Equilibrium 07 M07_CHSL_SB_IBD_9069_U07.indd /07/ :21

Transcription

1 07 Equilibrium

2 Essential ideas 7.1 Many reations are reversible. These reations will reah a state of equilibrium when the rates of the forward reation and reverse reation are equal. The position of equilibrium an be ontrolled by hanging the onditions. Imagine that you are part way along an esalator (a moving stairase) that is moving up and you deide to run down. If you an run down at exatly the same speed as the esalator is moving up, you will have no net movement. So, if someone were to take a piture of you at regular time intervals, it would seem as if you were not moving at all. Of ourse, in reality both you and the esalator are moving, but beause there is no net hange neither movement is observable. In hemial reations a similar phenomenon ours when a reation takes plae at the same rate as its reverse reation, so no net hange is observed. This is known as the equilibrium state. In this hapter, we explore some of the features of the equilibrium state and learn how to derive and use the equilibrium onstant expression. Appliation of the equilibrium law enables us to quantify reation omponents and to predit how far reations will proeed under different onditions. Industrial proesses rely signifiantly on this type of study to determine the onditions that will maximise the yield of produt. Equilibrium studies are also important in many biohemial and environmental proesses, suh as prediting the solubility of gases in the blood and knowing how ertain hemials in the atmosphere may reat together to form pollutants that ontribute to limate hange. By the end of this hapter, you will be ready to takle some of these appliations in subsequent hapters. 7.1 Equilibrium Understandings: A state of equilibrium is reahed in a losed system when the rates of the forward and reverse reations are equal. Guidane Physial and hemial systems should be overed. The equilibrium law desribes how the equilibrium onstant (K ) an be determined for a partiular hemial equation. The magnitude of the equilibrium onstant indiates the extent of a reation at equilibrium and is temperature dependent. The reation quotient (Q) measures the relative amount of produts and reatants present during a reation at a partiular point in time. Q is the equilibrium expression with non-equilibrium onentrations. The position of the equilibrium hanges with hanges in onentration, pressure, and temperature. A atalyst has no effet on the position of equilibrium or the equilibrium onstant. Eletron mirograph of a setion through human lung tissue, showing air spaes alled alveoli. Equilibrium onsiderations help us to understand how oxygen and arbon dioxide are exhanged between the blood and the air in these spaes. Snow and ie-overed peak in the Cordillera Huayhuash, Peru. Equilibrium onsiderations help explain the relationship between water vapour in the louds and preipitations in the form of liquid (rain) and solid (snow) at different temperatures and pressures. 17

3 07 Equilibrium Appliations and skills: The harateristis of hemial and physial systems in a state of equilibrium. Dedution of the equilibrium onstant expression (K ) from an equation for a homogeneous reation. Determination of the relationship between different equilibrium onstants (K ) for the same reation at the same temperature. Guidane Relationship between K values for reations that are multiples or inverses of one another should be overed. Appliation of Le Chatelier s priniple to predit the qualitative effets of hanges of temperature, pressure, and onentration on the position of equilibrium and on the value of the equilibrium onstant. Guidane Speifi details of any industrial proess are not required. Bromine stored in a sealed jar. The system is in dynami equilibrium, so the onentrations of liquid and vapour do not hange at onstant temperature. Bromine is the only non-metalli element that is liquid at room temperature. It is extremely toxi and takes its name from a Greek word meaning stenh. Figure 7.1 Establishing dynami equilibrium in the evaporation of bromine. Equilibrium is established when the rate of evaporation equals the rate of ondensation. Figure 7. The rates of evaporation and ondensation as liquid vapour equilibrium are established in a losed system. The rate of evaporation is onstant, while the rate of ondensation inreases with inreasing onentration of vapour. Equilibrium is established when the two rates are equal. 18 Physial systems Consider what happens when some bromine, Br, is plaed in a sealed ontainer at room temperature. As bromine is a volatile liquid, with a boiling point lose to room temperature, a signifiant number of partiles (moleules of Br ) will have enough energy to esape from the liquid state and form vapour in the proess known as evaporation. As the ontainer is sealed, the bromine vapour annot esape and so its onentration will inrease. Some of these vapour moleules will ollide with the surfae of the liquid, lose energy, and beome liquid in the proess known as ondensation. evaporation Br (l) U u Br (g) ondensation Br (g) Br (l) initial at equilibrium The rate of ondensation inreases with the inrease in onentration of vapour, as more vapour partiles ollide with the surfae of the liquid. Eventually, the rate of ondensation is equal to the rate of evaporation, and at this point there will be no rate of evaporation net hange in the amounts of liquid and gas present (Figure rate of 7.). We say that the system has evaporation rate of reahed equilibrium. This will ondensation only our in a losed system, rate of where the Br (g) annot esape ondensation as vapour but may ondense bak into the liquid. rate time

