Goldilocks I: Bronsted Acids and Bases p.1 The story of Goldilocks is familiar to many children and remembered by many adults. In that story, Goldilocks visits the house of the Three Bears while the Bears are temporarily absent, and as she tries out the Bears things, she discovers that in each set of three things bowls of porridge, chairs, and beds one item is too hot, too high or too hard, another is too cold, too low or two soft, while one is just right. Astronomers have used this concept to describe a habitation zone around suns, in which conditions are favorable for life, but outside which, life is unlikely to exist. Economists have used the same concept to describe conditions under which an economic system functions optimally. I am told there is a Swedish word, lagom that captures this idea. Its English translations begin with: "just the right amount", and extend to "enough, sufficient, and adequate, or even "in moderation", "in balance", "optimal", "suitable", and "average". Most of these include the idea of a special condition that exists between two extremes. In a series of articles, we shall explore some aspects of chemistry that may be better understood as including a "Goldilocks effect", beginning with Bronsted and. Students of chemistry should be familiar with definitions of Bronsted as proton (H + ) donors and of Bronsted as proton (H + ) acceptors, thus defining a Bronsted acid-base reaction as a proton (H + ) transfer. Further examination leads to noticing that as an acid donates a proton, what remains could reclaim the lost proton, and thus what is left is a base a species we call this the base of the acid. Likewise, when a base accepts a proton, what forms could subsequently lose that proton, and thus what forms is the acid of the base. Each acid exists, then, in a pair with its base, and each base in a pair with its acid. In order to function as an acid, a species must include a proton (H + ) in its chemical makeup, and each base must include a place to put a proton. Note, though, that the more an acid is able to force its proton onto another base, the less its base would be able to take that proton back or, in other words, the an acid is, the er its base would be, and vice versa: the er an acid is, the would be its base. With this simple conclusion, we can form three groups of acid-base pairs: (1) pairs in which the acid is strong ("too strong"), while its base is ("too "), (2) pairs in which the acid is ("too "), while its base is strong ("too strong"), and (3) pairs in which the acid and its base are both, but not too. What emerges is a "Goldilocks diagram" (or, more accurately, two Goldilocks diagrams back to back but running in opposite directions):
Goldilocks I: Bronsted Acids and Bases p.2 strong but not too but not too (figure 1) strong Some are than others. Indeed, the whole idea of acid strength is connected to how well a group of protonate a common, reference base, which is usually assumed to be water. Thus, a standard acid reaction for an acid, HA, would be: HA (aq) + (l) > (aq) + A (aq) (equation 1) and the the acid, the further the equilibrium for this reaction lies to the right. A closer examination of this reaction reveals that there are two ( and A ) competing for a proton. If the equilibrium for this reaction lies to the left, then A has won the competition, and thus A is a base than, from which it follows that HA is a er acid than. On the other hand, if the equilibrium for this reaction lies to the right, then has won the competition, and thus A is a er base than, from which it follows that HA is a acid than. In this way, we could divide strong from, with the strength of the acid as the dividing line. Note that since is the base of, this line is also defined in terms of the strength of as a base. Inverting this leads to a standard base reaction, in which acts as a reference acid to a series of : B (aq) + (l) > HB + (aq) + OH (aq) (equation 2) There are still two competing for a proton, B and OH, and parallel reasoning leads to the conclusion that strong are those that are than OH acting as a base, that is, they are more successful in connecting to and holding onto the proton (the H + ) than is OH. Make sure to notice that if B is than OH as a base, then the reaction will lie more to the right at equilibrium that is, if B is, it will have won the competition for the proton, and thus it will appear mostly as HB +, in which it is attached to the proton. In this way, we could divide strong from, with the strength of the base OH as the dividing line. And note that since is the acid of OH this line is also defined in terms of the strength of as an acid. These two conclusions give us the two dividing lines in our Goldilocks diagram:
Goldilocks I: Bronsted Acids and Bases p.3 strong but not too but not too OH (figure 2) strong Let us now place two into the diagram, and see what conclusions we can reach as to the locations of other, related species: both and. The two are, a strong acid, and HF, a, but not too acid (in fact, HF is among the of the, but not too ). HF OH (figure 3)
Goldilocks I: Bronsted Acids and Bases p.4 As we place these two into the chart, we can also place their (Cl and F ) even with them, but on the base side of the chart, because by the rules we are developing, their strength as should parallel (on the base side of the chart) the strengths of their. In addition, we can place a few more species as well. Ammonia ( ) and methane (CH 4 ) would be hydrogen compounds of the elements beyond F and O, so since we would predict the acid strength order to continue as HF > > > CH 4, we can put and CH 4 into the chart as increasingly. Further, since we have HF and placed, we could also place HBr and HI as increasingly than. (It is a subtle point, but while the reason for this trend turns out not to come from relative electronegativity (EN) values, we can note that the EN values for Br and I are only slightly different less that of Cl, which leads us to conclude that HBr and HI might not be a lot than, and this conclusion is correct. The effect is not due to EN values, but there is a correlation with them.) And of course, we can also put into the chart the for each of these species. HI HBr I Br Cl HF F OH NH 2 (figure 4) CH 4 CH 3 Now, it is worth noting that we suddenly have a number of and in our chart, but all this has come from the idea of a Goldilocks diagram, and from the placing of just three,,, and HF, into the chart. All the others have come as a logical consequence of this. Let's continue then. It is worth noting that appears twice in the chart once as an acid (with its base, OH ), and once as a base, with its acid,. We could therefore place the acid of the ammonium ion, NH 4 + into the chart, in parallel to how and are placed, and along with it, we can place as its base.
