, performane life span: length of life from birth to death longevity: length of life Basi Priniples Progressive and irreversible hange has been alled the single ommon property of all aging systems. When hange is reversible or self-maintaining, suh as one would see in a forest, for example, the effets of aging are often not observable. Growth of the forest is evident, but with the right onditions, trees within the forest may grow for hundreds of years in the absene of disease. Certain onditions of the forest system help to regenerate, renew, and reverse hanges that happen within that system. However, in animals some hange is not reversible. The hanges in the ells of the body aumulate over time and result in a steady downward trend. The end point of this trend is the death of the organism. Aging is a normal part of the life yle. This is known to be true beause aging hanges within populations are rather preditable. The hanges assoiated with aging that are seen in all animal speies may our for similar reasons. These may inlude hemial aging, extraellular aging, intraellular aging, and aging of ells. 8