4 Chemial systems Consider the reation of dissoiation between hydrogen iodide (HI) and its elements hydrogen (H ) and iodine (I ). Hydrogen and hydrogen iodide are both olourless, whereas iodine is released as a purple gas, so this helps us to see what is happening. HI(g) s H (g) + I (g) olourless gas olourless gas purple gas If we arry out this reation starting with hydrogen iodide in a sealed ontainer, there will at first be an inrease in the purple olour owing to the prodution of iodine gas. But after a while this inrease in olour will stop, and it may appear that the reation too has stopped. In fat, what has happened is that the rate of the dissoiation of HI is fastest at the start when the onentration of HI is greatest and falls as the reation proeeds. Meanwhile, the reverse reation, whih initially has a zero rate beause there is no H and I present, starts slowly and inreases in rate as the onentrations of H and I inrease. Eventually, the rate of dissoiation of HI has beome equal to the rate of the reverse reation of assoiation between H and I, so the onentrations remain onstant. This is why the olour in the flask remains the same. At this point, equilibrium has been reahed. It is desribed as dynami beause both forward and bakward reations are still ourring. If we were to analyse the ontents of the flask at this point, we would find that HI, H, and I would all be present and that if there were no hange in onditions, their onentrations would remain onstant over time. We refer to this as the equilibrium mixture. If we reversed the experiment and started with H and I instead of HI, we would find that eventually an equilibrium mixture would again be ahieved in whih the onentrations of H, I, and HI would remain onstant. These relationships are shown in Figure 7.3. (a) onentration time equilibrium HI H, I (b) onentration time equilibrium The equilibrium state has speifi harateristis HI H, I In studies of equilibria we are dealing with reversible reations those that our in both diretions. The onvention is to desribe the reation from left to right (reatants to produts) as the forward reation, and the reation from right to left (produts to reatants) as the bakward or reverse reation. The symbol s is used to show that the reation is an equilibrium reation. The examples of physial and hemial systems disussed have shown that at equilibrium the rate of the forward reation is equal to the rate of the bakward reation. These reations have also shown some of the main features of the equilibrium state, and these an now be summarized as they apply to all reations at equilibrium. Iodine gas in a stoppered flask. Iodine is a rystalline solid at room temperature, but sublimes on heating to form a purple gas. The study of hemial hange often involves both the marosopi and mirosopi sales. Whih ways of knowing do we use in moving from the marosopi to the mirosopi? Figure 7.3 Equilibrium is reahed when the onentrations of reatants and produts beome onstant. Note the same equilibrium mixture is reahed starting from (a) a mixture of H and I or (b) from pure HI. forward reation Y reatants produts bakward reation 19 Y

5 07 Equilibrium Stritly speaking, all reations an be onsidered as equilibrium reations. However, in many ases the equilibrium mixture onsists almost entirely of produts that is, it is onsidered to have gone virtually to ompletion. By onvention we use the symbol rather than the equilibrium symbol in these ases. In other reations there may be so little produt formed that it is undetetable and the reation is onsidered to have effetively not happened. Make sure that you use the equilibrium symbol s when writing equations for reations where the reverse reations are signifiant. For example, it must be used when explaining the behaviour of weak aids and bases (Chapter 8). At equilibrium the rate of the forward reation is equal to the rate of the bakward reation. Feature of equilibrium state Explanation 1 Equilibrium is dynami The reation has not stopped but both forward and bakward reations are still ourring at the same rate. Equilibrium is ahieved in a losed system 3 The onentrations of reatants and produts remain onstant at equilibrium 4 At equilibrium there is no hange in marosopi properties 5 Equilibrium an be reahed from either diretion A losed system has no exhange of matter with the surroundings, so equilibrium is ahieved where both reatants and produts an reat and reombine with eah other. They are being produed and destroyed at an equal rate. Marosopi properties are observable properties suh as olour and density. These do not hange as they depend on the onentrations of the omponents of the mixture. The same equilibrium mixture will result under the same onditions, no matter whether the reation is started with all reatants, all produts, or a mixture of both. It is important to understand that even though the onentrations of reatant and produt are onstant at equilibrium, this in no way implies that they are equal. In fat, most ommonly there will be a muh higher onentration of either reatant or produt in the equilibrium mixture, depending both on the reation and on the onditions. We an see, for example, in Figure 7.3 that when the dissoiation of HI reahes equilibrium, there is a higher onentration of HI than of H and I. Thinking bak to the analogy in the introdution to this hapter, of you running in the opposite diretion on a moving stairase where the top and bottom represent reatants and produts respetively, it would be possible for you to be at equilibrium near the top of the stairase, near the bottom, or anywhere in between. As long as you were moving at the same speed as the stairase you would still have no net hange in position. The proportion of reatant and produt in the equilibrium mixture is referred to as its equilibrium position. Reations where the mixture ontains predominantly produts are said to lie to the right, reations with predominantly reatants are said to lie to the left. It is, however, often useful to be able to apture this information mathematially to ompare the equilibrium mixtures of different reations and the effet of different onditions. In the next setion we will look at how this is done. What are the differenes between theories and analogies as forms of explanation? NATURE OF SCIENCE At equilibrium no hange is observed on the marosopi level, although partiles are reating at the mirosopi level. These hanges an be dedued using tehniques suh as isotopi labelling, whih allow the progress of a speifi reatant to be followed. Our power of understanding is enhaned by ontributions from instrumentation and sensors that may gather information beyond human sense pereption. 0

6 Exerises 1 Whih statements are orret for a reation at equilibrium? I II III The forward and reverse reations both ontinue. The rates of the forward and reverse reations are equal. The onentrations of reatants and produts are equal. A I and II only B I and III only C II and III only D I, II, and III Whih statement is always true for a hemial reation that has reahed equilibrium at onstant temperature? A The yield of produt(s) is greater than 50%. B The rate of the reverse reation is lower than that of the forward reation. C The amounts of reatants and produts do not hange. D Both forward and reverse reations have stopped. 3 Whih statement is not true for a mixture of ie and water at equilibrium at onstant temperature? A The rates of melting and freezing are equal. B The amounts of ie and water are equal. C The same position of equilibrium an be reahed by ooling water and by heating ie. D There is no observable hange in the system. The equilibrium onstant K an be predited from a reation s stoihiometry Consider now the reation H (g) + I (g) s HI(g) If we were to arry out a series of experiments on this reation with different starting onentrations of H, I, and HI, we ould wait until eah reation reahed equilibrium and then measure the omposition of eah equilibrium mixture. Here are some typial results obtained at 440 C. Initial onentration / mol dm 3 Equilibrium onentration / mol dm 3 Sometimes you may see the equilibrium sign written with unequal arrows suh as. This is used to represent the reation that lies in favour of produts. Likewise, is used to represent a reation that lies in favour of reatants. Challenge yourself 1 A losed system is defined differently in different disiplines. In thermodynamis it means that no matter an be exhanged with the surroundings, but energy an flow freely. To what extent an the Earth be onsidered a losed system? Experiment I H I HI Initial onentration / mol dm 3 Equilibrium onentration / mol dm 3 Experiment II H I HI Initial onentration / mol dm 3 Equilibrium onentration / mol dm 3 Experiment III H I HI At a glane these data may not appear to show any pattern. However, there is a preditable relationship among the different ompositions of these equilibrium mixtures, and the key to disovering it is in the stoihiometry of the reation equation. 1

