I previously described an attempt at gravimetric determination of magnesium in a sample of Epsom salt by precipitation of magnesium ammonium phosphate and ignition of the precipitate to magnesium pyrophosphate. The result was very bad, but there were possible improvements to be made. A second experiment, adopting some of these improvements, produced excellent results. The fifteen percent error of the first attempt was reduced to scarcely more than one percent in the second.

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So far, all the experiments I have conducted in analytical chemistry have used volumetric means. As I have earlier said, volumetric analyses use inexpensive equipment and simple lab techniques. They are often quick to carry out and capable of great specificity.

Volumetric methods also suffer from a few disadvantages. Not all chemical species, for example, undergo reactions easily adaptable to titration—the alkali metals, for example, or aluminum. Other species do undergo characteristic reactions, but require special equipment to detect their endpoints. The greatest disadvantage, however, is that volumetric analyses are almost always indirect. Solutions of most of the useful titrants—sodium hydroxide, potassium permanganate, sodium thiosulfate, and many others—cannot directly be prepared to a fixed concentration, and their concentrations are not stable with time, requiring periodic standardization. Extra manipulation of any kind, including standardizations, introduces possible error. The problem is worse when primary standards are difficult to find or use for a given titrant. Volumetric solutions of iodine, for example, are best standardized with arsenic trioxide, yet the intense toxicity of this compound almost forbids it use. In cases such as these, "secondary" standards can be used: a reagent (in this case, sodium thiosulfate) whose concentration is determined by titration with another solution, which has in turn been standardized with a primary standard. Again, more steps means more error.

Gravimetric determinations, on the other hand, are direct. The analyte is converted, usually with a single reaction, into a substance of known composition, which is then weighed. The quantity of the substance to be determined is thus obtained simply from the ratio of its molecular weight to the molecular weight of the weighed solid. Nothing could be simpler in theory.

The most serious, practical problem with gravimetric analysis is that they require balances of great precision. A balance precise to 0.1 milligram can scarcely be found for under $1000; a balance precise to 0.01 mg can cost tens of thousands. Volumetric analysis also require great precision in weighing primary standards, but more precision can be squeezed out a cheap balance by the simple trick of serial dilution. The only way to get more precision in a gravimetric procedure, though, is to scale the whole reaction up, like cooking a recipe for ten people instead of one. While manipulating larger volumes of liquids isn't really much harder than working with smaller ones, manipulating larger quantities of solids can be quite a bit trickier.

The great advantage, however, is simplicity. The reagents used for converting an analyte into a weighable form usually need not be of extreme purity, nor do solutions of reagents need to have precisely known concentrations. However, one must be certain that preparation of the weighable solid, usually a precipitate or a derivative of one, is entirely complete; that its composition be known with absolute certainty; and that it not be contaminated by other compounds present. This last criterion puts severe limitations on the usefulness of gravimetric methods, which often employ reactions of little specificity. There are many, many difficulties, too many to cover here, but discussed fully in any good text on analytical chemistry such as A. I. Vogel's. A gravimetric method is therefore, to my mind, best employed only when a good volumetric method is not available.

Such is the case with the determination of magnesium. There is one volumetric method possible for magnesium, using solutions of the disodium salt of ethylenediaminetetraacetic acid (Na₂H₂EDTA) and detection of the endpoint with certain azo dyes, but the method has its disadvantages and in any case I haven't yet the means to carry it out. Magnesium can be precipitated, however, as a characteristic salt, magnesium ammonium phosphate hexahydrate or MgNH₄PO₄·6H₂O. Unlike many precipitates, magnesium ammonium phosphate is crystalline, so it tends to be purer than (say) aluminum hydroxide and also easier to filter. When heated to redness it decomposes to a stable compound, magnesium pyrophosphate or Mg₂P₂O₇. Magnesium ammonium phosphate hexahydrate can be weighed directly, or dried at moderate temperature to the monohydrate, but magnesium pyrophosphate can be weighed without any uncertainty whatever about the water content of the original precipitate. This isn't to say that determination of magnesium in this way is a miracle of science, for it is subject to interference from other metals and precipitating the MgNH₄PO₄ in a predictable fashion requires some care. As my first try at gravimetric analysis, however, it seemed a good choice: I would determine the amount of magnesium present in a sample of commercial Epsom salt, magnesium sulfate heptahydrate or MgSO₄·7H₂O, which tends to be fairly pure.

