## Getting the facts right

Oliver Knill, 9/24/2006 (last edit: january 2014)

 Besides pedagogy or psychology, it can be also relevant just to get the facts right. The Water-Candle experiment is an illustrative example. It is a situation where many different effects play together and where it is hard to figure out which ones really matter. My own perspective about this experiment has shifted several times and comments of some who wrote me added valuable insight. Please look also towards the end of this page where some interesting links are added and information like why the great Lavoisier himself replaced the experiment since it was too subtle.

 Experiment: Cover a burning candle with a pitcher so that the candle is in an air-tight room sealed by the water at the ground. Observations: After some time, the candle dims and goes out. Just before the candle dies, the water level rises to almost 1/10 th of pitcher height. No air bubbles are seen. The water level stays up for many few minutes more.
The chemical aspect: oxygen O2 and paraffin Cn H2n+2 react. The burning produces water H 2O and carbon dioxide C O 2. For n=1 we balance the equation as follows:
 2 O2 + C H 4 = C O 2 + 2 H 2 O
Because twice as much oxygen is burned than carbon dioxide released, the air volume decreases.
The physical aspect: the candle heats the air and expands it. This cancels the depletion of the oxygen temporarily and the water level stays down. When the oxygen is depleted, the candle goes out and the air cools. The volume of the air decreases and the water rises. The temporary temperature change delays the rise of the water. As several readers have pointed out, also the water condensation should be mentioned. While water is initially gas, it condenses and helps to delay the effect.
 Summary: There are two different effects. Both a chemical and a physical reasoning are needed to explain what we can see. Both physics and chemistry matter. The initial cancellation effect can confuse the observer. Mathematics plays a role when the chemical equations are balanced.

## Photos of the experiment

Photos: Oliver Knill, September 19, 2006.

## An exhibit of explanations

Many explanations on the web contradict each other (September 2006). Actually, the primary hits in a search engine all lead to pages, which difficult. Here are some pitfalls:
• Argument: Oxygen is replaced by Carbon dioxide. So, there is the same amount of gas added than taken away. Therefore, heat alone most be responsible for the water level change.
Source of the Error: A simplified and wrong chemical equation is used, which does not take into account the quantitative changes. The chemical equation has to be balanced correctly. It is not true that each oxygen molecule is replaced by one carbon dioxide molecule during the burning process; two oxygen molecules result in one carbon dioxide molecule and two water molecules (which condense). Remember oxygen is present in the air as a diatomic molecule. [A reader clarifies the water condensation in an email to me as follows: If the experiment were done with the sealing fluid able to support a temperature greater than 212 F and the whole system held above this temperature then the water product of combustion would remain gaseous and the pressure within the vessel would increase as a result of three gaseous molecules for every two prior to combustion and the sealing fluid would be pushed out.]
• Argument: Carbon dioxide is absorbed by the water. Thats why the oxygen depletion has an effect.
Source of the Error: This idea is triggered from the fact that water can be carbonized or that the oceans absorb much of the carbon dioxide in the air. But carbon dioxide is not absorbed so fast by water. The air would have to go through the water and pressure would need to be applied so that the carbon dioxide is absorbed during the short time span of the experiment.
• Argument: The experiment can be explained by physics alone. During the heating stage, air escapes. Afterwards, the air volume decreases and pulls the water up.
Source of the Error: the argument could work, if indeed the heating of the air would produce enough pressure that some air could leave. In that case, some air would be lost through the water. But one can observe that the water level stays up even if everything has gone back to normal temperature (say 10 minutes). No bubbles can be seen.
• Argument: It can not be that the oxygen depletion is responsible for the water raising, because the water does not rise immediately. The water rises only after the candle dims. If gas would be going away, this would lead to a steady rise of the water level, not the rapid rise at the end, when the candle goes out.
Source of the Error: It is not "only" the oxygen depletion which matters. There are two effects which matter: the chemical process of the burning as well as a physical process from the temperature change. These effects cancel each other initially. Since these effect hide each other partially, they are more difficult to detect.