7 07 Equilibrium Remember square brakets [ ] are ommonly used to show onentration in mol dm 3. Many soures give units for K whih are a multiple of mol dm 3, depending on the stoihiometry of the reation. In fat this is not fully orret, as the terms in the equilibrium expression are really a thermodynami quality known as ativity that has no units. For this reason, we are omitting them in the values of K here, and you will not be required to inlude them in IB examination answers. The equilibrium onstant K has a fixed value for a partiular reation at a speified temperature. The only thing that hanges the value of K for a reation is the temperature. The equilibrium onstant expression will only give the value K when the onentrations used in the equation are the equilibrium onentrations for all reatants and produts. Stritly speaking, the subsript eqm should always be used in the equation, but by onvention this is generally left out. However, make ompletely sure that the only values you substitute into an equation to alulate K are the equilibrium onentrations. H (g) + I (g) s HI(g) If we take the equilibrium onentrations and proess them in the following way: [HI] eqm 1 eqm eqm 1 [H ] [I ] we find the following results: Experiment I (0.156) = = oeffiient of HI in the reation equation 1 = oeffiient of H in the reation equation 1 = oeffiient of I in the reation equation Experiment II (0.80) = Experiment III (0.100) = Clearly this way of proessing the equilibrium data produes a onstant value within the limits of experimental auray. This onstant is known as the equilibrium onstant, K. It has a fixed value for this reation at a speified temperature. In fat, every reation has its own partiular value of K whih an be derived in a similar way. First we use the balaned reation equation to write the equilibrium onstant expression. For the reation: aa + bb s C + dd the equilibrium onstant expression is [ C] [ D eqm ] a [ A] [ B] The value for K an then be determined by substituting the equilibrium onentrations of all reatants and produts into this equation. Note: eqm The equilibrium onstant expression has the onentrations of produts in the numerator and the onentrations of reatants in the denominator. Eah onentration is raised to the power of its oeffiient in the balaned equation. (Where it is equal to one it does not have to be given.) Where there is more than one reatant or produt the terms are multiplied together. d eqm b eqm = K Worked example Write the equilibrium expression for the following reations. (i) H (g) + O (g) s H O(g) (ii) Cu + (aq) + 4NH 3 (aq) s [Cu(NH 3 ) 4 ] + Solution (i) (ii) K = [ HO ] [ H ] [ O ] ( ) + [[Cu NH 3 ] ] K = [Cu ][NH ] 3

8 Exerises 4 Write the equilibrium onstant expression for the following reations: (a) NO(g) + O (g) s NO (g) (b) 4NH 3 (g) + 7O (g) s 4NO (g) + 6H O(g) () CH 3 Cl(aq) + OH (aq) s CH 3 OH(aq) + Cl (aq) 5 Write the equations for the reations represented by the following equilibrium onstant expressions: [NO ] (a) K = [N O] 4 3 [CO][H ] (b) K = [CH ][H O] 4 6 Write the equilibrium onstant expressions for the following hemial reations: (a) fluorine gas and hlorine gas ombine to form ClF 3 (g) (b) NO dissoiates into its elements () methane, CH 4, and steam reat to form arbon monoxide and hydrogen The magnitude of K gives information on the extent of reation Different reations have different values of K. What does this value tell us about a partiular reation? As the equilibrium onstant expression puts produts on the numerator and reatants on the denominator, a high value of K will mean that at equilibrium there are proportionately more produts than reatants. In other words, suh an equilibrium mixture lies to the right and the reation goes almost to ompletion. By ontrast, a low value of K must mean that there are proportionately less produts with respet to reatants, so the equilibrium mixture lies to the left and the reation has barely taken plae. Consider the following three reations and their K values measured at 550 K. H (g) + I (g) s HI(g) K = H (g) + Br (g) s HBr(g) K = H (g) + Cl (g) s HCl(g) K = The large range in their K values tells us about the differing extents of these reations. We an dedue that the reation between H and Cl has taken plae the most fully at this temperature, while H and I have reated the least. A good rule of thumb to apply to these situations is that if K 1, the reation is onsidered to go almost to ompletion (very high onversion of reatants into produts), and if K 1, the reation hardly proeeds. K very small Equilibrium lies to the left in favour of reatants K very large Equilibrium lies to the right in favour of produts The equilibrium onstant expressions desribed here apply to homogeneous reations, that is reations where reatants and produts are in the same phase, as gases, liquids, or in solution. It is good pratie always to inlude state symbols in your equations to ensure this is being applied orretly. Challenge yourself Why do you think the reations of the three halogens Cl, Br, and I with H have suh different values for their equilibrium onstant at the same temperature? What an you onlude about the strength of bonding in the three hydrogen halides? The magnitude of the equilibrium onstant K gives information about how far a reation goes at a partiular temperature, but not about how fast it will ahieve the equilibrium state. Figure 7.4 The larger the value of K, the further the equilibrium mixture lies to the right. Note that the magnitude of K does not give us any information on the rate of the reation. It informs us of the nature of the equilibrium mixture, but not on how quikly the equilibrium state will be ahieved. 3