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Succinic acid, HOOC-CH₂-CH₂-COOH, is one of the organic acids that I had begun attempting to prepare for possible use in alkalimetry. Such side projects in my hands tend to gain a life of their own, drawing other things in.

The method I first tried was adapted from H. D. Dakin's short J. Biol. Chem. article on the oxidation of glutamic acid and aspartic acid with hydrogen peroxide in neutral solution. Dakin obtained nearly half the theoretical yield of succinic acid by neutralizing 0.1 mol glutamic acid with ammonia then heating it with 0.3 mol of H₂O₂ as the 2.5% aqueous solution. He isolated the succinic acid by acidifying the reaction mixture and extracting it with diethyl ether, a technique not open to me. I hoped rather to separate the succinic acid as its sparingly soluble calcium salt. As earlier described, my first try did not work, and only a small amount of very dirty crystalline residue, presumably of succinic acid, was obtained.

For a second try I decided to use sodium carbonate-percarbonate as the source of hydrogen peroxide. This mixed solid is available under many brand names as a cleaner and stain remover, including Clorox "Oxi-Magic", which I used. "Percarbonate" is a misleading name, for it contains neither carbon in a higher oxidation state, as with the manganese in permanganate, nor does it contain -O-O- or -O-O-H functions bonded to the central atom, as in persulfate. Sodium percarbonate is simply crystalline sodium carbonate "hydrated" not with water but with hydrogen peroxide of crystallization in the ratio 2:3, 2Na₂CO₃·3H₂O₂. This compound is diluted with ordinary sodium carbonate in the commercial powders to make it more stable on storage.

Before using "Oxi-Magic" I needed a rough determination of its hydrogen peroxide content, which is not given on the label. The easiest technique for determining H₂O₂, on paper anyway, is to titrate an acidified sample with standard potassium permanganate solution, which oxidizes the H₂O₂ to oxygen:

2 MnO₄^- + 5 H₂O₂ + 6 H⁺ → 2 Mn²⁺ + 5 O₂ + 8 H₂O (Equation 1)

The products of this reaction are both essentially colorless, while even highly dilute solutions of KMnO₄ are colored deep purple, so when the reaction is complete the first slight excess of KMnO₄ gives the reaction mixture a violet tint.

I had already on hand an approximately 0.02M permanganate solution, which I was intending eventually to standardize properly, i.e. with as much precision as possible, but in this case I was content with results uncertain to 5% or even 10%. Several primary standards for KMnO₄ are used, of which the most common is sodium oxalate. Permanganate oxidizes it in acidic solution cleanly to carbon dioxide:

2 MnO₄ + 5 C₂O₄^2- + 16 H⁺ → 2 Mn²⁺ + 10 CO₂ + 8 H₂O (Equation 2)

Again, the KMnO₄ solution acts as its own indicator in this titration. I do have a bit of sodium oxalate on hand but used potassium tetroxalate instead, for I had more of it, and its inferiority as a standard hardly mattered in this case, and I knew already from my alkalimetric experiments that the salt I had prepared was of decent purity. Since one mole of potassium tetroxalate dihydrate, molecular weight = 254.19 g/mol, contains two moles of oxalate, and since one mole of oxalate reacts with ²/₅ moles of permanganate, the equivalent weight of the tetroxalate is ⁵/₄ of its molecular weight, or 317.74 g/mol KMnO₄.

