Homeopathic dilutions

Homeopathy often involves the preparation of remedies that are highly diluted. This article is meant to address the mathematical and physical nature of extreme dilutions.

Dilution calculation

;Calculation of numbers of molecules in dilutions:Number of moles in initial solution = concentration (M) x volume (L)

Also:Number of molecules in initial solution = number of moles x Avogadro's constant

Therefore, for 1 L of a 1 M solution:Moles = 1 × 1 = 1 mole:Molecules = 1 × 6.02×10²³ = 6.02×10²³ molecules

Molar limit

Serial dilution of a solution results, after each dilution step, in fewer molecules of the original substance per litre of solution. Eventually, a solution will be diluted beyond any likelihood of finding a single molecule of the original substance in a litre of the total dilution product becomes improbable.

The 10-fold dilution required to reduce the number of molecules to less than one per litre is 1 part in 1×10²⁴ (24X or 12C) since::6.02×10²³/1×10²⁴ = 0.6 molecules per litre

Homeopathic dilutions beyond this limit are unlikely to contain a single molecule of the therepeutic agent.

Common dilution examples

wimming pool

One illustration of dilutions used in common homeopathic remedies involves comparing a homeopathic dilution to dissolving the therapeutic substance in a swimming pool. [ [http://findarticles.com/p/articles/mi_qa3958/is_199904/ai_n8846565/pg_6 "Review, critique, and guidelines for the use of herbs and homeopathy"] , James Glisson, Rebecca Crawford and Shannon Street, Nurse Practitioner, April 1999
• [http://www.gordonresearch.com/answers/abc_news_20-20_debunks_homeopathy.html "An Open Letter to ABC News 20/20 with Barbara Walters and John Stossel"] , The editors of Explore Magazine
• [http://www.zianet.com/lcbiz/medtheory.htm "Medical Theory & Homeopathy"] , Dennis Hudson, 2001
• [http://homoeopathicworld.com/remedies.aspx Remedies] , Homoeopathicworld.com "The Way Of Permanent Cure" website] One example, inspired by a problem found in a set of popular algebra textbooks, states that there are on the order of 10³² molecules of water in an Olympic-size swimming pool [Assuming an Olympic swimming pool contains 2.5 × 10⁶ liters of water, there are about 8.3403 × 10³¹ molecules of water in an Olympic swimming pool.] and if such a pool were filled with a 15C homeopathic remedy, to have a 63% chance of consuming at least one molecule of the original substance, one would need to swallow 1% of the volume of such a pool, or roughly 25 metric tons of water. [ [http://philipmahler.name/Middlesex/MA1104/Chapter_5/Class%20Guide%205-3.pdf Section 5.3] , "Beginning Algebra, 10/E", Margaret L. Lial, John Hornsby, Terry McGinnis, Addison-Wesley, Copyright: 2008, Published: 01/02/2007, ISBN 0321437268] [The description in the algebra textbook suggests that there are about 100 molecules of therapeutic material remaining in the pool after 15C dilution, which is a reasonable assumption. However, the textbook incorrectly states that to expect to consume one molecule of the original substance, a person has to imbibe 1% of the pool's volume. Unfortunately, this claim is somewhat careless about probabilities; for example, to have a 95% probability of ingesting at least one molecule of the original material, a person has to drink about 3% of the pool, or about 75 metric tons of water (assuming that after dilution, 100 molecules of the original material remain). In general, consuming a fraction "r" of "N" molecules leads to a probability of approximately 1 − "e"^−"nr" of consuming at least one of the "n" molecules of the original substance, where "N" is assumed to be a large number. A 15C dilution prepared using one liter of original substance will produce a volume-volume concentration of 10⁻³⁰ liters of original material per liter of diluent, or 10⁻²⁷ milliliters of original substance per liter of diluent. In a 2.5×10⁶ liter pool, there is therefore 2.5 × 10⁻²¹ milliliters of original material. If the original material has a molar mass of "M" (in grams/mole) and a density of "D" (in grams/ml), then there will be 2.5 × 10⁻²¹ "D/M" moles of original material in the pool, or "n=1505.535 D/M" molecules of the original material. The textbook example assumes that "D/M" of the original material is about 0.0664 (for comparison, water has a value of "D/M" of about 0.0554).] cite web|url=http://altmed.creighton.edu/Homeopathy/philosophy/dilution.htm|title=Dynamization and Dilution |accessdate=2007-07-24 ]

Equivalent physical scale of dilution

For further perspective, 1 ml of a solution which has gone through a 30C dilution is mathematically equivalent to 1 ml diluted into a cube of water measuring 1,000,000,000,000,000,000 metres per side, which is about 106 light years. Thus, homeopathic remedies of standard potencies contain, almost certainly, only water (or alcohol, as well as sugar and other nontherapeutic ingredients). Homeopaths maintain that this water retains some "essential property" of the original material, because the preparation has been shaken after each dilution. [cite book |last=Resch |first=G |coauthors=Gutmann, V |title=Scientific Foundations of Homoeopathy |year=1987 |publisher=Barthel & Barthel Publishing] Hahnemann believed that the dynamisation or shaking of the solution caused a "spirit-like" healing force to be released from within the substance. Even though the homeopathic remedies are often extremely diluted, homeopaths maintain that a healing force is retained by these homeopathic preparations.

See Also

*Serial dilution

References