In chemistry we use a measure known as a “mole” which is simply the molecular weight of a substance in grams. The convenience of using moles is that no matter what the substance is, one mole always contains the same number of atoms or molecules: 6.022x1023* (Avogadro’s number).
As an example, let’s consider the compound Sodium Chloride (common salt). The molecular weight of Sodium Chloride (NaCl) is 58.44, therefore 58.44 grams of NaCl is one mole or 6.022x1023 molecules.
A '1 molar' solution.
This is simply where one mole of substance is dissolved in a total volume of 1 litre of solvent. In our case 58.44 grams of NaCl dissolved in water to a total volume of one litre would give us our starting solution. That is one litre of water that contains 6.022x1023 molecules of Sodium Chloride dissolved in it.
Now that we know how many molecules we have in the starting solution, it’s just a case of keeping track of the numbers.
In “C” potencies, there is a dilution of 1 in 100 at each step. That means that of out of our 1 litre (1000cc) starting solution we take 10cc and dissolve it in another 990cc of water. This means that the number of molecules present reduces by a factor of 100 at each step.
A 1C dilution would therefore contain 6.022x1021 molecules of NaCl.
A 2C dilution would contain 6.022x1019 molecules of NaCl.
A 3C dilution would contain 6.022x1017 molecules of NaCl.
And so on with the number of molecules present reducing by 100 (or 102) with each step.
A 10C dilution would contain 6.022x103 molecules of NaCl; in other words 6,022 molecules in the solution.
At 11C we have 60 molecules present.
At 12C we have 0.6 molecules present, or more strictly a probability of 0.6 that 1 molecule is present.
The Avogadro limit.
Once we pass this dilution point, the Avogadro limit, there is no more starting material in the solution. Any dilution beyond 12C (or 24X) simply means that water is being dissolved in more water. This is why homeopathic remedies that have potencies of 30C, and even 200C, are simply ludicrous.
I have done the calculations based on a starting solution that is a 1 molar solution. In reality, homeopaths are unlikely to be starting with a 1 molar solution, especially with the more expensive materials they may use. This means that the point of diluting out all of the starting material will be reached a long time before the 12C dilution.
* scientific notation.
This is shorthand way of representing large numbers.
For example, one million, 1,000,000 has six places after the first digit. In scientific notation this would be represented as: 1x106
1,250,000 would be represented as: 1.25x106
1,250,000,000 would be represented as: 1.25x109
The power to which 10 is raised, i.e. 10x, indicates how many places there are after the first figure - the blanks are filled in with zeros.