A 0.245 g sample of KHC₄O₄·H₂C₂O₄·2H₂O, dissolved in about 75 mL of purified water with 3.2 g of sulfamic acid—the TileLab brand acid, used directly from its box and not from the recrystallized material I used for alkalimetry—was microwaved for 45 sec. before titration. Titrations with KMnO₄ are a bit trickier than acid-base titrations; a full discussion is not appropriate here, but it will suffice to say that permanganate oxidations are usually slower than acid-base reactions, often much slower, particularly at the start of a KMnO₄ titration, requiring more care to avoid overrunning the endpoint. I was a little hasty in this titration and went past the endpoint by a drop or two, but in this case it didn't matter. About 34.3 mL of the KMnO₄ solution was used. A blank of 3.2 g sulfamic acid in 50 mL water was carried through; one drop of KMnO₄ was enough for a permanent endpoint, so no blank correction was applied. Calculation yields an approximate concentration of (0.254 g tetroxalate ÷ 317.74 g/mol KMnO₄) / 0.0343 L → 0.0225M KMnO₄.

What the best conditions were for using this KMnO₄ solution to determine hydrogen peroxide I wasn't sure. I knew the solution had to be acidic, but H₂O₂ decomposes rapidly in strongly acidified solutions. Weak acids, however, tend to stabilize hydrogen peroxide (phosphoric acid is used in commercial solutions.) Therefore I tried titration of a 0.212 g sample of "Oxi-Magic" dissolved in 50 mL water and 5 mL of glacial acetic acid. The permanganate reaction, however, was so slow, each drop taking many seconds to be decolorized, that the titration was abandoned.

Next I tried an 0.192 g sample with 3.1 g sulfamic acid in 50 mL water. This titration proceeded more rapidly although still not very fast, and required 11.23 mL of 0.0225M KMnO₄. Using Equation 1, the amount of H₂O₂, molecular weight = 34.01 g/mol, in the sample is calculated to be 0.000632 mol or 0.0215 g, for a percentage by weight in "Oxi-Magic" of 11.2%. For comparison, pure 2Na₂CO₃·3H₂O₂ contains about 32% H₂O₂ by weight.

Two more titrations were carried out to confirm this result. For the second, I used 0.206 g "Oxi-Magic" and 5.0 g sulfamic acid, thinking that more acid would speed the titration, but the titration only consumed 7.95 mL of 0.0225M KMnO₄—way, way off. After this I looked online for anything I could find about determination of hydrogen peroxide with permanganate. Scattered information such as this and this showed that the usual procedure for peroxide determination called for acidifying the sample with dilute sulfuric acid. I was resisting this, because my supply of sulfuric acid is small, and I don't know how easily I can get more; therefore I was hoping to substitute the weaker but more convenient sulfamic acid. After the failed second titration, however, I conducted a third with 0.222 g "Oxi-Magic" dissolved in 50 mL water and acidified with 12 mL 3M H₂SO₄. This titration required 11.27 mL of 0.0225M KMnO₄, corresponding to an H₂O₂ percentage of 9.7% by weight.

These results were bad, but sufficient to conclude that there was about 10% active hydrogen peroxide in "Oxi-Magic". If I had had more time I would have tried to confirm this finding with iodimetric titration, but I didn't want to go to the extra effort.

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With this information, I began the second attempt at preparing succinic acid starting with about 35 g of monosodium glutamate monohydrate, approximately 0.19 mol, and 130 g of "Oxi-Magic", corresponding to about 13 g of H₂O₂ or 0.38 mol. This was suspended in a 600 mL beaker in 400 mL of water. A brisk effervescence began almost immediately. Dakin, however, calls for oxidation in approximately neutral solution. Therefore over several minutes I added glacial acetic acid, a few drops at a time, with constant stirring and monitoring of pH. The mixture's pH, originally about 10, eventually dropped to below 8 once about 100 mL of glacial acetic acid was added. Then, taking a hint from Dakin's oxidation of aspartic acid, a few drops of 0.1M ferrous sulfate solution was added as a catalyst. Then the solution was allowed to stand, with occasional stirring, at room temperature.

The reaction mixture bubbled constantly for almost two hours. The effervescence eventually decreased, whereupon the mixture was brought very slowly to a boil and evaporated down from about 500 to about 200 mL. The pH of the solution was now above 8.