Goldilocks I: Bronsted Acids and Bases p.5 HI HBr I Br Cl HF F NH 4 + OH NH 2 (figure 5) CH 4 CH 3 It's important to notice that we can use the chart we have made to answer questions about relative acidbase strength. For example: a. Which is a acid, HF or HBr? b. Which is a base, or F? With the chart, it is easy to see that HBr is a acid than HF (HBr is higher in the acid listings), and that is a base than F ( is lower in the base listings), though in considering the second case, it is important to remember that the order of base strength is reversed (upside down) from the order of acid strength. A more subtle question would be: will act as an acid or as a base, when put into water solution? A look at the chart tells us that while is capable of acting as either an acid or as a base, it is in fact a acid, while it is a, but not too, base. Its base strength is therefore greater than its acid strength (an awkward but useful way to express this conclusion), and we would thus expect to see behave as a base in water solution, at least in the absence of other species. Since it is, it will not react much, but such solutions would be ly basic. Now, let's add two more to the chart, sulfuric acid (H 2 SO 4 ) and phosphoric acid (H 3 PO 4 ). Sulfuric acid is strong, close to, while phosphoric acid is but not too, close to HF in strength in fact, H 3 PO 4 is about 100,000 times er than H 2 SO 4. The important thing to notice first for these two is that they are "oxy" (some sources say "oxo-"). Oxy consist of a central atom with one or more oxygens attached, and with at least one hydrogen (proton) attached to the oxygens. Most e oxyacid, then has its protons attached not to the central atom but to the oxygens surrounding the central atom. (There are exceptions, but such exceptions are not common.) As a result, it is wise to learn to write the formula of an oxyacid in such a way as to show this connectivity. Thus,
Goldilocks I: Bronsted Acids and Bases p.6 H 2 SO 4 would be rewritten as (HO) 2 SO 2, and H 3 PO 4 would be shown as (HO) 3 PO. And this reveals a most important feature of these compounds. In the neutral, parent oxyacid, the number of "free oxygens", that is, oxygens that do not carry a proton, is the most important measure of the strength of that oxy-acid. There is a slight variation for individual oxy in each family, but all oxy with one free oxygen will have an acid strength close to that of H 3 PO 4, while all those with two free oxygens will have an acid strength close to that of H 2 SO 4. Further, oxy with two free oxygens are about 100,000 time than those with only one free oxygen. Since there are also oxy with no free oxygens and at least one with three free oxygens, we can (correctly) predict that this pattern would extend to cover them as well. Oxy with 3 free oxygens (e.g., O 4, which would be written in oxy-acid notation as HOClO 3 ) would be about 100,000 times than H 2 SO 4, while oxy with 0 free oxygens (e.g., H 3 BO 3 or O, which would be rewritten as (HO) 3 B or HOCl), would be about 100,000 times er than H 3 PO 4. Moreover, there is an additional thing to note with oxy. Many oxy have more than one proton in their formulas (as neutral, "parent" species), and when one proton is lost, (one of) the remaining proton(s) could, in principle, be lost in a subsequent reaction. For example, while HSO 4 is the base of H 2 SO 4, it is also capable of acting as an acid in its own right. Now the principle is that if an oxyacid still has a proton on an oxygen after losing one, the resulting species will have an acid strength about 100,000 times er than that of the original species. Thus, as an acid, HSO 4 will be about 100,000 times er than H 2 SO 4, which is about