The Chemical Adventures of Sherlock Holmes The Case of the Stoichiometric Solution Thomas G. Waddell and Thomas R. Rybolt University of Tennessee at Chattanooga, Chattanooga, TN 37403 The following story describes a chemical mystery with an emphasis on the utility of stoichiometry calculations. This is the fifth article presenting a scientific problem in mystery f o m in the context of the popular and beloved There is characters Sherlock Holmes and Dr. Watson (14). a break in the story where the reader (students and teachers) can ponder and solve the mystery. Sherlock Holmes provides his solution in the paragraphs following this break. The Story "It's a puzzle to me, Mr. Holmes," said Inspector Tobias Gregson. "Bishop was found a t the old limestone quarry in a small rwm, locked from the outside. Dead as a flounder, but without a bruise, a wound, or a mark on him." "Curious, indeed" replied Mr. Sherlock Holmes. "But a case of homicide, nevertheless." 'That's the way it looks to me." Inspector Gregson, the tall and flaxen-haired Scotland yard officer, flapped his ever-present notebook on his knee as he and Holmes leaned toward each other across our brandy table at 221B Baker Street. Holmes always regarded Gregson as the smartest of a bad lot a t Scotland Yard and their wllaboration was marked by a mutual respect often lacking in Holmes' dealings with Gregson's arch rival at the Yard, Inspector LeStrade. "Bishop was one of the last employees of the old quarry, Mr. Holmes. They were cutting back and it was either Bishop or . . . . " he opened his notebook. . . . "one of his coworkers Elmer Dunbar or John Mackenzie who was going to be axed." "Have you talked to Dunbar and Mackenzie?" Holmes inquired. "Certainly," Gregson countered. "We were a t Dunbar's flat this morning. He keeps snakes, of all things! "A shudder of disgust shook Gregson's narrow shoulders. I felt compelled to inteject. "Shades of The Speckled Band, Holmes! We may need our clubs again on this investigation." Holmes ignored me. 'What have you learned about Mackenzie?" "In addition to his work a t the quarry, he runs a rather peculiar business out of his flat," said Inspector Gregson. "When we stopped to see him, we found several bottles marked Acidum Aceticum Glaciale." "Glacial Acetic Acid," said Holmes, leaning back in his chair. "Rather nasty stuff and quite corrosive to human flesh. However, it does find some use in the removal of warts and moles." "Quite right," said the surprised Inspector. *He had a sign on his door giving notice to just such a business--wart and mole removal. "Great Scott," I said. "Do you suppose Mackenzie poured glacial acetic acid upon the poor fellow?" Holmes cast an annoyed glance in my direction. "My dear Watson, need I remind you that Mr. Bishop had no marks on his body. I usually find it most efficacious to for-
mulate a theory after all relevant facts are known and not before." Holmes turned back to the Inspector. "What else have you done, Inspector? Bring me up to where you are." "Bishop had one friend, Mr. Holmes, an acquaintance, really, a Mr. Burke Lyons. He's a vinegar and food oil manufacturer over on Wellington Street. It seems that Lyons owed Bishop money; the two of them were involved with quite a bit of gambling. I can't for the life of me figure what killed Bishop in that locked room, Mr. Holmes, not to mention who. I would be grateful if you and Dr. Watson a u l d take a run out to the quarry with me to look things over. " "We shall be most delighted, Inspector," Holmes cheerfully replied. 'Watson and I are a t a low ebb, are we not, Watson? London's criminal element has momentarily submerged to unimaginative scurryings of little interest." It was a bright, summer day of dry and perfect weather as the three of us climbed into Gregson's official cab for the trip through the City to the limestone quarry where a London criminal had apparently emerged in a fashion of interest to Mr. Sherlock Holmes. Arriving a t our destination we found that the small guard hut was unattended and we passed into the yard of the quarry without seeing a soul. Our cab glided smoothly over the surface of dry, powdery limestone, and Gregson took us immediately to where the body of Bishop had been discovered. The sturdy oak door leading into the fatal room stood before us. "The key is still in the lock! " I exclaimed. 