## What do we learn?

An important aspect in pedagogy is to understand "how students learn" and how to produce a classroom atmosphere, in which students learn well. But teaching is complex. Already the material itself can be complex. Getting the facts straight can matter too. It is often the reason for pedagogical failures. A first step is to get the sources right. How can students learn if the sources are incorrect?

## Appendix: The chemical equation for general n

We have simplified the chemical reaction and taken n=1 above. For general n, balancing the chemical equation

 O2 + x Cn H 2n+2 = y C O 2 + z H 2 O
leads to the system of linear equations
 ```n x = y ( C atom balance ) (2n+2) x = 2 z ( H atom balance ) 2 = 2 y + z ( O atom balance ) ```
which has the solution x = (4/(1+6n), y = 4n/(1+6 n), z = 2( 1+2 n)/(1+6 n). This is where linear algebra kicks in.

 (1+3 n) O2 + 2 Cn H 2n+2 = 2 n C O 2 + (2+2n) H 2 O

For large n, it is rather 1/3 instead of 1/2 of the oxygen amount which matters. With 20 percent of oxygen in our air, we get about 8 percent of the air volume removed. This fits pretty well with our experiment shown in the photos, where about 1/11 to 1/12 of the air has been replaced by water. For paraffin (wick) used in candles, n is larger than 20.

## Appendix: the ideal gas equation

We see from the balancing equation that two oxygen molecules are replaced by one carbon dioxide molecule. Since CO2 has one carbon atom more than O2, it is heavier. Will this not imply that it takes up more volume? It turns out that only the number N of molecules matters. The ideal gas law relates the gas pressure p, the volume V, the temperature T with the number of molecules N as follows
 p V = N k T

The letter k is a constant called the Bolzmann constant. Like any physical law, this is an idealisation and approximation but it is accurate enough for the experiment in question. In the candle experiment, the pressure and temperatures at the beginning and the end are essentially the same. But since the number N of oxygen molecule is replaced by N/2 carbon dioxide molecules, the corresponding volume gets divided by half too. A refinement of the law, the van der Waals equation also incorporates the size of the molecules.

Jonathan Lavian, who writes a research paper for an education minor, writes:

 Many people try to explain the problem with physics alone with a different argument. They argue that less hot air is captured in the cup. In other words, the cup covers a volume of less dense air because the air is heated around the candle. When the air cools after the candle goes out, the pressure decreases almost entirely from less dense air cooling. Regardless, some may argue that the chemical aspect is very minimal because the water level sometimes rises to one third of the volume, but under perfect conditions reaction condition, the reaction chemistry can only account for a maximum ten percent water level rise. You suggest that the water level rises to one tenth of the height, however it can be much higher if more candles are used. I agree that the chemical reaction can have an effect, but how would you rank the contribution of each? Is one effect minimal or more important? How does the size of the candle or container play a factor?

I myself did not make the experiment with several candles but I can imagine that one can boost the physics part like this: if one would take a lot of candles, burn them for a while until the air around it is hot and then place the container around it, the physics portion of the argument gets a boost. I can imagine that this can be substantial and would not be surprised to see the water level rise to 30 percent without contradicting anything said above. I myself have lighted the candles and then immediately placed it and not waited until the air around it got hot.

One could do the experiment with an other heat source which does not use any chemical processes. Then the chemistry part would be ruled out and the physics contribution alone can be measured. To completely rule out preheating, one could light the candle from inside the container. This would have to be done carefully however as gas lighters might contribute additional gas and heat for example. I think it is better to light the candle, place the candle down and then immediately place the pitcher around it. Excessive preheating is excluded like this.

The size of the pitcher certainly will have an effect. If the pitcher is too large, then both the effect of the physics as well as the chemistry will be smaller simply because only part of the room will be affected. What I liked about the experiment is that with household size objects, one can get directly to a situation where the balance between physics and chemistry is initially equal. The initial cancellation of different effects is what makes the experiment so interesting and puzzling.