9 07 Equilibrium The reation quotient, Q, enables us to predit the diretion of reation Remember that the value of K is alulated from substituting the equilibrium onentrations of all reatants and produts into the equilibrium onstant expression. Any other values used will not give the equilibrium value K for that reation at that temperature. This in itself an be useful. If we take the onentrations of the reatants and produts at the same moment in time when the reation is not at equilibrium, and substitute these into the equilibrium onstant expression, we obtain a value known as the reation quotient, Q. As time passes and the reation ontinues, the onentrations of all reation omponents hange and eventually reah the equilibrium onentrations. In other words, the value of Q hanges in the diretion of K. This enables us to predit the diretion in whih the reation will proeed. For example, if we again onsider the reation: H (g) + I (g) s HI(g) for whih K = 49.5 at 440 C, as we saw on page. The table below shows experimental data for the onentrations of the reation omponents from experiments I and II at a time when the reation mixture was not at equilibrium. Experiment I: onentration at time t / mol dm 3 Experiment II: onentration at time t / mol dm 3 H I HI The reation quotient, Q, is a measure of the relative amounts of reatants and produts present in a reation at a partiular time. Its value is determined from substituting onentrations of reation omponents, all measured at the same time, into the equilibrium expression. Note that the value of Q for a reation does not have a fixed value as it an be measured at any interval of time, whereas the value of K for a reation is a onstant at a speified temperature. 4 [HI] The equilibrium onstant expression = [H ][I ] (0.100) Experiment I, time t Q = = 4.00 (0.0500)(0.0500) Experiment II, time t (0.300) Q = = 103 (0.050)(0.0350) In experiment I, Q < K and so Q must inrease as the reation moves towards equilibrium. This means that the net reation must be to the right, in favour of produts. In experiment II, Q > K and so Q must derease as the reation moves towards equilibrium. This means that the net reation must be to the left, in favour of reatants. We an summarize the use of the reation quotient, Q, in determining the diretion of reation as follows: if Q = K, reation is at equilibrium, no net reation ours; if Q < K, reation proeeds to the right in favour of produts; if Q > K, reation proeeds to the left in favour of reatants.

10 Worked example The equilibrium onstant K for the reation is at 500 K. N (g) + 3H (g) s NH 3 (g) Determine whether the reation mixture is at equilibrium when the onentrations of the omponents at this temperature are as follows: [N ] = 1.50 [H ] = 1.00 [NH 3 ] = If it is not at equilibrium, state and explain in whih diretion the reation will proeed. Solution Comparison of the value of the reation quotient, Q, at a speifi time in a reation with the value of K for the reation, enables us to predit the diretion of hange. First write the equilibrium onstant expression. [NH 3 ] 3 [N ][H ] Calulate the value of Q at these onditions by substituting the given onentration values into the equilibrium expression. (8.00) Q = = (1.50)(1.00) Compare the value of Q at the given onditions with K. 4.7 < Therefore the reation is not at equilibrium. It will proeed to the right in favour of produts, as the value of Q must inrease to be equal to K at equilibrium. Relationships between K for different equations of a reation As K is defined with produts on the numerator and reatants on the denominator, eah raised to the power of their stoihiometri oeffiients in the balaned equation, we an manipulate its value aording to hanges made to these terms. For this disussion we will onsider the generi reation: for whih the equilibrium onstant is: aa + bb s C + dd K = [ C] [ D] a [ A] [ B] d b 5

11 07 Equilibrium 1 K for the inverse reation The inverse reation C + dd s aa + bb defines the produts as reatants and vie versa. We will denote its equilibrium onstant as K. a b [ A] [ B] K = d C D [ ] [ ] 1 1 We an see that K = or K = K. K In other words the equilibrium onstant for a reation is the reiproal of the equilibrium onstant for its inverse reation. K for a multiple of a reation Consider now the reation aa + bb s C + dd We will denote its equilibrium onstant as K x. K x = [ C] [ D] a [ A] [ B] d b We an see that eah term has been squared in K x relative to its value in K. So K x = K. By similar thinking, we an onlude that tripling of the stoihiometri oeffiients would lead to a ubing of the value of K, halving of the stoihiometri oeffients would lead to a square rooting of the value of K, and so on. These manipulations of the value of K are summarized below. inversing the reation Effet on equilibrium expression inverts the expression Effet on K 1 K or K 1 doubling the reation oeffiients squares the expression K tripling the reation oeffiients ubes the expression K 3 Challenge yourself 3 In heterogeneous equilibrium, the terms for pure solids or liquids are not shown in the equilibrium expression. Suggest why this is the ase. halving the reation oeffiients square roots the expression K adding together two reations multiplies the two expressions K i K ii 6

12 Worked example The equilibrium onstant for the reation HI(g) s H (g) + I (g) is 0.04 at a ertain temperature. What would be the value of the equilibrium onstant, K, for the following reation at the same temperature? Solution ½H (g) + ½I (g) s HI(g) K [ H ][ I ] [ HI] [ HI] 1/ [ H ] [ I ] = K = Note that the reation is reversed and the oeffiients in the equation are halved. Overall, the value of K is the square root of the value of K. 1 So K = or ( K ) 1. K 1 K = = Exerises 7 When the following reations reah equilibrium, does the equilibrium mixture ontain mostly reatants or mostly produts at the speified temperature? Assume that the value for K given orresponds to the temperature of the reation mixture. (a) N (g) + H (g) s N H 4 (g) K = (b) N (g) + O (g) s NO(g) K = () NO(g) + O (g) s NO (g) K = The equilibrium onstant for the reation H O(g) + Cl O(g) s HOCl(g) is at 98 K. Determine whether the following sets of onditions represent an equilibrium mixture for the reation at this temperature. For those not at equilibrium, determine in whih diretion the reation will proeed. [H O] [Cl O] [HOCl] (a) (b) () At a given temperature, the reation SO + O (g) s SO 3 (g) has a value of K = 78. Determine values of K for the following reations at this temperature. (a) 4SO + O (g) s 4SO 3 (g) (b) SO 3 (g) s SO + O (g) () SO 3 (g) s SO + ½O (g) When equilibrium is disrupted A system remains at equilibrium so long as the rate of the forward reation equals the rate of the bakward reation. But as soon as this balane is disrupted by any hange 1/ Henri-Louis Le Chatelier was a Frenh hemist who published his equilibria priniple in Amongst other researh, he also investigated the possibility of ammonia synthesis, but abandoned his efforts after suffering a devastating explosion in his laboratory. After Haber s later eluidation of the onditions required in the reation, Le Chatelier realized that he had been very lose to the disovery himself. Late in his life he wrote I let the disovery of the ammonia synthesis slip through my hands. It was the greatest blunder of my areer. We an only speulate on how history might have been re-written if this disovery had in fat been made in Frane rather than in Germany before World War I. When a system at equilibrium is subjeted to a hange, it will respond in suh a way as to minimize the effet of the hange. 7