'We were told," Gregson replied, "that the key is left there permanently. The caretaker and watchman, a Mr. Clyde Montly, found the door locked as it should be, and opened it to look in as a part of his routine. He discovered the body this morning. The door cannot be locked from the inside." "What is this mom used for?" Holmes asked as he turned the key and entered the small, darkened space. Gregson followed him. "Storage of explosives, Mr. Holmes. See. There are a few cartons left." Holmes did not follow Gregson'~pointing finger. Instead, Holmes was sauintina uv at the ceilinn. -. at a small vatch of sunlight visibie overhead. "That's the ventilation shaft," said Gregson when he saw where Holmes attention was directed. "Come with me. I'll show you." We left the mom and went into the bright sunlight. The rwm in which the body had been found was completely embedded in limestone walls and ceiling. On the ground above the room, protruded a narrow stack, the ventilation shaR from the room below. Holmes prowled the grounds above the sunken room. While he did this, I wandered about myself looking for clues to the strange death of the man Bishop. Some 50 feet from the shaft I stopped short. Below me in the powdered surface was the footprint of an animal! "Holmes, come here, quickly!" I shouted. With Holmes and Gregson peering over my shoulder I asked, "Is it the footprint of a Gigantic Hound?" Volume 70 Number 12 December 1993
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Gregson laughed. "Easy, Dr. Watson. The caretaker has a large and foul mutt which keeps him company on his rounds. We had best pay them a visit later on." "What is this?" ~ o - ~remarked e s in a serious tone. He had left my side and had moved in a direction toward the ventilation shaft. 'This is curious," he said. Holmes was on his knees and Greeson and I followed his gaze to a soursmelling hole in tge limestone powder, about one foot in diameter. The interior of the hole was rough and pockmarked. T h i s hole was not dug by a shovel,"~olmesmurmured. Without moving from his position, his eves shifted left to a pair of narrow,-but extremely deep wheel ruts left by some heavily loaded wagon which had passed recently. Holmes rose and with his characteristic long strides he quickly walked away like some large bird toward a barn where the vehicles used by the quarry were housed. He was not gone long and upon returning was silent despite our urgings to reveal his thoughts. It turned out not to be necessarv to visit the caretaker. As we conversed near the strange and malodoruus pot hole, we suddenly heard a deer, roar and the beast that was the cai-etaker'shog lunged up to us. The panting animal was fat, short-haired, and of a color I cannot yet describe. The limping caretaker himself followed behind his dog. "Down now, Ginger, down, down," he addressed the dog affectionately Gregson said, "Mr. Holmes, Dr. Watson, this is Clyde Montly, the watchman and caretaker so-to-speak of .mis ~uw." Mr. Montly bowed slightly to each of us and remained silent. After a few,moments, Holmes broke the silence with a question. YMr.Montly, I only want to ask you one thing. When you discovered the body after opening that room, did you close the door again before you summoned the police?" "No," Montly replied slowly, "I recall now that I left the door wide open. It remained so I believe until the Inspector here and his men arrived." "I expected that to be the case," Holmes remarked to both of us. "Why was that, Mr. Holmes?" asked Gregson. "Inspector, I need to make a few calculations, but I will tell you this now. That deep wheel rut we observed near the stack was not made by any of the wagons or vehicles operated by the quarry." Back in the cab, as we rattled our way through the streets of London toward Baker Street, I heard Holmes mutter to himself something about the room being seven by seven by eight feet. Holmes scribbled furiously upon a page tom out of the Inspector's notebook: "Stoichiometry, Watson, stoichiometry," he mumblsd when I inquired as to what he was doing. Soon he snatched a second notebook page from Gregson, wrote out a sentence or two, and handed the page back to the Inspector. "You need to question this person more thoroughly, Inspector. I have written on the note what incriminating evidence I expect that you will find when you do." Upon reaching our quarters and after Gregson had departid hastily, we settled into our chairs. Holmes slowly filled his briar pipe with tobacco from the Persian slipper and began to explain it all. Stop Here and Solve the Mystery This mystery can be solved by remembering some General Chemistry Can you answer these questions? (1) How was Bishop murdered?