Remigius Fresenius suggests that succinic acid could be isolated through the insolubility of its sodium salts, both mono- and dibasic, in ethyl alcohol. This was my plan. Hence I diluted the boiled-down solution to about 500 mL with hardware-store denatured alcohol. (I've never liked this stuff. It turns cloudy on dilution, suggesting that it's been denatured with kerosene or something else not miscible with water.) A whitish precipitate immediately formed. The mixture was allowed to cool overnight in the freezer. The next day, a dense layer of white solids had formed at the bottom of the flask. This, I hoped, consisted largely of sodium succinates. However, it ought to be noted that many other sodium salts are sparingly soluble in alcohol.

The solid was filtered off and then dissolved by dropwise addition to the filter of 10M hydrochloric acid, followed by water. Much bubbling occurred during this, suggesting that the solid contained sodium carbonate. Eventually about 200 mL of liquid was obtained. This was boiled down to about 100 mL, in the hope that succinic acid would crystallize from the solution on cooling. Succinic acid is moderately soluble in cold water, to the extent of 4% at 10° C according to Solubilities of Inorganic and Organic Substances (1919 edition), but slightly soluble enough that if any useful quantity of the acid were present in this liquid, it should have separated on cooling. Instead, after refrigeration, there was obtained only a scattering of square crystals that looked like sodium chloride. Succinic acid, monoclinic in crystal structure, should not have made perfectly square crystals.

I thought then of evaporating the solution to dryness and extracting it with hot alcohol. Sodium chloride would not dissolve appreciably in the alcohol, but succinic acid would. I tried this, evaporating the mixture and then boiling the semicrystalline residue with three 25 mL portions of 99% isopropyl alcohol and one portion of denatured ethyl alcohol. The quantity of undissolved solid was great; indeed, it seemed hardly to have been diminished at all. The combined alcoholic extracts, boiled down to 75 mL and then cooled in the freezer overnight, deposited no crystals. Succinic acid is soluble in ethyl alcohol at -1° C to the extent of 5%, and in propyl alcohol at the same temperature to 2%, so if there were any significant amount of succinic acid in the solution, some of it should have crystallized out.

I could only chalk this up as another failure.

As I detailed in my previous post, I had attempted to prepare pure sebacic acid for possible use in alkalimetry by the method of heating sodium ricinoleate, prepared from castor oil and sodium hydroxide, to yield sodium sebacate and 2-octyl alcohol:

Twice I had tried this and failed, but the third attempt looked as though it would produce at least some sebacic acid. The solid residue from heating the sodium ricinoleate, dissolved in water and acidified, deposited a whitish sediment. This was filtered off, washed with ice-cold water, dissolved in about 50 mL of boiling water, filtered, and then allowed to cool. After about twelve hours in the refrigerator the yellowish solution again deposited a white solid. It was noted, however, that the solid did not appear crystalline. It was collected, washed, and recrystallized from hot water in the same fashion. The same behavior was noted: the filtered solution did not behave as was expected. Usually, when a crystallization is carried out, the solution remains clear as the crystals form. Instead, the solution of the presumed sebacic acid grew uniformly white and cloudy before eventually depositing a fine, granular precipitate with no apparent crystallinity. By contrast, Gmelin and others report that sebacic acid crystallizes from water in needles or thin plates.

The white solid from the last crystallization was collected on filter paper, washed with ice-cold water, and the paper spread out to dry. After a half-hour at room temperature, the paper was placed into a 170° F oven, almost a hundred degrees F below the melting point of sebacic acid, which melts at 130° C or 268° F, tending to sublime as well, without decomposition. I checked the progress of drying about 30 minutes later. The solid had disappeared, and there was nothing but a greasy spot on the filter paper. It is possible that the oven had far exceeded its supposed temperature, but it did not feel that way; the plate on which the filter paper had been sitting was warm to the touch but not painfully hot, as it would have been if the oven had gotten too hot.

My guess is that the white solid was some residue of fatty acids from the saponification of the castor oil. It could have been sebacic acid so impure as to lower its melting point below 100° C.