Paul Martin from Colorado School of Mines kindly informed me about this paper of Harkirat S Dhindsa which is the best writing I have seen about this topic. Here is a local copy retrieved September 26. The section on "What is happening in the experiment" confirms the above picture. It mentions some additional details like (1) that little Carbon monoxide is produced or (2) that almost all the Oxygen gets used up or (3) that the circular current within the jar makes sure that also Oxygen from above gets used and (4) that before closing the jar over the candle some air might escape. The text also mentions (5) some bubbles which might escape if one is not careful and (6) that water vapor can condensate on the jar. An other subtlety is that (7) through increase in temperature, air becomes unsaturated to accommodate additional water vapors.
[To 4) This can be neglected or avoided by making sure that as soon as the candle is lighted the jar is dropped over it. To 5) This is a major misunderstanding in many explanations. As the text mentions there are no bubbles if the experiment is done right. The text later says "if any". If some reader should notice any bubbles in the candle experiment, I would love to hear about it.] Here is a section from Dhindsa's paper:

 What is happening in this experiment? When we ignite the candle, the hydrocarbon reacts with oxygen (in excess) to produce carbon dioxide and water. The burning sets an air current which gives dome shape to candle flame and it helps to get complete combustion at the bottom and the outer surface of the flame. The hot air and products of combustion rise up above the flame. As soon as the gas jar comes over the flame, the hot gases moving upward enter the jar and air inside the jar expands pushing some of the air out of the jar. This process goes unnoticed. As soon as the jar touches the water, the burning occurs in a closed environment. Further pressing the jar into water helps to retain the air in jar which is less in quantity than at room temperature and pressure. However, due to thermal expansion, the pressure is higher than atmospheric pressure which is balanced by pressure from the water. The burning of hydrocarbon in the jar produces about 30% more molecules of carbon dioxide and water than the molecules of oxygen consumed in the reaction (see below the title expectedchemical reaction). The increased heat and number of molecules increases the pressure in side as a result if not careful some bubbles of gas will escape from the jar. Over the time the oxygen in the jar is reduced and conditions for burning are changed. Burning under reduced oxygen may not produce carbon dioxide rather carbon monoxide (very little). When the candle is put out, the temperature decreases followed by also a decrease in pressure due to condensation of water vapour and decreased quantity of air due to thermal expansion during the process of placing the jar on the candle. The overall situation is a decrease in pressure inside the jar as compared to atmospheric pressure. Therefore, despite water is heavier that air, it is pulled into the jar. How much water rises as a result of dissolving of carbon dioxide? Very little practically negligible during 30 - 40 minutes, the time the experiment usually takes for performing in a classroom situation. If the number of candles is increased in the jar, the heat produced is more therefore more air is likely to escape from the jar due to thermal expansion during the process of pacing the jar over them. Therefore, more water will rise in the jar with more candles. The nature and quantity of the products will depend upon the composition of candle material. However, it is assumed that combustion of saturated hydrocarbons is taking place during burning. CnH2n+2(s) + (1.5n+0.5) O2(g) = n CO2(g) + (n+1) H2O(g) For n=1, two moles of oxygen reacts with a mole of CH4 to produce three moles of product molecules. Assuming that supply of methane was controlled and it is stopped as soon as the flame is put out, otherwise there will be an explosion. The number of moles of the product molecules is 1.50 times that of oxygen. As n increases, the multiple factor decreases from 1.50 and approaches 1.0 at n = ? For n=30 (a typical paraffin wax), the factor will be 1.34. The overall understanding of the experiment is that all the oxygen is not used up (I have rested the presence of oxygen after the candle is put out in our laboratory using yellow phosphorus) and the consumption of oxygen does not create empty space rather the number of product molecules in the jar increases over that of the consumed oxygen. Thus giving rise to an increase in overall pressure in the jar (see above equation). Moreover, almost equal number of molecules of CO2 and H2O are produced. A quick rise of water in the jar after the candle is extinguished is mainly due to a decrease in pressure as a result of a decrease in amount of air in the jar due to thermal expansion during the process of placing the jar on the candles, bubbles escaping (if any) through the water and may be the condensation of the water vapour. The amount of condensation of water will depend upon the temperature difference between initial and final temperature of the air in the jar. Since air is above water, therefore saturated water vapour pressure is considered in the beginning of the experiment. Increase in temperature, during the candle burning, will make air unsaturated to accommodate additional water vapours especially produced as a product of burning. A decrease in temperature over time after the candle is off to the initial temperature will help water vapour to condense. This condensation will decrease the pressure inside the jar and will help water rise in the jar. The amount of water vapours condensed during a small change of temperature as usually occurs in this experiment may even be small to notice. The amount of CO2 dissolved in water is minimal in the 30-40 minutes during which experiment is conducted.

