articulo equilibrioquimico 19661

8/13/2019 Articulo Equilibrioquimico 19661

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Chemical Equilibrium

Many chemical reactions do not proceed to completion;instead, they establish a dynamic equilihrium in which twoopposing reactions occur at the same rate.' For example,mixing solutions containing cerium(1V) and iodide ions givesrise to th e reaction2Ce& 31Gqr= Cef , I&

On the other hand, when cerium(II1) is added to a solution oftriiodide ion, significant quantiti es of cerium(1V) and iodideions are produced. Th e extent of either reaction is easilygauged by the intensity of the orange-red color of the triiodideion. The concentration of this colored ion rapidly reaches aconstant level tha t is independent of the route hy which it isformed. I t makes no difference whether Ce4+ and I- or Ce3+and 1; are selected as the original reactants; the same condi-tion of equilihrium will result. In the beginning, if Ce4+ andI- are the original reactants , the concentrations of Ce4+ andI- will he high, and consequently the forward reaction willproceed rapidly. No reverse reaction is possible a t the sta rt,since Ce3+ and I: are not yet present. As Ce3+ and I; areformed, th e reverse reaction will begin slowly and graduallyincrease in rate as Ce3+ and 1 accumulate. Meanwhile theforward reaction is slowing down as Ce4+ and I- are heing usedup, as shown in Figure 1.Conditions of chemical equilihrium that most chemicalreactions can atta in may he compared to a person running ona treadmill, which moves faster as the runner increases hisspeed. When the runner and the treadmill are in equilihrium,the runner is apparently stationary to an observer. If therunner increases his speed, he advances a short distance.However, as the treadmill also moves faster, the runner againappears to he stationary; although, his position is in advanceof his previous stationary position.In a reversible reaction, such as

2NOw Oxg, N02 dthe equilibrium amounts of NO, 02, and NO2 remain constankyet like the runner a nd th e treadmill, the reactions proceedin opposite directions at the same rate.The Law of Mass ction

In 1864, the Norwegian chemists Cato M. Guldberg andPeter Waaze ~r ooo sedha t the rate of a chemical reaction isproportion& to th e active masses of the reacting substances;the molecular concentration of a substance in solution or inthe gas phase is used as a measure of its actiue mass.2 Thesignificance of this statement, which is called the Law of MassAction (the rate law in kinetics) is more apparent as thequantitative notions of chemical equilihrium are developed.For example, consider the general reversible reaction in whichan equilibrium exists between four suhstances A, B D, andE

A + B * D + ETwo reactions are proceeding, one t o the right (called theforward reaction), in which A and B react to form D and E and

Mickey, C. D., J. CHEM. EDUC., 57,659 (1980)Glasstone,S. Textbook of Physical Chemistry, D. Van Nos-trand Company, Inc., New York, 1946, p. 817.

Charles D. MickeyTexas A8M University at GalvestonGalveston. TX 77553

The variation in conwmratimof reactamandpmductsasahlnction of time.a) nitially, staid llm lr ic amolntJofCe4+and I-are mixedandallowedtoreadl

equilibrium. b)Staichiometric amountsof b tnd I are allowed to reactatthe same temperature. In both instances the final equilibrium concenhationsof all species are the same.

the other to th e left (called the reverse reaction), in which Dand E react to form A and B.Accordine to t he Law of MassAction, the rate of the forward reactLon r proportronal lo theconcentrations oft he reactants A and R whilr the rate of therrwr.*e rrnctron rsproportlonal to the


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The Equilibrium Constant and Ideal BehaviorThe expression

