Rebellion by the Minority: Prophecies by Molecules on Paper and Computers

Abstract

Here is a cup of coffee. If you divide it in half, both halves will be the same coffee. If you divide it in half again, it will still be the same coffee. Of course, we know that coffee is made of a mixture of molecules such as water and caffeine. However, the number of molecules in a cup of coffee is immense; therefore, there is no difference in properties between a cup and a drop of coffee. Counting all of the individual molecules would be inconvenient, so they are grouped together in vast units of approximately 6 × 10²³ (Avogadro’s number); this number of molecules is referred to as 1 mole. Two moles of hydrogen molecules and 1 mole of oxygen molecules react to produce 2 moles of water (2H₂ + O₂ → 2H₂O), while 0.02 moles of hydrogen molecules and 0.01 moles of oxygen molecules would react to produce 0.02 moles of water. Thus, if the overall volume is changed but the proportions are constant, the same behavior will be exhibited. Or will it? What happens when you divide a cup of coffee? Do individual molecules never show themselves in our daily lives?