Explaining Activation Energy & the Arrhenius Equation: Chemical Reaction Roles, Exercises of Biology

An in-depth explanation of activation energy, its significance in chemical reactions, and how it is related to the rate of reactions through the Arrhenius equation. the definition of chemical reactions, reaction rate, and activation energy, as well as the mathematical representation of the Arrhenius equation and its application to various reactions.

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Activation energy
FIELDS OF STUDY
Physical Chemistry; Inorganic Chemistr y; Biochemistry
SUMMARY
The activation energy of a process is defined, and
its importance in chemical processes is elaborated.
Activation energy is a widely variable quantity in dif-
ferent reactions but is nevertheless characteristic of
any specific reaction process.
PRINCIPAL TERMS
Arrhenius equation: a mathematical function
that relates the rate of a reaction to the energy
required to initiate the reaction and the absolute
temperature at which it is carried out.
catalyst: a chemical species that initiates or speeds
up a chemical reaction but is not itself consumed
in the reaction.
chemical reaction: a process in which the mole-
cules of two or more chemical species interact with
each other in a way that causes the electrons in the
bonds between atoms to be rearranged,
resulting: in changes to the chemical identities of
the materials.
reaction rate: how much of a particular reaction or
reaction step occurs per unit time.
transition state: an unstable structure formed
during a chemical reaction at the peak of its poten-
tial energy that cannot be isolated and ultimately
breaks down, either forming the products of the
reaction or reverting back to the original reactants.
Activation Energy in Chemical Reactions
Activation energy can be thought of as a barrier that
the reactants in a chemical reaction must overcome if
the reaction is to proceed to the formation of prod-
ucts. The molecules 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 chemical structure formed
during a reaction process that can often be captured
and isolated by chemical means. Once this structure
is formed, the reaction process can either progress to
form products or revert back to the original reactants.
Activation energy is the energy required for a spe-
cific chemical reaction to occur. In a reaction, two
reactant molecules contact each other with the en-
ergy of their ambient states.(The ambient state of a
material can be thought of as its “default” state—the
state it takes at one atmosphere of pressure and what
is commonly considered to be room temperature.) In
the case of a spontaneous reaction, the energy of the
collision is sufficient to initiate the formation of the
transition state or intermediate. In a nonspontaneous
reaction, the energy of the molecular collision is not
sufficient, and the two molecules will not interact.
The input of some additional energy is required to
drive the two molecules together so that the transi-
tion state or intermediate is formed and the reaction
can proceed. The energy released in the transforma-
tion of reactants into products is generally sufficient
to drive the reactions of other molecules in the reac-
tion mixture.
Another way to look at activation energy is to think
of it as the minimum amount of energy that two inter-
acting molecules must gain in order to weaken bonds
between atoms in both molecules so that those bonds
can be rearranged. Since chemical reactions are es-
sentially processes of breaking and making bonds,
having sufficient energy to overcome the strength of
the appropriate bonds is essential if there is to be any
reaction between the two molecules.
Activation Energy and Reaction Rates
Reaction rates can be related directly to their ac-
tivation energies. This relationship is defined by
the Arrhenius equation, formulated in 1884 by the
Swedish scientist Svante Arrhenius (1859–1927), who
received the Nobel Prize in Chemistry in 1903.The
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Activation energy