13 07 Equilibrium in onditions that unequally affets the rates of these reations, the equilibrium ondition will no longer be met. It has been shown, however, that equilibria respond in a preditable way to suh a situation, based on a priniple known as Le Chatelier s priniple. This states that a system at equilibrium when subjeted to a hange will respond in suh a way as to minimize the effet of the hange. Simply put, this means that whatever we do to a system at equilibrium, the system will respond in the opposite way. Add something and the system will reat to remove it, remove something and the system will reat to replae it. After a while, a new equilibrium will be established and this will have a different omposition from the earlier equilibrium mixture. Applying the priniple therefore enables us to predit the qualitative effet of typial hanges that our to systems at equilibrium. Experiment to show the effet of hanging the onentration of hloride ions on the obalt hloride equilibrium reation: [Co(H O) 6 ] + (aq) + 4Cl (aq) s CoCl 4 (aq) + 6H O(l) The flask on the left has a low onentration of hloride ions, giving the pink olour of the ompex ion with water. As the onentration of hloride ions is inreased, the equilibrium shifts to the right, hanging the olour from pink to blue. Adding water would shift the equilibrium in the opposite diretion. Cobalt hloride is often used to test for the presene of water beause of this olour hange. Changes in onentration Suppose an equilibrium is disrupted by an inrease in the onentration of one of the reatants. This will ause the rate of the forward reation to inrease while the bakward reation will not be affeted, so the reation rates will no longer be equal. When equilibrium re-establishes itself, the mixture will have new onentrations of all reatants and produts, and the equilibrium will have shifted in favour of produts. The value of K will be unhanged. This is in keeping with the predition from Le Chatelier s priniple: addition of reatant auses the system to respond by removing reatant this favours the forward reation and so shifts the equilibrium to the right. Similarly, the equilibrium ould be disrupted by a derease in the onentration of produt by removing it from the equilibrium mixture. As the rate of the bakward reation is now dereased, there will be a shift in the equilibrium in favour of the produts. A different equilibrium position will be ahieved, but the value of K will be unhanged. Again this onfirms the predition from Le Chatelier s priniple: removal of produt auses the system to respond by making more produt this favours the forward reation and so shifts the equilibrium to the right. The graph in Figure 7.5 illustrates these disruptions to equilibrium for the reation N (g) + 3H (g) s NH 3 (g) Figure 7.5 Effets of the addition of reatant and removal of produt on the equilibrium N (g) + 3H (g) s NH 3 (g). When H is added some N reats and more NH 3 is formed as the equilibrium shifts to the right. When NH 3 is removed, more N reats with H as the equilibrium again shifts to the right. After eah hange a new equilibrium mixture is ahieved. onentrations NH 3 N H equilibrium H added here equilibrium NH 3 removed here equilibrium 8 time After H is added, the onentrations of N and H derease (in a 1 : 3 ratio in keeping with their reation stoihiometry), while the onentration of NH 3 rises (in a : 1 ratio relative to N ) as the rate of the forward reation inreases and the equilibrium shifts

14 to the right. The new equilibrium mixture has a higher proportion of produts. In the seond part of the graph, removal of NH 3 from the equilibrium mixture auses a derease in the onentrations of N and H as they reat to form more NH 3. Often in an industrial proess the produt will be removed as it forms. This ensures that the equilibrium is ontinuously pulled to the right, so inreasing the yield of produt. Applying Le Chatelier s priniple, an you think what onentration hanges would ause an equilibrium to shift to the left? The answer is either an inrease in onentration of produt or a derease in onentration of reatant. Changes in pressure Equilibria involving gases will be affeted by a hange in pressure if the reation involves a hange in the number of moleules. This is beause there is a diret relationship between the number of gas moleules and the pressure exerted by a gas in a fixed volume. So if suh a reation at equilibrium is subjet to an inrease in pressure, the system responds to derease this pressure by favouring the side with the smaller number of moleules. Conversely, a derease in pressure will ause a shift in the equilibrium position to the side with the larger number of moleules of gas. A different equilibrium position will be ahieved but the value of K will be unhanged, so long as the temperature remains the same. For example, onsider the reation used in the prodution of methanol: CO(g) + H (g) s CH 3 OH(g) In total there are three moleules of gas on the left side and one moleule of gas on the right side. So here high pressure will shift the equilibrium to the right, in favour of the smaller number of gas moleules, whih inreases the yield of CH 3 OH. Note that many ommon equilibrium reations do not involve a hange in the number of gas moleules and so are not affeted by hanges in pressure. For example, the reation H (g) + I (g) s HI(g) has two moleules of gas on both sides of the equation. Changing pressure for this reation will affet the rate of the reation but not the position of equilibrium or the value of K. Changes in temperature We have noted that K is temperature dependent, so hanging the temperature will hange K. However, in order to predit how it will hange we must examine the enthalpy hanges (see Chapter 5) of the forward and bakward reations. Remember that an exothermi reation releases energy ( H negative), whereas an endothermi reation absorbs energy ( H positive). The enthalpy hanges of the forward and bakward reations are equal and opposite to eah other. So if we apply Le Chatelier s priniple, inluding the energy hange in the hemial reation, we an predit how the reation will respond to a hange in temperature. Consider the reation: NO (g) s N O 4 (g) H = 57 kj mol 1 brown olourless Changes in the onentration of reatants or produts alter the equilibrium position and so hange the omposition of the equilibrium mixture. But the value of K stays the same. Changes in pressure or volume will affet the position of equilibrium of a reation if it involves a hange in the number of gas moleules. The value of K remains unhanged. When desribing the effets of volume or pressure on equilibrium reations, you must state it depends on the relative number of gas moleules on both sides of the equation. Solids and liquids are hardly affeted by hanges in pressure. An inrease in pressure favours the side of an equilibrium reation that has the smaller number of gas moleules. When H is given for an equilibrium reation, by onvention its sign refers to the forward reation. So a negative sign for H means that the forward reation is exothermi, and the bakward reation is endothermi. Challenge yourself 4 Use information from this setion to explain why there is very little NO in the atmosphere under ordinary onditions, and why severe air pollution is often haraterized by a brownish haze. 9