Who did it? (3) What incriminating evidence did Holmes expect Gregson to find? (2)
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The following paragraphs contain Holmes' chemical solution to the mystery. Compare your solution to his. The Solution "Contrary to popular belief, Watson, a locked room murder is usually quite simple in principle to solve. We, of course, suspected that Bishop did not die naturally since the room could only be locked from the outside. There is a murderer then. but how was the murder done? What caused 13ishop's death?" "A snake, Holmes? As we encountered before?" "h'o, Watson, a~suredlynot. There were no marks on the body, no swelling. Rut just as we encountered in the Speckled Hand, my attention was drawn to a subtle mode of entry into the locked mom." "The ventilation shaft!" I exclaimed happily. "Exactly, Watson. Recall that we examinedcertain peculiarities about the limestone surface above the room and near the stack." "Holmes, I must apologize for my uneasiness over the animal print. That paw print appears not to be related to this case." Holmes laughed memly "It is not, Watson! But what an a ~ ~ r o ~ r ireminder ate of the Gieantic Hound of bveone my good fellow. i&ay dais! knd it served a good not otherwise have noticed the sour-smellinghole and the deep wheel ruts, which are very much related to the case." "What do you mean, Holmes?" "You have smelled that sourness many times before, Watson. What is it? Where in this investigation did we encounter its name?' I wondered. "Vinegar!" It suddenly came to me. "Exactly, Watson, Addum Aceticum Dilutum. Vinegar is a dilute solution of Acetic Acid, well done." "But, what.. ."I stammered. "So Lyons had access to dilute acetic acid and Mackenzie had access to concentrated, 99 percent pure, glacial acetic acid. As I mentioned before, I estimated the room to be seven by seven by eight feet and the murder took place in a limestone quarry. Surely the murderer is obvious. Limestone is mostly calcium carbonate. The addition of two parts of acetic acid to one part of calcium carbonate yields one portion of carbon dioxide gas." "It all fits, Watson. The pock-marked, sour-smellinghole we found was formed when the murderer dropped some acetic acid on the limestone. Remember from your school days; we could write the equation as," said Holmes as he scratched upon a piece of paper.
CaCO8 + 2CH8COOH+ Ca(CH3C00)2+ C02+ H20 "But, Holmes, where is the poison?" "Watson, the murderer carried out this reaction in a large, mobile vat and through pipes to the ventilation shaft filled the room with carbon &oxide! Bishop died for lack of oxygen!" "And there would be no visible signs on the body." I knew this from my medical training. "But Holmes, this reaction could have been done by either Lyons with dilute acid or Mackenzie with concentrated acetic add. How are we ever to know which one did it?" "Stoichiometry, my dear fellow. Surely you recall from your school days the utility of the definite relations of mass. volume. and amount between constituents in chemical reactions." "Well. I am not certain I recall all the details which I mav have learned. I am afraid I still don't see how this the key." "I did that calculation in the cab. Look here. I paced the room and measured its height by jumping up to the ceiling. I can tell you the room was seven by seven by
eight feet. . . 392 cuhic feet. I happen to recall that one cubic foot is equal to 0.0283 cuhic meters so the mom volume is 11.1cubic meters or 11,100 liters. As you may recall or deduce there are 1000 liters in one cubic meter." "Holmes, why do you convert our British units to those used by the French?" "Watson, the winds of change from the French Revolution have blown new ideas in many directions including the system of metric units. With no disloyalty to my English roots, I must say that the metric system is far superior to our English system for scientific calculations. Now, let us continue." "I am afraid I still don't see in which direction to continue." "What volume of vinegar, which is five percent acetic acid, would be required to produce enough carbon dioxide to fill such a room?" said Holmes. "Use equations, Watson. Use stoichiometry!" "One imperial gallon is equivalent to 4.55 liters and the density of dilute acetic acid or vinegar is 1050 grams per liter. Therefore, for a five percent solution we may write: 1.00 gal (0.0500) (4.55 