In any case, I doubt whether I will ever succeed in preparing sebacic acid with the crude means available to me. I won't be trying again.

I have briefly discussed in a previous post some experiments in standardizing volumetric solutions of sodium hydroxide and the problems I had with the standards I used: potassium hydrogen tartrate, sulfamic acid, potassium tetroxalate, and oxalic acid. All of these compounds have been used as primary standards, although none of them is a preferred standard. After a frustrating series of variable results, however, I gave thought to preparing other acidic compounds that might be used for standardizing NaOH.

A primary standard for volumetric work must fulfill certain criteria. It must be obtainable in a state of high purity. Its composition must be entirely certain. It must be reasonably stable upon storage, preferably without any tendency to absorb or lose water or to react with atmospheric oxygen or carbon dioxide. It must react quantitatively with the reagent to be standardized. Few substances satisfy all of these criteria, and there are presumably good reasons why certain compounds have found common use while others that might seem suitable have not. My requirements are fairly lax, however; I like to make work for myself; and I had a few ideas. I tried to think of all of the mildly acidic compounds which I could prepare from readily available ingredients, which were stable in air (so far as I could determine from what literature is available to me), and which were hopefully easy to purify by crystallization.

So far, I have only prepared two compounds successfully, glutamic acid hydrochloride and nicotinic acid, and tried only glutamic acid hydrochloride with poor results. More detailed accounts of my work lie beneath the cut.

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One of the simplest methods of identifying an organic compound and estimating its purity is to determine its melting point, and the easiest way to do this is the obvious one: heat a sample of the compound and watch it melt. There are cleverer, more accurate methods, of which differential scanning calorimetry is by far the coolest, but the basic method is easy to carry out with simple equipment. Lately I have been trying to prepare a number of pure organic acids in the hope of finding another substance useful for standardizing solutions of alkali. Such acids often, but not always, tend to be solids with relatively low melting points, less than 250° C, and therefore good candidates for melting-point determinations of purity.

For the best results, a number of criteria must be satisfied.

1. The sample must be as small as possible to minimize its heat capacity and therefore minimize the amount of heat needed to melt it.

2. Heating of the sample must be controlled and uniform.

3. The temperature sensor, whether an ordinary thermometer or an electronic transducer, must be as close to the sample as possible to minimize the possibility that it's not actually at the same temperature as the sample.

4. Inspection of the sample to see when it melts must be easy.

Here's how I do it.

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I have previously described how I went about preparing and standardizing, with much trouble, a dilute solution of sodium hydroxide for alkalimetric titrations. I had prepared about a liter of the solution but wasted so much of it on standardization that I didn't have much left over to do anything useful with, but I did accomplish two things, both of which are fairly standard undergraduate experiments: the determination of aspirin and the determination of the molecular weight of a weak acid.

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In the past couple of weeks I have been conducting a number of experiments, most of them extremely repetitive and tedious, designed to test the limits of my chemicals and equipment for volumetric analysis, starting with the simplest of all volumetric methods, titration with standardized solutions of sodium hydroxide. In analytical chemistry this is called alkalimetry and is usually carried out with better supplies than I have.

The glassware is easy enough to get. I've already talked a little about burets and how to use them; $20 will get you a serviceable low-end model (e.g. this one from Cynmar), and $50 will get you one as good as anything you're likely to use in a real lab. Other glassware used in volumetric analysis, such as volumetric flasks and pipets, are equally inexpensive. $100 judiciously spent will easily get you a serviceable collection of labware capable of dispensing volumes to a precision of four significant digits.

The other piece of vital equipment, though, a scale capable of weighing small quantities (less than a gram) to four significant digits, is not so cheap. A new electronic balance with a precision of 0.0001 gram, an "analytical balance", can scarcely be found for less than $1000. Even balances with 0.001 gram precision, sometimes called "semi-analytical balances", run to several hundred dollars. I eventually bought such a balance, a Sartorius ELT103, for a little more than $350. It's a nice bit of machinery but an order of magnitude worse than what proper analytical work demands.