the same strength as oxy with one less "free oxygen" than H 2 SO 4. Note how this works, then there will be clusters of, all with approximately the same acid strength, including both neutral, parent oxy along with "oxyacid anions" that still have at least one proton attached. These clusters will be spaced such that species in one cluster are about 100,000 er or than species in an adjacent cluster, but the species in one cluster will all have about the same acid strength. There will be small variations arising from differences in the total number of oxygens or in electronegativity, but those differences will be small in comparison to the 100,000 times difference between clusters. Thus we would have, with differences between them of about 100,000 times in strength:, strong: O 4 strong (100,000 er, but still strong): H 2 SO 4, HNO 3, O 3, H 2 SeO 4 upper end of, but not too : H 3 PO 4, HNO 2, O 2, H 2 SO 3, H 5 IO 6, plus HSO 4 and HSeO 4 middle of, but not too : H 3 BO 3, O, plus H 2 PO 4 and HSO 3 almost at the bottom of, but not too : HPO 4 2 and of course, along with each acid entry, we can put in an additional entry for the base of that species on the other side of the diagram where base strengths are shown. This gives us a busy chart, with lots of entries, but all generated from a small number of points and a small number of concepts: the idea of a Goldilocks diagram, and the relative acid strengths within that diagram of 6 species:, HF, and, plus H 2 SO 4, H 3 PO 4, and HSO 4.
Goldilocks I: Bronsted Acids and Bases p.7 O 4 ClO 4 H 2 SO 4, HNO 3 O 3, H 2 SeO 4 HI HBr I Br Cl HSO 4, NO 3 ClO 3, HSeO 4 H 3 PO 4, HNO 2, O 2 H 2 SO 3, H 5 IO 6, HSO 4 HF F H 2 PO 4, NO 2, ClO 2 HSO 3, H 4 IO 6, SO 4 2 H 3 BO 3, O H 2 PO 4, HSO 3 NH 4 + H 2 BO 3, ClO HPO 4 2, SO 3 2 HPO 2 4 OH PO 3 4 NH 2 CH 4 CH 3 (figure 6)
Goldilocks I: Bronsted Acids and Bases p.8 Before leaving this, we want to add one specific example of each of two additional classes of : alcohols and organic. For the organic acid, we will choose acetic acid, H 3 C OH, which looks a bit like an oxyacid, except with an organic group, (a methyl = CH 3 ), included on the central carbon. As an acid, acetic acid is only a bit er than HF (about 1/10 th as strong), and thus its base, the acetate ion, CH 3 CO 2, would be just a little than F (about 10 times ). Other organic will have a wide variety of organic groups in place of the methyl group. Depending on the nature of the specific organic group used, the resulting acid strength can vary significantly, but the acid strength of acetic acid is a good starting place when making such estimates. For the alcohol, we will chose ethanol, CH 3 CH, which is only a little er (about 100 times er) than, thus making its base, CH 3 C only a little than OH as a base. Other alcohols may vary a bit in the acidity of their OH proton, but the acid strength of this alcohol will serve as a good starting place for estimating such things. It might be noted at this point that, while a proton might be lost from its bond to C or O in this species, it is the OH bond that is acidic. We should have been able to predict this. CH 4 is an exceedingly acid, while, though still, is considerably. We would therefore expect CH bonds in a molecule or ion almost never to lose protons, while OH bonds should lose protons much more readily. O C
Goldilocks I: Bronsted Acids and Bases p.9 O 4 ClO 4 H 2 SO 4, HNO 3 O 3, H 2 SeO 4 H 3 PO 4, HNO 2, O 2 H 2 SO 3, H 5 IO 6, HSO 4 H 3 BO 3, O H 2 PO 4, HSO 3 HI HBr I Br Cl HF F CH 3 CO 2 H CH 3 CO 2 NH 4 + HSO 4, NO 3 ClO 3, HSeO 4 H 2 PO 4, NO 2, ClO 2 HSO 3, H 4 IO 6, SO 4 2 H 2 BO 3, ClO HPO 4 2, SO 3 2 HPO 2 4 OH PO 3 4 CH 3 CH CH 3 C NH 2 CH 4 CH 3 (figure 7)