FIELDS OF STUDY

Physical Chemistry; Inorganic Chemistry; Biochemistry SUMMARY The activation energy of a process is defined, and its importance in chemical processes is elaborated. Activation energy is a widely variable quantity in dif- ferent reactions but is nevertheless characteristic of any specific reaction process. PRINCIPAL TERMS ƒ Arrhenius equation: a mathematical function that relates the rate of a reaction to the energy required to initiate the reaction and the absolute temperature at which it is carried out. ƒ catalyst: a chemical species that initiates or speeds up a chemical reaction but is not itself consumed in the reaction. ƒ chemical reaction: a process in which the mole- cules of two or more chemical species interact with each other in a way that causes the electrons in the bonds between atoms to be rearranged, ƒ resulting: in changes to the chemical identities of the materials. ƒ reaction rate: how much of a particular reaction or reaction step occurs per unit time. ƒ transition state: an unstable structure formed during a chemical reaction at the peak of its poten- tial energy that cannot be isolated and ultimately breaks down, either forming the products of the reaction or reverting back to the original reactants. Activation Energy in Chemical Reactions Activation energy can be thought of as a barrier that the reactants in a chemical reaction must overcome if the reaction is to proceed to the formation of prod- ucts. The molecules 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 chemical structure formed during a reaction process that can often be captured and isolated by chemical means. Once this structure is formed, the reaction process can either progress to form products or revert back to the original reactants. Activation energy is the energy required for a spe- cific chemical reaction to occur. In a reaction, two reactant molecules contact each other with the en- ergy of their ambient states.(The ambient state of a material can be thought of as its “default” state—the state it takes at one atmosphere of pressure and what is commonly considered to be room temperature.) In the case of a spontaneous reaction, the energy of the collision is sufficient to initiate the formation of the transition state or intermediate. In a nonspontaneous reaction, the energy of the molecular collision is not sufficient, and the two molecules will not interact. The input of some additional energy is required to drive the two molecules together so that the transi- tion state or intermediate is formed and the reaction can proceed. The energy released in the transforma- tion of reactants into products is generally sufficient to drive the reactions of other molecules in the reac- tion mixture. Another way to look at activation energy is to think of it as the minimum amount of energy that two inter- acting molecules must gain in order to weaken bonds between atoms in both molecules so that those bonds can be rearranged. Since chemical reactions are es- sentially processes of breaking and making bonds, having sufficient energy to overcome the strength of the appropriate bonds is essential if there is to be any reaction between the two molecules. Activation Energy and Reaction Rates Reaction rates can be related directly to their ac- tivation energies. This relationship is defined by the Arrhenius equation, formulated in 1884 by the Swedish scientist Svante Arrhenius (1859–1927), who received the Nobel Prize in Chemistry in 1903.The

Activation energy Principles of Biology Arrhenius equation relates the rate constant of a re- action to its activation energy and the absolute tem- perature and has the form

k = Ae − E / RT

where k is the rate constant for the reaction or pro- cess; A is the pre-exponential factor, also known in some cases as the frequency factor; E (or E a) is the activation energy for the reaction or process; R is the gas constant; T is the absolute temperature; and the mathematical constant e is the base of the natural logarithm, so that the natural logarithm (ln) of e is equal to 1.The Arrhenius equation has been found to apply not only to chemical reactions but to physical processes as well. T he relationship can be most clearly seen by plotting experimen- tally determined logarithmic values of k against the inverse of the absolute temperature, 1/ T. This results in a straight line plot, from which the activa- tion energy of the reaction or process can be cal- culated. The pre-exponential factor A is identified as the value that the specific rate constant k would have if the activation energy E were zero (a sponta- neous reaction).In that special case, the exponent −E/RT would also be equal to zero, making e −E/RT equal 1 and thus causing the value of k to be equal to A. For different specific reactions, the value of A ranges over several orders of magnitude, but the rate constant k is determined almost solely by the value of e −E/ RT, which can range over several hundred orders of magnitude, de- pending on the relative values of E and T. The course of a reaction depends on the relative difference between the energy of the reactants and that of the products. The greater this dif- ference is, the more impetus there is for the reaction to proceed to the formation of products. This is typi- cally illustrated in a plot of energy versus the reaction coordinate, a symbolic representation of the prog- ress of a reaction. In the plot, the energy level of the reactants, on the left, is either higher or lower than that of the products, on the right. In between, a curved line rises from the energy level of the reactants to a maximum value before falling to the energy level of the products. The difference be- tween the energy level of the reactants and this peak energy value represents the activation energy for the reaction, while the difference between the energy levels of the reactants and the products represents the energy released in the reaction, also called its enthalpy. The specific rate of any individual reaction is de- termined by its activation energy. However, in mass quantities, the energy differences between reactants and products in the system also play a role. This can be understood by considering the Boltzmann frac- tion e −E/RT, which describes the fraction of mol- ecules in the system having energy greater than E. As energy is released from several reactions, the frac- tion of molecules present at any given time with suf- ficient energy to react increases, and more reactions can occur in any given time period. Each reaction re- quires the same activation energy, and the amount of energy that is available in the system to permit reac- tions to occur may be anything from “barely enough” to “excessive.” The activation energy of a reaction can be greatly reduced by the inclusion of a catalyst, a material that takes part in the reaction mechanism but is not con- sumed in the reaction. Catalysts function by forming an activated complex with the reactants, typically Activation Energy (Ea)