 Question by a reader, November 20, 2011: We have two setups, one is with 1 candle and the other with 4 candles. We see that that level of water will rise more in 2nd setup. Why? Answer: theoretically, if you assume that the candles will burn up all the oxygen in the container, and assume the room is completely air tight and assume that both water and air incompressible, it does not matter. You will have the same water level at the end in both setups after the candles have burned out and the situation cooled down. In real experiments, there are differences but they depend on the actual experiment: First of all, the candles themselves will take up some volume so that in the second setup there is less air to burn. This will make the water rise less in the second setup. It is less, not more because there is less air to be burned. This should be negligible if the candles are reasonably small in comparison to the container. Since more candles will heat up the air more, the initial expansion effect can be faster. It is feasable depending on setups that the expansion of the air is so large that some air might escape leading to higher water level rising. In general however, if you should see air escape, the experiment is not designed well. Put more water to make it air tight around the boundary of the pitcher you use as container. You might do the experiment by lighting the candles first then cap it with the container. The air around the candles might now already be partly depleted of oxygen at the start. This happens with more candles even more. This effect could lead to less water level rising in the second case. Again this can be neglected because most of the air in the container will be air you had initially in the container. If the candles are small and the container large, then more candles heat up the air faster than one candle. It will take much longer to see the effect for one candle. Additionally, air is not totally incompressible. If you make the experiment in a larger room even if it is air tight, the water might not rise because it would take too long to burn up all the oxygen and air gets slightly expanded. Burning a large fire inside the room however would do the job. This argument can lead to the water rising more with more candles.

 Simo Tolvanan from Helsinki kindly informed me about the Article of Vera, Riviera & Nuez in "Science and Education". The article explains things very well and also contains much history and references. This paper makes the story again interesting. It points to the fascinating story of Lavoisier, who first realized that the total mass does not change during this process and who noticed that only a fraction of the oxygen reacts before the candle goes out by demonstrating that a mouse still can breath afterwards. The authors of the article provide also experiments The classical candle experiment is compatible what is seen by everybody else and which matches the stoichiometry computations. The artificial wick experiments demonstrate only a one percent increase. The authors conclude that bubbling and hot air trapping are responsible for the rising water. The setup for the candle experiment and the artificial wick experiments are very different. In the later case, the candle burning is violent and the container is very long. Heavier CO2 (which the ignition already produces in the first moments) can kill the candle before much of the oxygen is out.

January 27 2012: the bubbling effect. Here is an illustration why many teachers report bubbles. If you place the pitcher flat on then bubbles escape initially. One can avoid this by tilting the glass first. We just want initially to have the same level of water and the same pressure inside and outside. The experiment starts then.

 Candle experiment done carefully so that initially the water level inside is close to the water level outside. Bubbles which escape.

How can the Vera-Riviera-Nuez (VRN) experiments be explained? They report only a 2 percent water increase. Here are some additional effects, which includes comments some readers have mentioned over the years:
• Water: The above stoichiometric computations assume that water condenses. If the temperature in the glass is high, then this can keep water in gas form and decrease the effect.
• Initial air escape Because initially, the water level is near the bottom, the initial heating will have a stronger effect than the depletion of oxygen and the water level drops, and air will leave the container. This happens especially with narrow containers which have a neck.
