Chemical Equilibrium

1. Chemical Equilibrium Will a given reaction ever take place spontaneously, even if one waits forever? The answer was that any reaction that leads to a lower free energy will occur spontaneously. Any reaction that requires an increase in free energy will not; it will be spontaneous in the reverse direction instead. Now we come to a more difficult but very practical question in this and the following chapter: Granted that a given reaction is spontaneous, how far will it go, and will it take place within a reasonable time? What factors determine the rates of chemical reactions?  Some chemical reactions appear to go essentially to completion, ending with products and an undetectable or negligable amount of reactants. Some but not all of these reactions also are very fast (e.g., explosions). Other reactions stop short of completion and remain a mixture of reactants and products after all visible chemical change is over. Still other reactions do not appear to take place at all within a reasonable time, even though their calculated free energy change is quite negative.

2. Chemical Equilibrium HCl synthesis is an example of the first kind of reaction: fast, and apparently complete (see previous page). If hydrogen gas and chlorine gas are mixed in a container with a window and kept in the dark, no reaction will occur. But light will trigger an explosion:H2 (g) + Cl2 (g) →2HCl (g) ΔG = - 45.54 kcal per 2 moles of HClAfter the explosion almost no detectable quantities of H and Cl will remain. The large negative free energy change indicates that the reaction should be spontaneous, and the light-triggered explosion shows that this is so. Then why is there no reaction in the dark? The answer is that the reaction in the dark is still spontaneous, but is so slow that we do not notice any changes.

5. Chemical Equilibrium

7. Chemical Equilibrium Hydrogen and oxygen gases behave similarly. The reaction: 2H2 (g) + O2 (g) → 2H2O(g) ∆ G = - 109.3 kcal per 2 moles of H Ohas a large negative free energy change and threfore is highly spontaneous. Yet we can allow a mixture of hydrogen and oxygen to sit for years without seeing an appreciable reaction. We have only to bring a lighted match up to the mixture, however, for a vivid demonstration of how intrinsically spontaneous the reaction is. The same effect can be produced by a catalyst such as platinum black, a finely divided form of metallic platinum that has a large surface area.

9. Chemical Equilibrium One of the villains in automotive smog is nitric oxide, NO. If we calculate the free energy of decomposition of NO, 2NO(g) → N2 (g) + O2 (g)ΔG = -41.4 kcal per 2 moles of NO we arrive at the conclusion that the reaction should be spontaneous. The breakdown of NO to harmless atmospheric gases should be quite complete. Yet any inhabitant of the Los Angeles basin can tell you that this is only wishful thinking. Oxides of nitrogen are among the most difficult components of the smog problem. They do not break down to N and O at an appreciable rate, although breakdown is thermodynamically spontaneous. By analogy with the water reaction, you might expect that a catalyst could be found that would speed up the decomposition of NO, and this is true.

11. Chemical Equilibrium The other factor that we have mentioned that speeds up reaction is temperature. Changing the temperature can do more than just accelerate a reaction; it can also affect the nature of the products. As an example, the synthesis of ammonia is important as a means of fixing atmospheric nitrogen for use in fertilizers and explosives:N2 (g) + 3H2 (g) 2NH3 (g) ΔG = -7.95 kcal per 2 moles of NH3If the reaction is run at room temperature, the final mixture is almost entirely NH3 with very little N2 and H2 left. A disadvantage is that the reaction is extremely slow, but it can be speeded up with an iron-manganese catalyst. Trying to accomplish the same result by raising the temperature leads only to trouble, since at 450K, the product is no longer virtually pure NH3 , but is a mixture of N2 , H2 and NH3 in roughly equal proportions. The standard free energy change at this temperature is zero. (The standard starting condition of 1 atm partial pressure for each gas is, in fact, the equilibrium condition at 450K.) Even worse, at 1000K the standard free energy change is +29.6 kcal (compared with -7.95 kcal at 298K), and almost no ammonia is formed.

14. Chemical Equilibrium From these examples, we can make two observations:1. Not all chemical reactions go to completion. Even after an infinitely long time, some systems remain mixtures of reactants and products.2. Some reactions that are highly spontaneous by free energy criteria do not proceed at a measurable rate. Catalysis or heat sometimes can help.

16. Chemical Equilibrium Analogy Let us introduce the idea of chemical equilibrium by an analogy, seemingly far-fetched at first sight, but actually mathematically correct. Imagine that a crabapple tree sits on the dividing line between two homes, one inhabited by a crochety old man, and the other by a father who has told his young son to go out and rid the back yard of crabapples. The boy quickly realizes that the easiest way to dispose of the crabapples is to throw them into the neighbouring yard. He does so, arousing the ire of the old man.  The boy and the man start throwing crabapples back and forth across the fence as fast as they can. Who will win?The battle is outlined in five phases, as shown on the following pages.

19. Chemical Equilibrium Analogy Assuming that the boy is more energetic and agile than the old man, you might think at first that the conflict would end with all of the apples on the old man's side (Phases I and II).It is true that with equal numbers of crabapples on either side, the boy will throw apples across the fence faster than the old man can return them. But this only means that apples will become more plentiful on the old man's side, and easier to reach.

20. Chemical Equilibrium Analogy They will become scarcer on the boy's side, and require more running around to locate. Eventually a standoff, or equilibrium, will be reached, in which the number of apples crossing the fence is the same in both directions.The old man will throw less quickly but will have less trouble finding apples (Phase III); the boy will throw more rapidly but will waste time scurrying around hunting for the relatively few crabapples on his side (Phase IV). The ratio of apples on the two sides of the fence ultimately will be determined by the relative agility of the two combatants, but all of the apples will not end up on one side (Phase V).

23. Chemical Equilibrium Analogy We can express the rate at which the old man throws apples by RateM = kMCM The rate is measured in apples per second across the fence, and CM is the concentration of apples on the man's side of the fence in apples per square foot of ground. The rate constant, kM , has units of square feet per second: The value of kM expresses the agility of the old man, and his speed in covering the territory on his side of the fence. The rate at which the boy throws apples back across the fence is given by RateB = kBCBin which CB is the concentration of apples in the boy's yard, and kB is the rate constant, or agility constant, which tells how fast the boy gets around on his side of the fence, in square feet per second. Since we have assumed that the boy is livelier than the man, kB is greater than kM .

25. Chemical Equilibrium Analogy If the boy had cleaned up his yard completely before the old man came out, then as the battle began,RateM would be greater than RateB , and there would be a net flow of apples to the boy's side. His agility would do him no good if there were no apples on his side to pick up. Conversely, if the battle had begun with equal concentrations of apples on each side, then RateB would have been greater than RateM because the agility constant kB is greater than kM .With the same number of apples at their disposal, the boy always can do better than the old man because he gets around faster.In either case, a neutral observer would have found to his surprise that the battle eventually settled down into a stalemate, or equilibrium in which RateM = RateB , at a point where the extra apples on the old man's side just compensated for the extra agility of the boy.

29. Reference: VIRTUAL CHEMISTRY http://www.chem.ox.ac.uk/vrchemistry/