The great difficulty of measuring precise weights and the relative ease of measuring precise volumes is, by the way, why volumetric methods of analysis became so popular. Getting the exact weight to 0.1 mg of a sample of some chemical may be tough, but volumetric equipment allows one to measure a tenfold larger quantity with a precision of 1 mg—thus getting the same number of significant figures, even though the precision of the balance is tenfold worse—and then dividing this quantity into accurate tenths by, say, dissolving it in a solution of precisely 100.0 mL volume and then taking a 10.00 mL portion, or "aliquot". This more elaborate technique of obtaining precise quantities, while requiring cheaper equipment, has its downside. Each bit of equipment, each manipulation that a sample undergoes, introduces its own potential error. But it is cheaper, and in the days when weighing anything to 0.1 mg precision was impossible, it was the only way to go.

Aside from equipment, volumetric analysis requires certain chemicals of trustworthy purity, called primary standards. In most cases the exact concentration of a freshly prepared solution of a volumetric reagent can't be known without measuring it experimentally. Moreover, some titrants decay slowly with storage, requiring periodic redetermination of their concentration. Titration of carefully weighed quantities of primary standards is used to make these determinations.

But, as I have said before, I can't just buy these standards off the shelf, so I have had to resort to what I can prepare and purify by myself. My results with these homebrew standards have been, in the past, uncertain. This time, though, I resolved to find out if possible how good my standards were, instead of preparing them and hoping for the best.

Actually, before making that resolution, I carried out a small number of titrations whose dodgy results convinced me that I needed to work harder on improving my materials and my technique.

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In a previous post I related how, for the purpose of obtaining primary standards for volumetric analysis, I recrystallized borax and prepared potassium tetroxalate from oxalic acid and potassium carbonate. Borax, or sodium tetraborate decahydrate, is one of the few usable primary standards for standardizing acid solutions. Potassium tetroxalate has been advocated in the past as a standard both for acid-base and redox titrations.

Both should be stable. Borax has a tendency to effloresce, lose water of crystallization, although it happens slowly in a well-closed container. Potassium tetroxalate, at least according to the Merck Index 11th edition, is stable to air.

A few days after preparing these salts, however, I noticed that both were showing signs of deliquescence. When I shook the bottle into which I'd put the borax (or the potassium tetroxalate), the salt that had previously looked like a perfectly dry, crystalline solid was sticking a bit to the sides of the bottle. The crystals sticking to the sides had a definite sheen of water on them. Something had gone wrong.

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Both in first- and second-year college lab classes in chemistry, here in the Seattle junior colleges anyway, require students to conduct at least one or two titrations, always using sodium hydroxide and phenolphthalein to determine a weak acid. Molecular weight determinations of organic acids are popular student labs.

What I've yet to learn is how the students are expected to know how to do titrations in the first place. I suppose it's assumed that they picked it up in high school. It's where I did, but I went to high school eighteen years ago, an unusually good and well-stocked high school at that, and in any case I was doing a lot of playing around with volumetric analysis on my own and not in class. From what I've seen in recent classes I don't think it's safe to assume that freshmen college students know much about titration—or, frankly, about a lot of basic techniques in manipulating laboratory glassware.

I'm hardly an expert, just an overenthusiastic amateur, but I've carried out maybe a hundred titrations or more of various kinds, and I've gotten the technique down pretty well. I don't know where I learned it exactly, although Skoog and West's Fundamentals of Analytical Chemistry, a book I've cherished since 10th grade, was one influence. I've put together a short list of tips that a newcomer to volumetric analysis may find useful.

