Bond Energies and Enthalpies An Often-Neglected Difference Richard S. Treptow Chicago State University, Chicago, IL 60628
Bond energy is a measure of the strength of a chemical bond. It is commonlv defined as the enerw reauired to break the bond between two atoms. This definition is not as easily a ~ ~ l i as e done might hove. In order to evaluate a bond enerw ;select a chemical reaction in which the bond is broken. w e must then choose the thermodvnamic ~ r o ~ e rof t vthat reactim t h uill ~ a:nv ;IS tht: mt!:liurt! i,f tmnd m(!rAr\: Chemists cmnnmly u.w \//I.,,fir rhii purpose. This pttprr asks il'the enrhalpy c h a n ~ eat standard conditions is the correct prop. clzy 11, aiwciiue with the itren#h i f a tn~nd.Tht. iuhjrct is bt, Dasent I , and Bcnson 21. trenred in a l'aqh~onsuggested . . The practice of taking AH;,, for a bond-breaking reaction a s a measure of bond energy can be challenged on two counts. Let u s consider the dissociation of the hydrogen molecule to illustrate the point. When the reaction u.
.
takes lace a t standard conditions. vressure must remain constaht a t 1 atm. Because the nun;der of moles of gas doubles. the volume of the reaction svstem also doubles. AH = AE + PAV for such a process. ~ e k c ethe , enthalpy change is greater than the change in the internal energy of the system by the amount PAV, the work done by the system on its surroundings as i t expands. There is no justification for including this work in the value assigned to bond energy. A second complicating factor arises because the hydrogen molecules have vibrational, rotational, and translational energy before they react. Also, the hydrogen atoms they produce have translational energy when the reaction is complete. The total kinetic energy of the reactant differs from that of the product. Although these energies are not relevant to the strength of the bond, their difference is unavoidably incorporated in the value of AH;gg.
Thermodynamic cycle for the dissociation of hydrogen. Internal energy is plotted vertically (not to scale).
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Number 6 June 1995
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Table 1. Thermodynamic Properties for the Dissociation of a Mole of Hydrogen Thermodynamics of Hz Dissociation The energy terms introduced above can he put into perspective by assemDescription Value (kJ) Method or Reference Symbol bling them into a thermodynamic cycle as shown in the figure. The cycle Bond energy for molecule at rest 457.8 cycle AEe concerns a system in which 1 mol of 25.5 ref 4, p 132 Vibrational energy at 0 K AE"ib hydrogen molecules dissociate into their atoms. Various states of the sysK 432.3 cycle Bond energy at 0 AEO tem are numbered 1-5 in the figure. 3.7 (312)RT Translational energy of H2 at 298 K AEirans The internal energy of each state is indicated approximately by its vertical 2.5 FIT Rotational energy of H2 at 298 K AEmt placement. The temperature of the 7.4 Z(312)RT Translational energy of 2H at 298 K system is either 0 K or 298 K throughAE'trans out. ' h a hydrogen molecules or the atBond energy at 298 K 433.5 A&E - PAV A&E oms formed by their dissociation are Expansion work at 298 K drawn for each state. In keeping with PA V 2.5 AnRT thermodynamic convention, we will Bond enthalpy at 298 K 436.0 ref 3,p 1211 t r e a t both Hz(g) a n d H(g) a s ideal gases. In state 1the svstem has a temperaapplies, where PAV is the work done by the system on its ture of 0 K. Its diatomic molecul& are completely motionsurroundings as it expands. Asecond path to state 5 begins less and not in contact. This state is purely hypothetical. I t with state 3. I n step 3+5 the hydrogen atoms a t rest are differs from the actual state of hydrogen a t 0 K i n two imset into motion a s they are warmed to 298 K. In the process portant ways: they acquire energy AE,'. Only translational energy is required for this process because the gas is monatomic. The specification that its molecules are motionless contradicts the fact that real molecules have vibrational motion even Thermodynamic Properties Evaluated at absolute zero. The requirement that the molecules be separate contradicts The thermodgnamw propertoes for the dissor~at~on of 1 the fact that hydrogen is a solid at this temperature. mot of hydrocen property . - are iumman7ed in Tnhle 1. Each . . . is given a description and assigned a value. Our discussion Although state 1is only hypothetical, it offers a good starting point for our discussion. Thermodynamic studies are of how the values are