15 07 Equilibrium The negative sign of H tells us that the forward reation is exothermi and so releases heat. If this reation at equilibrium is subjeted to a derease in temperature, the system will respond by produing heat and it does this by favouring the forward exothermi reation. This means that the equilibrium will shift to the right, in favour of the produt N O 4. A new equilibrium mixture will be ahieved and the value of K will inrease. So here we an see that the reation will give a higher yield of produts at a lower temperature. Conversely, inreasing the temperature favours the bakward endothermi reation, and so shifts the equilibrium to the left, dereasing the value of K. The reation mixture beomes a darker olour as the onentration of NO inreases. The table below illustrates the effet of temperature on the value of K for this reation. Temperature / K K for NO (g) s N O 4 (g) Experiment to show the effet of temperature on the reation that onverts NO (brown) to N O 4 (olourless). As the temperature is inreased, more NO is produed and the gas beomes darker, as seen in the tube on the left. Combustion reations are generally desribed as exothermi, but the reation N (g) + O (g) s NO(g) is endothermi. When is it appropriate to refer to an exeption to a rule, and when does the rule need to be reonsidered? Even though in this ase a lower temperature will produe an equilibrium mixture with a higher proportion of produts, remember from Chapter 6 that low temperature also auses a lower rate of reation. And so, although a higher yield will be produed eventually, it may simply take too long to ahieve this from pratial and eonomi onsiderations if this was an industrial-sale reation. We will ome bak to this point later in this hapter. Now onsider the following reation: N (g) + O (g) s NO(g) H = +181 kj mol 1 In this ase we an see that the forward reation is endothermi and so absorbs heat. So here the effet of a dereased temperature will be to favour the bakward exothermi reation. Therefore the equilibrium will shift to the left, in favour of reatants, and K will derease. At higher temperatures, the forward endothermi reation is favoured, so the equilibrium shifts to the right and K will inrease. The table below illustrates the effet of temperature on the value of K for this reation. Temperature / K K for N (g) + O (g) s NO(g) Inreasing the temperature auses an inrease in the value of K for an endothermi reation and a derease in the value of K for an exothermi reation. 30 The reation N (g) + O (g) s NO(g) takes plae in motor vehiles where the heat released by the ombustion of the fuel is suffiient to ause the nitrogen and oxygen gases from the air to ombine together in this way. Unfortunately, the produt NO is toxi, and, worse still, quikly beomes onverted into other toxins that form the omponents of aid rain and smog. It is therefore of great interest to vehile manufaturers to find ways of lowering the temperature during ombustion in order to redue the prodution of NO in the reation above. These examples illustrate that, unlike hanges in onentration and pressure, hanges in temperature do ause the value of K to hange. An inrease in temperature inreases the value of K for an endothermi reation and dereases the value of K for an exothermi reation. This is beause hanges in temperature have a different effet

16 on the rates of the forward and bakward reations, due to their different ativation energies, as disussed in Chapter 6. In the next hapter, we will use this fat to explain why the ph of pure water is temperature dependent. Addition of a atalyst As we learned in Chapter 6, a atalyst speeds up the rate of a reation by providing an alternate reation pathway that has a transition state with a lower ativation energy, E a. This inreases the number of partiles that have suffiient energy to reat without raising the temperature. E a of forward reation unatalysed reation E a of forward reation energy reatants produts extent of reation E a of bakward reation energy reatants atalysed reation produts extent of reation lowering of E a in presene of atalyst E a of bakward reation Figure 7.6 The effet of a atalyst in lowering the ativation energy of both forward and bakward reations. Beause the forward and bakward reations pass through the same transition state, a atalyst lowers the ativation energy by the same amount for the forward and bakward reations. So the rate of both these reations will be inreased by the same fator, as shown in Figure 7.6. The atalyst will therefore have no effet on the position of equilibrium, or on the value of K. In other words the atalyst will not inrease the equilibrium yield of produt in a reation. It will, however, speed up the attainment of the equilibrium state and so ause produts to form more quikly. Catalysts are generally not shown in the reation equation or in the equilibrium onstant expression as they are not hemially hanged at the end of the reation, and have no effet on the equilibrium onentrations. Catalysts are widely used in industrial proesses to inrease the rate of produt formation, and are involved in every single biohemial reation. One of the key priniples of Green Chemistry is that atalyti reagents, hosen to be as seletive as possible, are superior to stoihiometri reagents as they are not onsumed in the reation. Catalysts, inluding the differenes between homogeneous and heterogeneous atalysts, are disussed in more detail in Option A: Materials, topi A.3. Summary We an now summarize the effets of hanges in onentration, pressure, temperature, and atalyst on the position of equilibrium and on the value of K. Observations of shifts in the position of hemial equilibria Full details of how to arry out this experiment with a worksheet are available on your ebook. Catalysts do not hange the position of equilibrium or the yield of a single reation, but they enable the equilibrium mixture to be ahieved more quikly. Catalysts do not hange the value of K. Effet of Change in position of equilibrium Change in value of K 1 onentration hanges no hange pressure hanges if reation involves a hange no hange in the number of gas moleules 3 temperature hanges hanges 4 atalyst no hange no hange A partiular reation at a speified temperature an have many different possible equilibrium positions, but only one value for the equilibrium onstant K. 31