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Iodometry is one of the most versatile methods in volumetric analysis, adaptable to the quantitative analysis of a wide range of substances, both inorganic and organic. The basis of the technique is the reaction of an oxidizing analyte—copper(II), hydrogen peroxide, bromine, many others—with iodide to produce elemental iodine. The quantity of iodine liberated is then determined by titration with a solution of sodium thiosulfate of known concentration. Thiosulfate very cleanly and quickly reacts with iodine under a wide range of conditions to form iodide and tetrathionate:

2S₂O₃^2- + I₂ = S₄O₆^2- + 2 I^-

When all of the free iodine has disappeared from the solution, the titration is over, and the volume of thiosulfate solution used is a measure of how much iodine was liberated by the analyte, and therefore a measure of how much of the analyte was originally present. Knowing when all of the iodine has been titrated is made easier by the fact that elemental iodine in the presence of excess iodide forms a deep blue-black complex with starch. If some starch solution is added to the mixture being titrated, the end of the titration is marked by the disappearance of the blue starch-iodine color.

That's the theory, anyway. I've conducted a number of experiments in iodometry, with varying results, and one of the many things that's given me trouble is the starch.

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Analytical chemistry is a strange hobby of mine, and not the easiest one to indulge. Even the most basic equipment for carrying out chemical analyses can be costly, beginning with the requirement of an analytical balance of great reliability and accuracy. (Precision to 0.0001 grams is regarded as necessary, but I'm making do with a cheaper balance of 0.001 gram precision.) But equipment is easy enough to get hold of, if you have the money. What's really getting difficult to find are the chemicals. More and more supply houses are not selling to the general public.

Some chemicals used in analysis need not be very pure. For example, it is never expected that even good grades of sodium hydroxide, used in acid-base titrations, is very certain in its composition. The same is true to a lesser extent of hydrochloric acid, another valuable reagent in volumetric analysis. The trick is to prepare solutions of approximately known concentration and then experimentally determine their exact concentration by using them to titrate carefully weighed samples of substances (almost always solids) of trustworthy composition and purity. This technique is called standardization, and it means that I can use cheap household lye instead of high-grade sodium hydroxide, and hardware store muriatic acid instead of pure hydrochloric acid, as long as I can standardize the solutions prepared from them.

But you still need those pure compounds, the primary standards. A real chemist can easily get (say) reagent-grade potassium hydrogen phthalate for standardizing NaOH, or pure electrolytic iron for standardizing potassium permanganate, and not think twice about it. I, however, can't get either of these things without going to a lot of trouble and probably spending a lot of money.

There are, however, substitutes, some of which are within an amateur's grasp. Sulfamic acid, for example, is available at hardware stores, and it too can be used for standardizing NaOH. Straight out of the box, though, it's probably not to be trusted, but it can be recrystallized to improve its purity.

Other compounds I have learned to make in one or two steps from commonplace chemicals. Sodium oxalate, for example, of use as a standard for KMnO₄, can be made from oxalic acid and sodium bicarbonate, both readily found. Ferrous ammonium sulfate or "Mohr's salt" can be made from ammonium sulfate and ferrous sulfate, both of which are used in gardening. I have learned to work with chemicals from grocery stores, hardware stores, photographic shops, artist's supply houses, even mineral samples. I'll never get the sort of quality that I'd get from J. T. Baker, and some of my preparations have failed or given uncertain products, but at least it's sort of fun. It's like making your own chocolate chip cookies or pretzels from scratch instead of getting them ready-made.

I'm planning to try a few volumetric experiments soon, but before I can do that, I need to prepare compounds for use in standardizing both acid-base and redox solutions. My method is to have at least two standards prepared for each reagent to be standardized and preferably three; in this way, I check the various results against each other. Some standards I already have on hand. I prepared some recrystallized potassium bitartrate for standardizing NaOH, for example, about a year ago, but the substance keeps indefinitely. Others I either don't have on hand, or have basically expired.

I intend to post notes of my work to this journal regularly and at some length and detail. It may be useful to someone else at some other time, for all I know, but mostly I'd like to have both written and photographic records of my work in one place that I can access from anywhere and which isn't going to disappear (the way that my paper notes sometimes do, although I'm striving to keep detailed and organized written notes.)

Details of particular experiments under the cut.

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I've been attempting to photograph halos around the sun for some years now, a task now made much easier with the advent of digital cameras and programs for stitching smaller photos into larger panoramas, e.g. OmniStitcher (which I use), necessary if I'm trying to photograph enormous regions of sky with one small camera.