• Oxygen level VRN mention Lavoisier who demonstrated that not much of the oxygen actually reacts. If Lavoisier was able to place a mouse inside, then this means that his containers were rather large. It could be that only the area close to the candle gets depleted by oxygen, and convection is not fast enough to keep substantial part of the room still filled with oxygen. Also, CO2 is about 1.5 times heavier than air and sinks to the ground so that the upper part of the container still contains oxygen. Especially in a larger room, this must be substantial. This could also matter in the VRN experiments, where the pitcher is narrow and long. The artificial wick lightening is quite violent and could deplete the neighborhood of the candle rather quickly from oxygen. The candle could go out because CO2 has accumulated below and suffocates the candle. The narrow cylinder also does not help convection. To the mouse story of Lavoisier: NASA experiments show that one can survive even with 20 percent of oxygen levels. This indicates that the mouse can survive even if 80 percent of oxygen is gone. Also, a candle is hot and sucks the air from below it, just where the carbon dioxide accumulates. The candle can go out much earlier at the bottom of a large room.
• The water level increase depends on the "n" used in the stoichiometric computation. With different paraffin, different water level increase have to be expected.
In summary, the candle-water experiment has become again very interesting. If you are a student, I suggest to start your own experiments, do your own thinking and see what is right.

 Peter Dureen had a great idea to modify the experiment. He wrote: ```I wanted to test Avogadro's hypothesis by doing the following. I would take a piece of burning charcoal, throw it in a glass, and immediately cover the glass with plastic wrap. I hoped that some carbon monoxide would be produced. In that instance, I expected an increase in volume, or pressure, as the case may be, since every oxygen molecule that entered into the reaction would produce two carbon monoxide molecules. In any case, to the extent that carbon dioxide was produced, there would be no change in pressure, I thought, since each molecule of oxygen would be replaced by a molecule of carbon dioxide. fully expected the plastic wrap to bulge upward with the increase in gas pressure, even after the piece of charcoal ceased to burn due to the lack of oxygen, and the temperature fell to room temperature again. What happened amazed me. The plastic wrap bulged downward into the cup. This indicated, to me, a reduction in pressure exerted by the gas in the glass, and thus indicated a reduction in the number of molecules. You may try this interesting and simple experiment yourself. I have no explanation for what happened, although one conjecture is that the carbon absorbed the carbon dioxide. ``` The stoechimetry for coal is different than for paraffin. In the case of only carbon, one has ``` C + O2 = CO2 ``` and one would indeed expect that the volume would stay the same. Since the pressure decreases afterwards, this could indicate that indeed some air has gone out when the heat has expanded the inside. After cooling, the plastic wrap collapses. Peter Dureen again: ```The second experiment is a parallel one to the candle experiment. I and an associate made a little stand from aluminum foil, so that it could support a piece of burning charcoal. This little stand basically replaces the candle in the burning candle experiment. We had a shallow reservoir of water in a pan, the water surrounding the little stand. I took a piece of charcoal, which I had fetched earlier from my fireplace, and took a propane torch to all sides of it to ensure it was well lit, and then placed it on the stand. My accomplice then quickly placed a jar over the assembly. Remarkably, water eventually rose in the jar after the apparatus had a chance to cool down. It, in fact rose to precisely the same level as it had in a candle experiment using the same jar. So it seems that charcoal has the same effect as a candle. Now in your analysis, you mention that the candle burns hydrogen, and produces water, and that seemed quite reasonable to me at the time. But after conducting this experiment, I must ask why burning carbon alone should produce precisely the same result. It is hard for me to explain to my students these two experiments. I now await further discussion of this matter, and hopefully, an analysis that explains the results of these recent experiments. ``` I think this is more indication that some hot air has left the container before it started to cool down. I have repeated the experiments also with different type of containers and seen also some air, as other teachers have observed too. ```I thank you for posting your explanation. I hope the above adds something to the discussion. Maybe we should consult Faraday. Did he not write something called the history of the candle? ``` Faraday had been a fantastic experimenter and assisted as a chemist before for a long time. Lavoisier was definitely a great pioneer in this context.