17 07 Equilibrium NATURE OF SCIENCE Knowledge of how systems at equilibrium respond to hange has many appliations, as we will see in the next setion. Le Chatelier s priniple is a useful preditive tool for this purpose, and has the advantage of being relatively simple to apply and effetive. But it has some disadvantages too. Firstly, it leads only to qualitative preditions of the system s response. In some ases, suh as investigations of when a preipitate will form in aqueous solution, this is insuffiient. Seondly, Le Chatelier s priniple offers no explanation for the response it predits what will happen, but not why. It an even be misleading in that it an suggest a false sense of purpose to systems responses if the language used is suh as the system tries to. On the other hand, use of the reation quotient, Q, to predit the onsequene of hange an often provide an effetive explanation. As disturbanes in onentration or pressure hange the value of Q, the system responds as Q progresses towards K. But hanges in temperature are different beause they hange the value of K in this ase the system responds as Q progresses towards the new value of K. The response of K to temperature an be explained through thermodynamis and the fat that the forward and bakward reations respond differently to temperature hanges due to their different ativation energies. Inreased temperature favours the endothermi reation as it has the higher ativation energy. Sientifi explanations often draw on different approahes and theories in this way. So long as the approahes do not ontradit eah other, together they an larify and strengthen the understanding. Note that you are not expeted to learn speifi onditions for any reation, so there is no need to fous on the names of atalysts, speifi temperature used, et. But you should be able to apply an understanding of equilibria to any given example, and predit the onditions likely to be effetive. 3 Fritz Haber Exerises 10 The manufature of sulfur trioxide an be represented by the equation below: SO (g) + O (g) s SO 3 (g) H * = 197 kj mol 1 What happens when a atalyst is added to an equilibrium mixture from this reation? A B C D The rate of the forward reation inreases and that of the reverse reation dereases. The rates of both forward and reverse reations inrease. The value of H * inreases. The yield of sulfur trioxide inreases. 11 What will happen to the position of equilibrium and the value of the equilibrium onstant when the temperature is inreased in the following reation? Position of equilibrium Br (g) + Cl (g) s BrCl(g) A shifts towards the reatants dereases B shifts towards the reatants inreases C shifts towards the produts dereases D shifts towards the produts inreases Value of equilibrium onstant H * = +14 kj 1 Whih hanges will shift the position of equilibrium to the right in the following reation? I II III adding a atalyst dereasing the oxygen onentration inreasing the volume of the ontainer CO (g) s CO(g) + O (g) A I and II only B I and III only C II and III only D I, II, and III 13 For eah of the following reations, predit in whih diretion the equilibrium will shift in response to an inrease in pressure: (a) CO (g) s CO(g) + O (g) (b) CO(g) + H s CH 3 OH(g) () H (g) + Cl (g) s HCl(g) 14 How will the equilibrium: CH 4 (g) + H S(g) s CS (g) + 4H (g) H = +ve respond to the following hanges? (a) addition of H (g) (d) removal of CS (g) (b) addition of CH 4 (g) (e) inrease in temperature () a derease in the volume of the ontainer

18 15 The reation CO(g) + O (g) s CO (g) H = 566 kj mol 1 takes plae in atalyti onverters in ars. If this reation is at equilibrium, will the amount of CO inrease, derease, or stay the same when: (a) the pressure is inreased by dereasing the volume? (b) the pressure is inreased by adding O (g)? () the temperature is inreased? (d) a platinum atalyst is added? Equilibrium theory is applied in many industrial proesses In reations involving the manufature of a hemial it is obviously a goal to obtain as high a onversion of reatant to produt as possible. Appliation of Le Chatelier s priniple enables hemists to hoose onditions that will ause the equilibrium to lie to the right, and so help to ahieve this. But the yield of a reation is only part of the onsideration. The rate is also learly of great signifiane as it would be of limited value if a proess were able to laim a high equilibium yield of produt, but took several years to ahieve this. The eonomis of the proess will depend on onsiderations of both the equilibrium and the kinetis of the reation in other words on how far and how fast the reation will proeed. Sometimes these two riteria work against eah other, and so the best ompromise must be reahed. A few ase studies of industrial proesses are disussed here. The Haber proess: the prodution of ammonia, NH 3 Fritz Haber was born in what is now Poland but moved to Germany early in his areer. Together with Carl Bosh, also of Germany, he developed the proess for the industrial synthesis of ammonia from its elements, and the first fatory for ammonia prodution opened in Germany in 1913, just before World War I. This development had enormous signifiane for the ountry at war: it enabled the ontinued prodution of explosives despite the fat that imports of nitrate from Chile, used for produing nitri aid and explosives suh as TNT, were barred through the blokaded ports. This effetively enabled Germany to ontinue its war efforts for another 4 years. Haber was awarded the Nobel Prize in Chemistry in In many ways history has reorded this as a ontroversial hoie not only had Haber s work helped to prolong the war, he had also been responsible for the development and use of hlorine as the first poison gas. Ironially, despite his evident patriotism towards Germany, he was expelled from the ountry in 1933 when the rising tide of anti-semitism onflited with his Jewish anestry. It is estimated that as muh as 130 million tonnes of ammonia, NH 3, are produed worldwide every year. China is responsible for nearly one-third of this, and India, Russia, and the USA also produe signifiant amounts. Approximately 80% of the ammonia is used to make fertilizers, notably ammonium nitrate, NH 4 NO 3. Other uses inlude synthesis of textiles suh as nylon and powerful explosives. In April 013, a major explosion ourred in a fertiliser fatory in Texas, USA, killing and injuring hundreds of people. It was aused by a fire in a stok of 50,000 kilograms of ammonium nitrate. Aidents suh as this in industrial plants raise many questions regarding health and safety, storage, and handling of hemials and the balane of reponsibility between ompanies, governments, and individuals. The book The alhemy of air: a Jewish genius, a doomed tyoon, and the sientifi disovery that fed the world but fueled the rise of Hitler is written by Thomas Hager. It is a fasinating aount of the histori disovery of the proess to synthesize ammonia, and its ontinuing mixed onsequenes these inlude the revolution in global food prodution, the death of millions through wars, and growing onerns of nitrate pollution and obesity. The Haber proess is based on the reation N (g) + 3H (g) s NH 3 (g) H = 93 kj mol 1 The following information an be derived from this equation: all reatants and produts are gases; there is a hange in the number of gas moleules as the reation proeeds: four gas moleules on the left and two on the right; Trator applying a hemial solution of fertilizer to the soil. Ammonium salts suh as ammonium nitrate and sulfate are partiularly effetive fertilizers as they supply nitrogen needed by plants and are readily soluble. It is estimated that without the use of ammonium fertilizers, two billion people would starve. 33