Atmospheric halos are caused by the refraction and reflection of sunlight or moonlight in hexagonal ice crystals found in high-altitude cirrus and cirrostratus clouds. According to the shape of the crystals, their orientation in space, and the path traced through the crystals by the rays of light, many different arcs and spots of light appear in the sky, near and far from the sun or moon, and often but not always colored somewhat like a rainbow. The variety of observed halos is great; a few of them are common enough to be seen dozens of times a year, while others have only been observed a few times, often only in certain climates, and so transient that they form and disappear within minutes. Comprehensive discussions of ice-crystal halos are to be found in Marcel Minnaert's textbook The Nature of Light and Colour in the Open Air (a little outdated but still an excellent reference) and online. Good sites include the Atmospheric Optics pages on halos and Jarmo Moilanen's Halos site, featuring photographs of almost every conceivable halo and links to many more, along with detailed explanations of their formation.

The most common halo by far is the 22° halo or "small halo", a ring of delicately colored light, 22 degrees of arc in radius, around the sun or moon. During the spring and fall months here in Seattle, a 22° halo or at least part of one can probably be seen two or three times a week. In this halo, the side faces of the hexagonal crystals act like the faces of a common triangular prism. A cloud of these crystals, randomly oriented in space, sends the most sunlight towards the eye at the "angle of minimum deviation", which for a triangular prism made of ice is about 22 degrees, the radius of the halo. This composite photograph, put together from thirty-six digicam pictures taken on 9 April 2008 and somewhat enhanced for contrast, shows a typical complete 22° halo (links to much larger image):

From Atmospheric P...

Since the 22° halo doesn't require any specific orientation of the ice crystals, it's almost always visible. When at least some of the crystals in the cloud are oriented in a particular way, though, other arcs appear along with it. I luckily caught such a halo display on the late afternoon of 3 April 2008, and put this composite image together from seventeen separate photographs, with its prominent features labeled.

From Atmospheric P...

To bring out the fainter arcs I've employed a technique recommended to me by Ismo Luukkonen, a Finish observer: applying the Photoshop "Unsharp Mask" filter with a radius of 50, a threshold of 0, and an amount of 500%. This method of processing introduces many artifacts, especially the "auras" around any objects silhouetted against the sky, but it's better than anything else for emphasizing the low-contrast, faintly colored bands of light, which are often, frustratingly, clearly visible to the eye but scarcely to be seen in photographs.

Prismatic ice crystals that are longer than they are wide, column crystals, tend to fall through the air with their long axes horizontal. Light passing through two side faces of these horizontal crystals forms the upper and lower tangent arcs to the small halo, which touch the 22° halo above and below and which change shape according to the height of the sun in the sky. Even the most boring 22° halo, like the one in the first image in this post, often shows brighter spots at its top and bottom, which are traces of the tangent arcs. Under exceptional circumstances the tangent arcs extend all the way around the sun and merge to form the "circumscribed halo", which I've only ever seen once in its entirety. A part of the upper tangent arc is pretty clearly visible in the 3 April image.

Another halo formed by horizontal ice-columns is rarer, and I was surprised to see it, the supralateral arc. It too is formed by horizontal ice crystals, but from rays passing through an end face of the crystal as well as a side face. The end faces are less likely to be well-formed than the sides, hence the rarity of the supralateral arc. Another halo, the 46° halo or "large halo", appears in approximately the same place, but while the the rarer 46° halo is weakly colored and associated with a strong 22° halo and a weak upper tangent arc, the supralateral arc is associated with a bright upper tangent arc and is strongly colored. Both features are clear in the 3 April display.

A somewhat creaky but useful Windows application, HaloSim, produces images of simulated halo displays. You supply it with the altitude of the sun at the time and a list of the crystal types and orientations that you guess to be present in the cloud. The following image is a simulation of the halos I observed on 3 April, based on a sun altitude of 29° (about what it was that afternoon, according to an ephemeris).

From Atmospheric P...

All of the features in the photograph are found in the simulated image, which however shows other halos that I didn't see in the sky.