. .. .is only rigorously valid in situations where all reactants andproducts behave like ideal eases or are comnonents of an idealBo~ution.For example, just as conductiviiy in concentratedsolutions of strong electrolytes fails to indicate completeionization, because of the interference of ions with the motionsof other ions, th e presence of high concentrations of ions in-terferes with the reactions of any ion. If the rates of reactionsin concentrated solutions of strong electrolytes are calculatedand compared with the measured rates of these same reac-tions, there are discrepancies which increase with the increasein concentration. Moreover. these discrenancies will he re-flected in the equilihrium cdnstant. 1f thlac tiuit y of the re-acting particle is substitued for i ts concentration or partialpressure a correct rate of reaction isfound and the equilihriumconstant will he rieorouslv valid. The correction factor usedas a multiplier octhe actual pressure or concentration toproduce the actiuity is called the actiuity coefficient (7). Theexperimentally determined value of the actiuity coefficientvaries, not only from one substance to another, but also withpressure, conc tration, and temperature. he magnitude ofthe actiuity coefficient is always less than one and approachesunity as t he partial pressure or concentration decreises. Theactiuity (a ) of a reaction component is its molar concentrationor partial pressure times an actiuity coefficient (y) ,or a = yMfor solutions and a = y P for gases. The actiuity of a pureliquid or a pure solid, at, cons tant temperature, is defined asunity.One of the great theoret ical outcomes of chemical thermo-dynamics was the rigorous derivation of equilihrium constantsusing actiuities, rather than molarities or ~a r t i a lressures.~ l t h o u g ht is not possible within the icopid his.nrtirle, itcan be shown that the thermnd\namicanaloc of the nrecediwequilibrium-constant expression is

K - UDaEeq aADBFreauentlv. as in this discussion. eauilihrium constants arebased bn milarities or partial pressures instead of the moreexact activities, for three reasons: 1) he measurement ofreagents are usually made in grams and put into solutions interms of erams or moles per liter: (2) the activitv coefficientof any ion changes not oily with its own concentration, hutwith that of other ions in the solution; (3) all substances forwhich equilibria are calculated are either in dilute solutionsof their kinds of ions and molecules or are weak electrolytes,so the approximations secured by the use of molarities orpartial pressures instead of activities are sufficiently accu-rate.General Form of the Equillbrlum Constant

Fortunately, i t is not necessary to know the mechanism orrate laws for a reversible reaction to he able to write theequilibrium-constant expression. Even if a reversible reactionproceeds through a series of complicated steps, each individualstep is reversible and, a t equilihrium, the reversible reactionsproceed a t the same rate in both directions. Thus, the equi-librium-constant expression can be derived from the balancedequation for the overall reaction. Consider the reaction

COacaqi 3 H z 0 ~ 1 + H@ &l+ CO&IIf the forward reaction is a single-step termolecular reaction,its r ate will he expressed as:

Ra te f= kr[C02][H20I3Likewise, if the reverse reaction is a single-step trimolecularreaction, its ra te will be given by the equation:

Rate. = k,[H30+I2[CO -]

and a t equilibrium,Rr = R,

therefore,krICOnl[H~0I3 kr[H30+]Z[CO -]

hence

Alternately, assume that the reaction proceeds by the fol-lowing two-step mechanism:COac,) 2H zO u1= H sO t,) HCO,I,l (Step1HCO,I,I H 2 0 ~ H B O L I CO (aq l Step 2For the first step

Rr = kr[C021[Hz012R, = k,[H3Otl[HCO3-I

At equilihrium, Rr = R,, and since the ratio of two constantsis a third constan tkr - - H3Ot1[HC0;lk r - [C0z11H~012Similarly, for the second step:

R; = k;[HCOJ[Hz0]R; = k:[H30+][COf]

A t equilibrium,R i = R,'and

The product of two constants is a third constant; therefore,the product

Consequently, t he equilibrium-constant expression turns outto be t he same; whether based on kinetic arguments or thebalanced equation. Thus , for the general reaction:r A + s B = x D + z E

in which r s, x and represent the coefficients of A, B, D, andE, respectively, in the balanced equation, the formulation ofKeq is

There are several different but interrelated types of eqni-librium constants, with the symbol K. generally used trepresent any of the various kinds. However, special desig-nations for equilibrium constants are frequently used tocharacterize a particular equilihrium system. T he symbolK pfor example, indicates a particular equilihrium constant inwhich the quant ities of gaseous reactants and products areexpressed in terms of their partial pressures. Concentrationscan he related to partial pressures through the ideal gas law(PV = nRT) ; therefore, t he partial pressure for any gaseousreactant or product, tha t behaves ideally, is proportional toits concentration. Hence, for the gas phase equilibrium:

N21g1 3 H w N H l ( g ~th e equilibrium-constant expression is

K - = 3.52 X 1 W7P-m at 1 DKThe symbolK c represents a particular equilihrium constantin which the quantities of reactants and products are ex-pressed in terms of their molarities. The Kc value for theprevious reaction is

8 2 / Journalof Chemical Education


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Two different reactions will generally have different equi-lihrium constants. t 1000K the reartion involving carbonmonoxide, oxygen, and carhon dioxide

2COIgl + 02 g1= COlldhas th e equilibrium constant value

The fact that in the lat ter reactionK s greater than Kc in theformer reaction means th at at 1000K carbon monoxide andoxygen are more completely converted to carhon dioxide thannitroeen and hvdroeen are to ammonia. Thus , the maenitude..of theequilibrium runstant may he used to gauge theexcenttt, which a eiven reartion proeresses toward completion. If allother factors are equal, vaiue of Keg > ndicates a highdegree of conversion of reactants to products and a value ofK. < ndicates a low degree of conversion.The Forward and Reverse Reactions

Since equations for chemical reactions may he written ina variety of different but equivalent ways, each value for anequilihrium must always he accompanied by the specificequation which it represents. For example, in the reactionCuL, +A , * U I 2Agbhe equilibrium constant is

Suppose the reaction is written asC U K I+2Ag?.1* Cuf.~ 2 A g h

consistency is maintained and ambiguity avoided, if theequilibrium constant is written a s

Quantitatively, for any reversible reaction th e value of theeauilihrium constant for the reverse reaction is the reciprocali f the equilibrium constant for the forward reaction. 1;otherwords,

As illustrated in the last two equations, i t is customary toexclude the concentration terms for solids from the equilib-rium expression. The concentrations of the silver and coppersolids e constant, hence the respective equilihrium-constantexpressions are simplified by comhining the constants. Sim-ilarly, the concentration of a pure liquid is constant, hence itsconcentration term is also excluded from the equilibrium-cons tant expression. For example, consider the reaction

the equilihrium constant is expressed by

Combining the two constants in this equation gives

Faclors Influencing Equillbrium.At equilibrium a chemical reaction is proceeding in theforward and reverse directions with equal velocities, thus itis expected that the parameters, such as temperature and

concentration, which affect he rate of any reaction will alsoaffect t he equilihrium; that is, these same parameters canchange the halance between the two opposing reactions. T ounderstand the nroblem more clearlv. aeain consider the.analogy hetwee'a chemical system in equilihrium and aoersou runnine on a treadmill which increases its speed as theperson advances. If the person while running and apparentlyremaining stationary with respect to some fixed point, in-creases his speed he advances; hut as he does so the speed oftreadmill also increases and aeain the runner comes to anapparent stationary position. For the second time, the runnerand the treadmill are in astateof equilihrium, but the runnerhas now orcuyied a position farthe; forward. If, on the otherhand, the runner tires he runs slower. Momentarily he shiftshis position backward; hut since the treadmill readjustedto a slower rate, the runner will soon assume a new positionof eauilihrium. nur ine the short interval that the runner ad-vances or falls hack, the position of equilibrium is shifted.In a analoeous manner. the eauilihrium position of achemical reaccon may be sGfted; and it is customaryw speakof a shi ft in euuilibrium to the riahr or to the left with refer-ence to'the chemical equation f the reaction taking place.Thus, in the eauilihrium between nitroeen, hydrogen, andammonia as represented by the equation-

N w + 3 H w * NH31g)all these substances are present in definite amounts and thereaction is proceeding in both directions. If now, t)y some in-fluence, the equilibrium is affected so that more ammonia isformed; the equilihrium id hif led o the right. During thechange from one equilibrium pusition to another, the reactionproceeds mumenurrily ft~ ite rrom left to right than from rightto left. This situation is analoguus to the momentary shift inthe position of the runner on the treadmill when he is inspiredto run faster.Le ha teller's Principle and Chemical Equlllbrlum