19 07 Equilibrium the forward reation is exothermi so releases heat; the bakward reation is endothermi so absorbs heat. Appliation of Le Chatelier s priniple to this reation enables us to onsider the optimum onditions. dyes, pigments, and paints ar batteries, eletroplating, pulp, and paper soaps, detergents, and plastis agriultural: both phosphate and ammonium sulfate fertilizers Figure 7.7 The uses of sulfuri aid. More sulfuri aid by mass is produed worldwide than any other hemial. It has been found that the prodution of sulfuri aid losely mirrors historial events suh as major wars that affet a ountry s eonomy. For this reason some eonomists use sulfuri aid prodution as a measure of a ountry s industrial strength. Sulfuri aid is used diretly or indiretly in nearly all industrial proesses, inluding the prodution of fertilizers, detergents, and paints and in ore proessing, steel prodution, and water treatment. Approximately 50 million tonnes are produed annually aross all ontinents. The proess gets its name the Contat proess from the fat that moleules of the gases O and SO reat in ontat with the surfae of the solid atalyst V O Conentration: the reatants nitrogen and hydrogen are supplied in the molar ratio 1 : 3 in aordane with their stoihiometry in the equation. The produt ammonia is removed as it forms, thus helping to pull the equilibrium to the right and inreasing the yield. Pressure: as the forward reation involves a derease in the number of gas moleules, it will be favoured by a high pressure. The usual pressure used in the Haber proess is about 10 7 Pa. Temperature: as the forward reation is exothermi, it will be favoured by a lower temperature. However, too low a temperature would ause the reation to be uneonomially slow, and so a moderate temperature of about 450 C is used. Catalyst: a atalyst will speed up the rate of prodution and so help to ompensate for the moderate temperature used. A atalyst of finely divided iron is used, with small amounts of aluminium and magnesium oxides added to improve its ativity. More reently, ruthenium has beome the atalyst of hoie, and this has helped redue the energy requirement. In fat, the Haber proess ahieves a onversion of H and N into NH 3 of only about 10 0% per pass through the reator. After separation of the NH 3 produt, the unonverted reatants are reyled to the reator to obtain an overall yield of about 95%. This reyling of unonverted reatants is ommonly used in industrial proesses, and allows proesses with low equilibrium yield to be made ommerially viable. The Contat proess: the prodution of sulfuri aid, H SO 4 The Contat proess involves a series of three simple reations. (i) the ombustion of sulfur to form sulfur dioxide; (ii) the oxidation of sulfur dioxide to sulfur trioxide: SO (g) + O (g) s SO 3 (g) H = 196 kj mol 1 (iii) the ombination of sulfur trioxide with water to produe sulfuri aid. It has been shown that the overall rate of the proess depends on step (ii), the oxidation of sulfur dioxide. So applying Le Chatelier s priniple to this step, we an predit the onditions that will most favour the formation of produt. These are summarized in the table below. pressure temperature Influene on reation forward reation involves redution in the number of moleules of gas from three moleules reatant to two moleules produt: high pressure will favour produt forward reation is exothermi: low temperature will inrease the equilibrium yield, but derease the rate Condition used 10 5 Pa (this gives a very high equilibrium yield, so still higher pressure is not needed) 450 C atalyst inreases the rate of reation vanadium(v) oxide

20 The prodution of methanol CO(g) + H (g) s CH 3 OH(g) H = 90 kj mol 1 Again, Le Chatelier s priniple an be used to onsider the onditions that will optimize the prodution. pressure temperature Influene on reation forward reation involves redution in the number of moleules of gas from three moleules reatant to one moleule produt: high pressure will favour produt forward reation is exothermi: low temperature will inrease the yield, but derease the rate Condition used Pa 50 C atalyst inreases the rate of reation Cu ZnO Al O 3 NATURE OF SCIENCE Sientifi researh is largely influened by the soial ontext, whih helps to determine funding and set priorities. A good example is Haber s work on ammonia synthesis, whih beame pressing in Germany in the early years of the 0th entury. Sientifi disoveries often have signifiant eonomi, ethial, and politial impliations. Some of these may be unintended onsequenes of the disovery, suh as the environmental degradation aused by the exess use of nitrate fertilizers as an outome of the Haber proess. This raises the question of who must take moral responsibility for the appliations of sientifi disoveries. The proess of siene inludes risk benefit analyses, risk assessment, and ethial onsiderations, but sometimes the full onsequenes annot be predited and do not beome known until muh later. Exerises 16 In the Haber proess for the synthesis of ammonia, what effets does the atalyst have? Rate of formation of NH 3 (g) A inreases inreases B inreases dereases C inreases no hange D no hange inreases Amount of NH 3 (g) formed 17 SO (g) + O (g) s SO 3 (g) H * = 00 kj Aording to the above information, what temperature and pressure onditions produe the greatest amount of SO 3? Temperature A low low B low high C high high D high low Pressure 18 Predit how you would expet the value for K for the Haber proess to hange as the temperature is inreased. Explain the signifiane of this in terms of the reation yield. Challenge yourself 5 Consider the atom eonomy of the reations desribed here using the formula mass of desired produt atom eonomy = 100 totalmassofreatants Land ontaminated by waste impurities from an old sulfuri aid plant lose to a residential area in Bilbao, Spain. The waste largely derives from smelting and ombustion proesses. The full onsideration of any industrial proess must inlude an assessment of its impat on the environment, both loally and globally. Methanol is used as a hemial feedstok, that is it is used to make other hemials. A high proportion is onverted into methanal, HCHO, whih is then onverted into plastis, paints, explosives, and plywood. Methanol is used as a laboratory solvent, an antifreeze agent, and in the proess of produing biodiesel fuel from fats. Interest has also foused on the potential of methanol as an energy storage moleule in the so-alled methanol eonomy. In ongoing efforts to redue dependene on imported fossil fuels, China has greatly inreased prodution apaity and onsumption of methanol for its transportation setor, and plans to produe five million alternative-energy vehiles a year by 00. Explain how this is different from the reation yield. 35