Getting the facts right

Photos of the experiment

An exhibit of wrong explanations

• 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.
• 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 from that ?

  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.