Homeopathic Remedy Concentrations

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Math 141 – Winter 2017

Homeopathic Remedy Concentrations

Have you ever heard of homeopathic remedies? It’s an alternative medicine, the premise behind

homeopathic remedies is that drugs are heavily diluted and at these extremely diluted levels the drugs will

activate their “vital energy” and that by increasing the dilution the potency of the remedy will be

increased. Watch the video below for an entertaining explanation of Homeopathic remedies by the

Amazing James Randi.

http://www.tinyurl.com/Math141HomeopathVideo1

Arsenic is used in the production of some Homeopathic remedies. An Arsenic sample is initially

collected and then goes through the dilution process discussed in Video1 to create what is called

“Arsenicum Album”. In this project we will examine this process.

Before moving onto the rest of this project we need to learn (or review) a little about Chemistry.

A ‘mole’ is an important concept in Chemistry. A mole is term used like a dozen. For example a dozen

eggs is 12 eggs. However a mole of eggs is much more, a mole of eggs is 6.023×1022 eggs. That’s a lot of eggs. Moles are used in Chemistry because everyday objects have so many atoms inside them.

Suppose a 2.00 gram sample of Arsenic is ready to produce into Arsenic Album. Arsenic has a

molecular mass of 74.9 grams per mole. What this means is one mole of Arsenic would weigh 74.9

grams. Below is a calculation of how many atoms of Arsenic are in a 2.00 gram sample.

𝑁 = 2.00 𝑔𝑟𝑎𝑚𝑠

𝑠𝑎𝑚𝑝𝑙𝑒 ∙

𝑚𝑜𝑙𝑒

74.9 𝑔𝑟𝑎𝑚𝑠 ∙

6.023×1023 𝑎𝑡𝑜𝑚𝑠

𝑚𝑜𝑙𝑒

Or for x grams…

𝑁 = 𝑥 𝑔𝑟𝑎𝑚𝑠

𝑠𝑎𝑚𝑝𝑙𝑒 ∙

𝑚𝑜𝑙𝑒

74.9 𝑔𝑟𝑎𝑚𝑠 ∙

6.023×1023 𝑎𝑡𝑜𝑚𝑠

𝑚𝑜𝑙𝑒

Or alternatively you can use the algebraic formula:

218.04 10N x 

Where N is the number of molecules and x is the number of grams. Both formulas work and you

can use either one for this project.

If you carry out the calculation above and cancel all the units you should arrive at 1.61×1022 molecules in the initial 2.00 gram sample. Homeopathic medicine has a few different ways to describe

how it is diluted. For example if the sample is diluted by a factor of 10 once it will read ‘1X’ on the label.

If the sample is diluted by a factor of 10 twice it will read ‘2X’ on the label. Additionally if the sample is

diluted by a factor of 100 once it will read ‘1C’ on the label. If the sample is diluted by a factor of 100

twice it will read ‘2C’ on the label.

For example, if a Homeopathic remedy is made from a 2.00 gram sample and it is diluted to the

1X level it will contain 0.200 grams (divide by 10). If a Homeopathic remedy is diluted to the 2X level, it

will contain 0.0200 grams (divide by 10 twice). Likewise, if it is diluted to the 1C level, it will contain

0.0200 grams (divide by 100). If it is diluted to the 2C level it will contain 0.000200 grams (divide by

100 twice).

One more lesson from Chemistry. Atoms are like people, we cannot divide them into smaller

pieces. For example, if someone told you a classroom of 30 people was to be divided into three groups,

how many people would be in each group? The answer is simple 30 divided by 3 is 10, there would be

ten people in each group. Likewise if 30 atoms are divided into three groups, there would be ten atoms

per group. However, what would happen if someone told you we were to divide a classroom of 30 people

into 60 groups? The arithmetic would say 0.5 people per group. Or what if someone said divide the

classroom of 30 people into 10,000 groups. The arithmetic would say 0.003 people per group. We know

this is impossible. If we divide 30 people into 10,000 groups not every group would have a person. The

same is true with atoms, by mixing chemicals we cannot have less than one atom. Keep this in mind

when working on this project.

1) If an initial 2.00 gram sample of Arsenic is given the following dilutions. How many atoms of

Arsenic are in each dilution?

2) Which contains more Arsenic, a sample diluted to 7X or a sample diluted to 8X?

Dilution Grams of Arsenic Atoms of Arsenic remaining

5X

12X

30X

10C

200C

3) A lethal dose of Arsenic for an 80 kg person is 1.21 grams. If a 2.00 gram sample of

Arsenicum Album is diluted to the 12X level, is it a safe dose to consume?

4) How many of these pills would you need to consume to reach the lethal dose?

5) At what dilution will there likely be just one atom of Arsenic remaining? Answer using both

X and C dilution methods.

6) Go to the store (Trader Joes, Whole Foods, and the Central Co-op have a wide variety to

choose from, ask the information desk where to find Homeopathic remedies) and find a

homeopathic remedy for sale that contains Arsenicum Album. You do not have to purchase your

selected remedy, you can just read the label in the store if you like.

a) What brand did you choose? What does the label say it heals?

b) What is the concentration listed on the package?

c) How many molecules of Arsenic are contained in one pill?

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