ACTIVATION ENERGY DIAGRAM

A+B C+D PotentialEnergy Reaction Progress

Active transport Principles of Biology Lafferty, Peter, and Julian Rowe, eds. The Hutchinson Dictionary of Science. 2nd ed. Oxford: Helicon, 1998.Print. Masterton, William L., Cecile N. Hurley, and Edward Neth. Chemistry: Principles and Reactions. 7th ed. Belmont: Brooks, 2012. Print. Raymond, Kenneth W. General, Organic, and Biological Chemistry: An Integrated Approach. 4th ed. Hoboken: Wiley, 2014.Print. Zumdahl, Steven S., and Susan Zumdahl. Chemistry. 9th ed. Belmont: Brooks Coles, 2013. Print. ACTIVATION ENERGY SAMPLE PROBLEM Use the Arrhenius equation to determine the activation en- ergy at 0°C for a reaction having a specific rate constant ( k ) of 0.023 moles per liter per second and a pre-exponential factor ( A ) of 2,303 moles per liter per second. Use the gas constant. 8.314^ J mol K R = Answer: Convert the temperature from degrees Celsius to kelvins, given that K = °C + 273.15: K = 0 + 273.15 = 273. The Arrhenius equation is k = AeE / RT Rearrange the equation using natural logarithmic (ln) relationships: / ln ln ln ln (l ln ln ln(e ) n ln ) E RT k A E RT E (^) A k RT E A k k A RT − =

= = − = − − Substitute in the values of (^) (8.314 J ) mol K R ,^ T (temperature), A (pre-exponential factor), and k (rate con- stant). Calculate, paying attention to the units throughout: (8.314 J 273.15 K)(ln 2303 ln 0.023) mol K J (8.314 273.15 K)[7.742 ( 3.772)] mol K 26147.938 J m ln l ) o ( ln E E R E T k E A = × − = × − − = = −

Active transport

FIELDS OF STUDY

Biochemistry; Molecular Biology; Genetics SUMMARY The process of active transport is defined, and its importance in biochemical processes is elaborated. Active transport is an essential feature of the bio- chemistry of living systems and helps maintain the necessary concentrations of various biochemical components and electrolytes for the proper func- tioning of cellular metabolism.

PRINCIPAL TERMS

ƒ adenosine triphosphate (ATP): a molecule con- sisting of adenine, ribose, and a triphosphate chain that is used to transfer the energy needed to carry out numerous cellular processes. ƒ cell membrane: a biological membrane that forms a semipermeable barrier separating the interior of a cell from the exterior. ƒ concentration gradient: the gradual change in the concentration of solutes in a solution across a spe- cific distance.

Principles of Biology Active transport ƒ diffusion: the process by which different particles, such as atoms and molecules, gradually become intermingled due to random motion caused by thermal energy. ƒ passive transport: the passage of materials through a membrane with no input of energy required. The Mechanics of Active Transport In living cells, biochemical processes transport mate- rials necessary for a properly functioning metabolism through cell membranes. Passive transport does not require an input of energy to move materials across cell walls because it operates in the same direction as the concentration gradient, moving the materials from an area of high pressure to one of low pressure. Active transport can be thought of as a “shuttle ser- vice” for ions and other polar materials that cannot pass through a cell membrane by diffusion, a kind of passive transport. Instead, those entities must be physically transported across membranes by various mechanisms collectively termed pumps. A pump is a type of mediated transport system that functions to conduct ions, amino acids, glucose, and other polar compounds through the nonionic lipid bilayer, the highly nonpolar material that makes up the cell wall. Pumps always work against the concentration gradient to move materials out of regions of low concentration and into regions of higher concentration, using energy derived from biochemical reactions. The transported material is subsequently used in other biochemical re- actions that return the energy used during transport. Cell Walls and Lipid Bilayers Long-chain fatty acids are organic molecules whose molecular structure consists of a single hy- drocarbon chain terminated by a carboxylic acid ATP ADP +P Outside of Cell Inside of Cell ACTIVE TRANSPORT

