Candle Under Water

8/6/2019 Candle Under Water

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Getting the facts right

Oliver Knill, 9/24/2006

Besides pedagogy or psychology, it can be also relevant just to get the facts right. Anillustrative example.

Experiment: Cover a burning candle with apitcher so that the candle is in an air-tight room

sealed by the water at the ground.

Observations: After some time, the candledims and goes out. Just before the candle dies,

the water level rises to almost 1/10 th of pitcherheight. No air bubbles are seen. The water level

stays up for many few minutes more.

The chemical aspect: oxygen O2 andparaffin

Cn H2n+2 react. The burning produces water H

2O and carbon dioxide C O 2. For n=1 webalance 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 volumedecreases.

The physical aspect: the candle heats the air

and expands it. This cancels the depletion ofthe oxygen temporarily and the water levelstays down. When the oxygen is depleted, the

candle goes out and the air cools. The volumeof the air decreases and the water rises. The

temporary temperature change delays the riseof the water. As several readers have pointed

out, also the water condensation should bementioned. 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 reasoningare needed to explain what we can see. Both physics and chemistry matter. The initialcancellation effect can confuse the observer. Mathematics plays a role when the

chemical equations are balanced.

Photos of the experiment


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Photos: Oliver Knill, September 19, 2006.


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An exhibit of wrong explanations

Many explanations on the web are wrong and confusing (September 2006). Actually, the primaryhits in a search engine all lead to pages, which are wrong or incomprehensible. By the way, if

this page should confuse you or contain errors, please mail [email protected]. Here are

some pitfalls:

y Argument: Oxygen is replaced by Carbon dioxide. So, there is the same amount of gasadded 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 balancedcorrectly. 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 dioxidemolecule 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 atemperature greater than 212 F and the whole system held above this temperature then thewater 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 combustionand the sealing fluid would be pushed out.]

y Argument: Carbon dioxide is absorbed by the water. Thats why the oxygen depletion hasan effect.

Source of the Error: This idea is triggered from the fact that water can be carbonized orthat 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 pressurewould need to be applied so that the carbon dioxide is absorbed during the short time

span of the experiment.y 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 lostthrough 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.y 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 twoeffects which matter: the chemical process of the burning as well as a physical processfrom 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 from that ?


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An important aspect in pedagogy is to understand "how students learn" and how toproduce 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 isoften 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 20percent 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 airhas 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


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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/2carbon 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.

Added March 20, 2011

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

Many people try to explain the problem with physics alone with a differentargument.They argue that less hotair is captured in the cup. In other words, the cup covers a

volume of less dense air because the air is heatedaround the candle. When the air coolsafter the candle goes out, the pressure decreases almost entirely from less dense air

cooling.

Regardless, some may argue that the chemicalaspect is very minimal because the waterlevel sometimes rises to one third of the volume, but under perfect conditions reactioncondition, the reaction chemistry can only account fora maximum ten percent water level

rise. You suggest that the water level rises to one tenth of the height, however it can bemuch higher if more candles are used.

Iagree that the chemical reaction can have an effect, but how would you rank thecontribution 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 whileuntil 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 besurprised 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 waiteduntil 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 alonecan 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 mightcontribute 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 preheatingis 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 partof the room will be affected. What I liked about the experiment is that with household


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size objects, one can get directly to a situation where the balance between physics andchemistry is initially equal. The initial cancellation of different effects is what makes the

experiment so interesting and puzzling.

Candle Under Water

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