determined will begin a t the bottom not limited to real states. for the reaction in which 1mol of Hz(g) of the table. Wz98 produces 2 mol of H(g) a t 1 atm is simply the standard Vibrational and Electronic Energy at 0 K enthalpy of formation of H(g) multiplied by 2. The thermodynamic literature (3) provides the required enthalpy of Let us now take the system through the transitions formation.'PAV, the work of expansion, is calculated from shown in the figure. In step 1+2 the molecules acquire the the equation vibrational motion that real molecules actually possess a t absolute zero. The arrows drawn in state 2 convey the idea PAV = h R T of molecular vibration. The kinetic enerw in this .,. acauired . where An = 1. proress is known as the zw-point energy; it is symbol~zed We next determine from the relationship L\E...h.In steo 2+3 the molrculrs disioc~atcinto hvdmeen atoms a t rest. The energy required for this process is &a, AE&, = AH& - PAV where the subscript indicates the temperature. The transition to state 3 can also be imagined to occur in a single The translational energy of a gas is (112)RTfor each direc= (312)RT for 1mol of hydrotion of motion. Thus, AE,. step. No kinetic energy is involved in step 1+3 because gen molecules, and AE',,, = 2(3/2)RT for the 2 mol of reactants and products are both motionless. The symbol AZ3, indicates that only electronic energy is involved. hydrogen atoms. The rotational energy of a diatomic gas is RT. This gives the value of AErE,,,.We next determine AEa Thermal Energy using the cycle and the fact that the internal energy is a state function. The value of AEvib,the zero-point energy for I n step 2+4 the vibrating but otherwise motionless the hydrogen molecule, is known from IR spectroscopy (4). molecules are warmed to 298 K and they become hydrogen Finally, AE, can be calculated from + AEo. gas a t the standard pressure of 1atm. In this process the molecules acquire translational energy AE, and rotaExtension to Other Molecules tional energy AE,. No additional vibrational energy is inOur study of the thermodynamics of molecular dissociavolved in this step because a t room temperature nearly all tion can be easily extended to substances other than hymolecules remain in the vibrational ground state characdrogen. Table 2 summarizes the results for N2, NH3, and teristic of absolute zero. Incidentally, the volume of the sysCH4 a s well as for Hz.The four thermodynamic properties tem in state 4 can he calculated from the ideal gas law: of greatest interest are listed for each molecular dissocia24.5 L. tion. For each reaction AH&,8is determined from enthalpy Bond Energy and Enthalpy of formation data (3). I n the case of the compounds NH3 at 298 K and CH4, the calculation requires application of Hess's law. AEqg8 is then determined by subtracting the appropriate Step 4-5 involves the dissociation of Hz(g) into H(g) a t standard conditions. To maintain standard conditions the ' ~ h $ ~ ~ v a l used u e s throughout this paper are from thecomprehenprwsurv must remain constant at 1 a m . The volume exsive J A N A F Therrnochernical Tables (3).This source follows the IUv m d s 10 49.0 L. The enerav -.change ibr this step. is s-~ m b o l PAC recommendation of taking standard pressure to be 1 bar, rather ;zed Because pressure is constant, the relationship than 1 atm. The choice of pressure has no effecton the AEor AH values. AE&, =AH&,, - PAV
498
Journal of Chemical Education
Table 2. Thermodynamic Propertiesfor Bond Dissociation Reactions (kJ)
Reaction
A&
AEo
A&
be98
PAVterm. Next, AEo is calculated by adding the net translational and rotational energy terms.'Finally, AE, is evaluated by adding t h e appropriate zero-point energy. The zero-point energies for N2, NH3, and CHa are 14.1,85,and 113 k J ( 1 , 4 ) . Table 2 reveals a consistent pattern. AE, is always considerably larger than AEo because more energy i s required to break a motionless molecule t h a n a vibrating one. AE& is always slightly larger than AEo, because the thermal energy of individual atoms is greater than that of the molecules from which they come. AHi98 consistently exceeds AE& because i t includes the energy needed to expand the system. Incidentally, the high values given in Table 2 for Nz are i n keeping with our notion that the molecule has a triple bond. The high values for NH3 and CHa simply result from the number of bonds broken. The average energy per bond for these molecules can be calculated by dividing the values by 3 and 4, respectively. Which Thermodynamic Property is Bond Energy?