Principles of Biology Active transport be calculated by one of two equations. The first equation represents the free-energy change for the transfer of neutral materials against a concen- tration gradient. This is described by the following equations: 2 1 ln c RT c G = 8.314^ J mol K where R is the gas constant and T is the absolute tem- perature in kelvins, ln is the natural logarithm func- tion, and c 1 and c 2 are concentrations on either side of the membrane in molars, or moles per liter (M), with c 2 being greater than c 1. The second equation, which represents the free-energy change for the transfer of electrically charged materials, needs to account for the charge on the material being transported and the differ- ence in electric potential across the membrane. The latter is determined by the neutral nature of the lipid bilayer, which causes it to act as a capacitor, or energy-storage device, and the presence of charge as maintained by the potassium ions in the cytosol. The free-energy expression for the transport of charged species across a cell membrane is given by the following equation: (^2) + ZF 1 ln c G^ = RT (^) c where Z is the charge on the ion, F is the Faraday constant (96,485.3365 coulombs per mole, the elec- tric charge on one mole of electrons), and is the difference in electric potential across the membrane in volts. ATP and Active Transport The energy used in active-transport systems is obtained through enzyme-mediated reactions of ad- enosine triphosphate (ATP). ATP molecules consist of a molecule of the nucleobase adenine that is bonded to a molecule of ribose sugar, which in turn is bonded to a triphosphate ion. A magnesium ion coordinates and stabilizes the second and third seg- ments of the triphosphate moiety. Energy is derived from the structure by the enzymatic cleavage of the third phosphate segment from the triphosphate moiety, transforming the molecule into adensosine diphosphate (ADP), and it is restored by concate- nating, or joining, a third phosphate ion to ADP to re-form ATP. The function of muscle cells depends on the ac- tive transport of calcium ions and sodium ions, a process termed the calcium ion pump or Ca2+^ pump. The calcium ion pump works in an organelle of muscle cells called the sarcoplasmic reticulum and is powered by ATP hydrolysis reactions mediated by the enzyme calcium adenosine triphosphatase. This process is critical to the contraction and relaxation of muscle fibers, especially heart muscles. The sar- coplasmic reticulum is a cell structure that stores and releases calcium ions to aid in this contraction and relaxation. In muscle cells, the rapid release of calcium ions from the sarcoplasmic reticulum into the cytosol, the cellular fluid outside of the organ- elles, triggers contraction of the muscle, while rapid removal of calcium ions from the cytosol and back into the sarcoplasmic reticulum triggers relaxation of the muscle. The normal concentration of free calcium ions in the cytosol is between 0.1 and 0.2 micromolar (μM, or 10−6^ moles per liter), increasing when the muscle contracts and returning to the normal value when it relaxes. Richard M. Renneboog, MSc Further Reading Lafferty, Peter, and Julian Rowe, eds. The Hutchinson Dictionary of Science. 2nd ed. Oxford: Helicon,

  1. Print. Lehninger, Albert L. Biochemistry: The Molecular Basis of Cell Structure and Function. 2nd ed. New York: Worth, 1975. Print. Lodish, Harvey, et al. Molecular Cell Biology. 7th ed. New York: Freeman, 2013. Print. Pelczar, Michael J., Jr., E. C. S. Chan, and Noel R. Krieg. Microbiology: Concepts and Applications. New York: McGraw, 1993. Print. Reece, Jane B., et al. Campbell Biology. 10th ed. San Francisco: Cummings, 2013. Print.

Aging Principles of Biology

Aging

FIELDS OF STUDY

Anatomy, cell biology, developmental biology, ge- netics, neurobiology, pathology, physiology SUMMARY Aging is the process of progressive and irreversible change common to all living organisms. There are striking similarities in the physical process of aging among all animal species. PRINCIPAL TERMS ƒ aging: a process common to all living organisms, eventually resulting in death or conclusion of the life cycle ƒ cognition: ability to perceive or understand death: the cessation of all body and brain functions ƒ function: ability, capacity, performance ƒ life span: length of life from birth to death ƒ longevity: length of life Basic Principles Progressive and irreversible change has been called the single common property of all aging systems. When change is reversible or self-maintaining, such as one would see in a forest, for example, the effects of aging are often not observable. Growth of the forest is evident, but with the right conditions, trees within the forest may grow for hundreds of years in the absence of disease. Certain conditions of the forest system help to regenerate, renew, and reverse changes that happen within that system. However, in animals some change is not revers- ible. The changes in the cells of the body accumulate 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 cycle. This is known to be true because aging changes within populations are rather predictable. The changes associated with aging that are seen in all animal species may occur for similar reasons. These may include chemical aging, extracellular aging, intracellular aging, and aging of cells. ACTIVE TRANSPORT SAMPLE PROBLEM Use the free-energy equation for active transport against a concentration gradient to determine the free energy associ- ated with transporting neutral amino-acid molecules across a membrane from a concentration of 20 μM to one of 43 μM. Assume normal body temperature of 37°C. Use. 8.314^ J mol K R = Answer: The materials being transported are electrically neutral. Therefore, use the equation 2 1 RT ln c c G = Convert the temperature from °C to K: K = °C + 273. K = 37 + 273.15 = 310. Convert the concentration values from micromolars to molars: c 1 = 20 μM = 20 × 10−6^ M = 0.00002 M c 2 = 43 μM = 43 × 10−6^ M = 0.000043 M Substitute in the values of R , T , c 1 , and c 2 and calculate, paying attention to the units throughout: 2 1 ln (8.314 J^ )(310.15 K) ln0. mol K 0. 1973.8 J mol c RT c = = = G G G The free energy of active transport of neutral amino acids across a concentration gradient from 20 μM to 43 μM is 1973.8 joules per mole, or 1.9738 kilojoules per mole.