 Robert Garisto sent the following interesting thoughts: ```I'm a physicist (a theorist, I now work as an editor for PRL). I was reading up on the discovery of oxygen, and I saw a mention of Lavoisier's experiment of a burning candle that causes the water to rise in a jar. I had never heard of the experiment, but it sounded great, and I immediately did it in my kitchen (I guess I am part experimentalist after all). It worked great. Someone posted this link, debunking the experiment. What do you think of this? ``` This is a pretty good simplification. It defuses well the myth that the oxygen is burned away. The reason why the myth persists because the rise of water matches the amount of oxygen in the air. Robert Garisto again: ```So I went and did a few other experiments. I used a much bigger jar, where there was almost no effect, probably in part because the candle went out in about the same amount of time despite the larger volume. I put the lit candle in quickly, took it out, and then quickly put the original jar in the water. It did take in some water about 1/2 as much as with the candle in over the next 10 sec, presumably due to air in the jar having been heated before the seal and then cooled afterwards. From this I judge that at least half the effect was due to Boyle's law, perhaps more. I also concluded that the candle went out at least in part due to condensation from the H2O produced in burning the candle wick was wet and hard to relight. Thus I decided that there was no way that Lavoisier could have learned much from this particular experiment. So I managed to locate his own account of his experiments. Note that he abandons the candle and water experiment as having potential flaws. He moves to mercury instead, and lights the candle after the jar is in place. What he ends up on is this: "In the middle of a glass stand, was placed a small wax candle; and on the top of the wick was fixed a small piece of Kunckel's phosphorus. The stand was then placed in a basin of mercury and covered with a jar. I made a piece of iron wire red hot then passed it through the mercury set fire to the little piece of phosphorous and by this means the candle was lighted." What he found was that the heated air initially pushed the mercury down, but when everything had cooled, there was a tiny loss in the volume of air, 1/300th the volume. But then he reacted the air with a CO2 absorber and the volume was reduced by 1/10. In other words he claims that the total volume was virtually unchanged, but (assuming air is 1/5 oxygen) about 1/2 the oxygen was converted into CO2 (with an unspecified amount turned into water. He may not have realized water was a byproduct yet). The combustion of paraffin is C25H52 + 38 O2 => 25 CO2 + 26 H2O. Depending on what fraction of the water remains as vapor, one goes from 38n moles to between 25n and 51n moles of CO2+H2O of vapor (with the rest in condensed H2O). Now it could be by chance that the C2O+H2O vapor happened to be near 38n, but that would be just chance. In your opinion, what fraction of the H2O condenses? ``` This should depend on the temperature and the humidity already present in the room. If we believe the account of Lavoisier, it could indeed be that things pretty much balances out when done as described. This makes the experiment so interesting. There are various effects which play a role: physical like temporary heating and cooling as well as condensation as well as chemical due to the reaction of paraffin with stochiometric computations which depending on the type of paraffin is used. The experiment depends on the size of the container, the surrounding temperature, air humidity present as well as on the experimenter (lightening the candle, allowing air to escape initially for example through bubbles or due to the expansion while removing the lightener).
 ```I'm helping a grandchild with a science experiment. It's similar to your experiment above, however, we taped a 300cc oxygen absorber to the inside "top" of the pitcher. We were told as the chemical reaction takes place inside the packet (rust/oxidation) the oxygen inside the pitcher is absorbed into the packet creating a void (vacuum). The water below is drawn in to fill the void. The oxygen absorber does heat up during the process of oxidation. Would this be the same effect as the candle? Is the absorber packet really absorbing oxygen or converting it? Your thoughts are appreciated. Thanks- Phil ``` My answer: ``` Hi Phil, oxygen absorbers produce rust from iron and oxygen which simplifies the situation because rust is not a gas and the chemical gas equations do not have to considered. So, one expects the water level to rise to the same amount as oxygen has been removed. The change of volume of the oxygen absorber can certainly be neglected I don't know how hot these absorbers get but I do not expect this to matter much. They probably absorb very slowly. It might initially push back the effect of depletion of oxygen but only little. I also do not know how much of the oxygen these absorbers are able to remove. Already in Lavoisier's case, the depletion of oxygen was not enough to suffocate a mouse so that also in the oxygen absorber case, only a fraction of the oxygen is removed. I have not made the experiment you describe but would estimate that the water level rises only little. Oliver ```