We can now return to the question that began this paper. AE, is the thermodynamic property that gives the true bond energy. It is the energy required to break a molecule into its atoms i n a reaction devoid of all extraneous energies. We have called AEe the electronic energy or the bond energy for the molecule a t rest. Another fitting term is chemical binding energy ( I ) . Admittedly, this energy is In general. !he Iranslauona energy of a gas s ( 3 2)RT Tne rolaona energy of a gas s RTlor near rno ecL es, s ~ c has r12ana N., and (32,RT lor non (near mo ecJles s x n as NH, ana CH,, I
never actually required in a chemical reaction because i t makes the impossible demand that all molecular motion ceases. Nevertheless, AE, gives the best measure of bond strength. I t is the property to which all models and theories of chemical bonding must properly relate. In the literature we commonlv find two other thermodvnurnic p r o p c r t ~ *uswl s x i t h v h : i k for%ond energies". o n e convention uses S,,, the bond cnerev at O K r.5. 6 . Hecall vibrational enthat AEo is less than AEa by the ~erG:~oint ergy. A molecule is easier to break apart if it is vibrating. Bond energies based on AEo are consistently less than true bond energies. Most general chemistry textbooks follow the practice of deriving "bond energies" from AH&,8. The implications of this convention can be seen by examining the relationship between m 2 9 8 and AE,. = AEe
- zero-point energy
-net translational and rotational energy
+ expansion work The zero-point energy is the largest of the last three terms. Hence, energies based on mig8 values are consistently less than the true bond energies. A few authors acknowledge this difference by using the term bond enthalpy for values derived from AH898 (7, 8).Bond enthalpies have great practical importance because they can be used to estimate AH398 for a reaction from knowledge of the bonds broken and formed. We should remind ourselves, however, that they are not strictly a measure of bond strength. More generally speaking, we need to occasionally acknowledge that enthalpy changes in chemical reactions reflect a hit more than the energy of bonds broken and formed. Literature Cited 1. Dasent, W.E.2norganieEnarg~fbs.2nd ed.; CambtidgeUniversity: Cambridge. 1982; pp 13-23, 102-111. 2. Benson, S. W J C h m . Edue 1965.42,502-518.
3. Chase, J L M. w: navies, C. A,: Downey, Jr, J. R.: h r i p , D. J.; McDonald. R. A ; Syuerud, A. N.JANAFTh~rmoch~micol Tobks. 3rd ed.; National Bureau of Standards: Washington, OC, 19R6. 4. Smith, E. 8. Basic Chemical Thermodynamics, 4th ed.:Oxford University: Oxford. 1990:p 132. 5. Huheey J. E.: Keiter, E. A ; Keiter. R. L. Inorganic Chemislry:P~incipiesafS!rudure ondR~ocliuily.4th ed.: Harper Collins: New York. 1993: pp A21LA34. 6 . Porterfield. W. W Inorganic ChmisLgv:A UnifidAppmoch. 2nd ed.: Academic: San Diego, CA, 1993: p 216. 7. Oxtoby, W. D.;Nachtneb, N. H.; Freeman, W. A. Chsmis!ry:Seienee ofchange:Saundem: Philadelphia, 1990: pp 127431. 8. Shtiwr D. E: Atkina. P W: Langfnrd, C. H.Inorgnnie Chemistry Freeman:New York. 1990: pp 68-69.
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