Extensive studies of reversible reactions and the equilibriaassociated with them led the French chemist, Henri Louis LeChatelier (1888), to make a simple generalization, commonlyreferred t o as Le Chatelier's Principle:A system at equilibrium, when subjected to any stress (such as

change in temperature, pressure, or concentration of matter) so thatequilibrium is disturbed, will tend to adjust itselfso as to remoue thestress and re-establish equilibrium.Of the three stresses, only a change in temperature will affectthe magnitude of the equilihrium constant. For example,

Reaction Temp OK) KNzie] 3H21g) 2NH xs1 623 2.66 x lo-'Nxg)+ 3H21g)= N H w 123 6.59 x lo-3N Z I ~ I 3Hzw= NH31x) 1000 2.37 xThe Effect of Temperature on an Equillbrium

All chemical reactions are accompanied hy energy changes.Some reactions are exothermic-produce heat durine thereaction; others are endotherrnic-ibsorb heat from the sur-roundings. In the reactionNz1.1 3H2(.) * NH3 22.08 kealnitrogen and hydrogen, in comhining to from ammonia, pro-duce heat. When ammonia decomposes into nitrogen andhydrogen ( the reverse reaction), an equivalent amount of heatmust he ahsorhed. When this system is at equilibrium, no heatchange occurs.A quantita tive relationship between the equilibrium con-

stant and temuerature can he derived from the Arrheniusequation for the specific rat e constant, since the equilihriumconstant. K. . is eaual to the ratio krlk The soecific rate. .con sta nt foi'the foiward reaction isk = @-EaIRT

Volume 57, Number 11 November 1980 1 803


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while the corresponding expression for the reverse reactionisk A , ~ - E o / R T

Substitu tion shows the temperature dependence ofK

(where Z, a constant , is the ratio of AyIA,). Thus, for exn-thermic reactionsK decreasesas temperature increases, andfor endothermic reactions K. increases as temperature in-creases. In other words, increasing the temperature will shiftth e position of equilibrium to the left for an exothermic re-action; whereas, increasing the temperature will shift theposition of equilihrium to the right for an endothermic reac-tion. This simplified derivation supports the generalizationof Le Chatelier.According to Le Chatelier s principle, if heat is added to thenitrogen, hydrogen, ammonia system (increase of tempera-ture ), the system will change in such a way as to minimize thestress. To relieve the stress (increase of temoerature). thesystem will absorb heat, i .e. , the formation of nitrogen andhvdrocen from ammonia will be favored since this reactionahsorl~s eat. In reality, pan of the heat is used u ncrense thetemperature of the svstem and p an is used tos hifi the eoui-The Effect o Changlng Concentration on th e Position ofEquilibrium

Another way to p ut a stress on a system is to alter the cnn-centration of one or more of the components. This can be ac-complished by adding or removing one or more of the equi-librium species. For example, consider the equilibrium

A stress can be placed on this system by adding sulfur dioxide,oxveen. or both. In either event. the oroduct of the molar-concentrations in the denominator of the equilibrium-con-stant expression exceeds the equilibrium value, and the ratioof the molar concentrations is now less than Keg.f the molarconcentration of sulfur dioxide is increased. the reaction rateto the r ight will increase, and the change which tends t useup sulfur dioxide and oxygen and thus remove the stress willbe favored. This conforms to Le Chatelier s principle whichindicates that the equilibrium system will shift so as t o min-imize the stress. Sulfur dioxide and oxygen will he used u pfaster than they are formed, and the molar concentration ofsulfur trioxide d l ncrease. However, as the molarity of sulfurtrioxide increases, the rate of its dissociation into sulfurdioxide and oxygen will also increase. Eventually, the forwardand reverse reactions will att ain equal rates and equilihriumwill be re-established. T he stress nlaced on the svstem. whenthe concentration of sulfur dioxide was increased, will havebeen removed by changes in the molarites of all the substancessuch that the value of K is restored. Note that when theconcentration of sulfur dioxide is increased. the ne t chanceswhichurrur in the system are such that theconcentratiooofoxygen is decreased while the concentration of sulfur trioxideis increased. In other words, oxygen can he used up mnrecompletely and sulfur trioxide can he produced more effi-ciently byincreasing th e concentration bf sulfur dioxide. Onthe other hand, t he introduction of more sulfur trinxide intothe system favors the reverse reaction, more sulfur dioxide andoxygen are formed while some sulfur trioxide is consumed, i.e.,804 Journal of hemical Education