Wgal) (1050 g acetic aeidn) = 239 g acetic acid which means 239 grams of acetic acid per imperial gallon of vinegar. Acomparison of the weight proportions of acetic acid (60.0 glmol) and carbon dioxide (44.0 g Imol) in the balanced chemical reaction where two acetic acids are required for each one carbon dioxide produced means that 120 grams of acetic acid are required for each 44 grams of carbon dioxide." "Therefore (239 g acetic acidX44.0 g carbon dioxiddl20 g acetic acid) = 87.6 g of carbon dioxide I should mention to you that a term which has not yet come to general use, but which I find most useful is the concept of a mole, so that we may say (87.6 g carbon dioxide) (moU44.0 g) = 1.99 moles of carbon dioxide." "But, Holmes, I don't see how this tells us the volume of vinegar necessary to produce the carbon dioxide to fill that room of death." "A combination of the laws of Boyle, Charles, and Avogadro will provide the final clue. Consider the verfect gas law where pressure times volume is proportional tomoles times temperature. For a pressure of 1.00 atmosphere and a temperature in the room of 77 Fahrenheit or 298 Kelvin, we may write: pV = nRT or V = nRTlp and V = (1.99 moll (0.08206 L atmlmol K (298 KY(1.00 atm) = 48.7 liters. This tells us that each gallon of dilute acetic acid can generate 48.7 liters of carbon dioxide." "To produce 11,100 liters of carbon dioxide would require the use of 228 imperial gallons of vinegar. It can be done, Watson. It was done. The deep wheel rut in the limestone surface indicated a very heavy vehicle. . . . a wagon carrying 228 gallons or more of vinegar!"
"But Holmes," I protested, "this proves nothing. Mackenzie had access to concentrated acetic acid so instead of 228 gallons that Burke Lyons would have had to use, many fewer gallons would be required to produce the same amount of carbon dioxide. It would be much more convenient to transport." "That is correct, Watson. About one twentieth as much as the five percent solution or only about eleven gallons. However, the deep ruts in the limestone clearly indicate a heavily loaded wagon. It must have been Burke Lyons carrying more than 2000 pounds of acetic acid. Deep ruts indeed." "Could Mackenzie not have diluted his acid to a larger volume." I said. "Watson, I am most gratified that you would consider this more subtle possibility. However, Mackenzie did not know Lvons so there would be no reason to choose such a more awkward means to transport his acetic acid. Also consider the fact that Mr. Mackenzie lived in a tiny flat and had no means to acquire barrels and vats and cany out such a project without attracting considerable attention. Whereas, Lyons was in the vinegar and food oil business and routinelv used larce barrels and vats for the fermentation procesi to produGe his vinegar. Transporting large quantities of vinegar would not be odd at all for such a man. Once he had reached the isolated quarry, the addition of powdered limestone completed his necessary ingredients. No, Watson, Lyons is the one." "Holmes, do we know how Bishop was locked into the room?" "Gregson will sort that out, Watson. Most probably Bishop and Lyons were meeting in the room to discuss their money problems. A quick shove and a turn of the key could well have locked Bishon in. And remember. that quarry is not a populous placethese days. This alloould easily have been done without the caretaker as a witness. Remember also, that Clyde Montly left the door wide open when he went to summon the volice. The room would have been well freshened with oxygen by the time they arrived. Inspector Gregson will find, I am sure, the wagon and vat, as well as pipes used to reach the ventilation shaft, when he questions Burke Lyons." "Holmes, I am always impressed with how often chemical principles apply to solving practical problems. The knowledge that I acquired during my college days has unfortunately left me. I must brush up so that I can be of more able assistance to you in the future." "Indeed, Watson. I thoroughly expect that these chemical adventures will continue as long as you and I can maintain the game afoot." Literature Cited 1.Waddell,' G.: Rybolt, T. R. J. Chom.Educ
1989,66,981.
2. Waddell, T C.;Rybolt, T R. J. C h .Edue 1990.67, 1007. 3. Waddell, T G.;Rybolt, T R. J. Chm.Edw. 1B1,68,1023. 4.Waddell, T G.; Rybolt, T. R. J. Chom.Edue 1994,69,999.
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