the position of th e equilibrium shifts to the left.Converselv. removal of a comonnent from an eauilibr iumsystem favors the reaction whirh replaces it. Fur example, theremoval of sulfur trioxide from the enuilibrium svstem shiftsthe position of equilihrium to the right. The forward rate willmomentarily be greater than th e reverse rate; the system istemporarily out of equilihrium and sulfur trioxide moleculeswill he produced faster than they are used u p in th e reversereaction. Similarly, if par t of the sulfur dioxide or oxygen isremoved, the reverse reaction, forming more sulfur dioxideand oxygen, will be favored.The Effecto Pressure on Equilibrium: Special Case ofChanging Concentration

Change of pressure is insignificant for liquids and solidsbecause of the ir low compressihilitv, but i t is extremelv im-portant for gases because the molarity of a gas, at constanttemperature, is directly proportional to its partial pressurePV n RT .Therefore, as the external pressure on agaseonssystem increases, the substances undergo compression andthe molarity increases. 1.e Chatelier s principle indicates that,if a .stress is placed on a rerr rsih le system by increasing theoressure. that rhemiral rhanee will he favored whirh will tend~-~~~to reduce the pressure. For a gaseous system, the increase inoressure is achieved bv increasine th e total number of mole-cules per unit volume. This procesi will favor the net chemical

chance that will reduce the total number of molecules ner unitvolume.Consider the reversible reaction2C01,l 02id= c02ig

A total of three moles of carbon monoxide an d oxygen formonly two moles of carbon dioxide. Th e formation of carbondioxide will therefore decrease the total number of moleculesin the system, and the total gaseous pressure will therefore bereduced. Thus, increasing the total external pressure on thesystem will favor the conversion of carbon monoxide andoxygen to carbon dioxide. Conversely, a decrease in the totalexternal pressure will favor the dissociation of carbon dioxideto carbon monoxide and oxygen.If PC15 is injected into a closed system a t 523 K, t disso-ciates to an equilibrium state:

pC15~ PCIw ClaigSince there are two moles of gaseous product compared to onlyone mole of gaseous reactant, an increase in the externalpressure will cause a shif t in th e equilibrium to the left, i.e.,less PCls dissociates: whereas a decrease in the externalpressurewill favor the dissociation of PClb. In other words,there is a shift in the eauilihrium to th e rieht.

Certain gaseous reactions are not affecied by changes inpressure, for example:

In this rase there are two moles of reactants and two moles ofproduct . Changes in the external pressure have no effect onthis system hecause the reareequ al numbersof m(~leculesnhuth sides of the equation.Catalysts and Equilibrium

While catalysts are used to increase the rate of a reaction,they cannot change the numerical value of the equilibriumconstant and hence cannot change t he relative amounts ofreactants and products present a t equilibrium. However, thecatalyst may greatly reduce the timenecessary for theestab-lishment of equilil~rium. his is extremely important from anindustrial viewpoint, since the rate a t which aproduct can beproduced is a primary consideration. Catalysts may be usedeffectively in manv reactions which allow conversion of onlva small percentage of reactants into products (position dfequilibrium shifted far to the left) because, from a productionstandpoint, it is far mnre important to ohtain a small yield ina few minutes than t o obtain a large yield in several days.

articulo equilibrioquimico 19661

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