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This commentary was written by Bob Lee explaining how Faraday's Equation can be used to calculate how much actual silver is deposited into distilled water when using a colloidal silver generator.

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Author: Bob Lee
Contact: E-mail
Source: silverlist@eskimo.com
Original Source Format: Text, in a two part series
Edited: Reformatted, emphasis ours, no technical information omitted, spelling, small linguistic modifications
Copyrights: Content copyright 2000 Bob Lee, released to public domain for educational use. HTML copyright 2001 The CSDW, rights reserved, released for noncommercial applications.

Items both in brackets and italicized are editor additions to the text.

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Greeting to all astute silver makers and users,

A friend of mine asked,"How much silver is in that spoon of CS." Told him I didn`t know, but would calculate it for him. This is what I did and you can too. This is going to be technical but try it any way, you're probably smarter than you thought.

We will start buy determining what a *chemical equivalent* is.

The chemical equivalent is the atomic weight of an element divided by its valence number. That will be (w)/ (z).

Atomic weight = w
Valence number = z

Look at this table:

Element
Atomic Weight in Grams

Valence Number

Cu Copper 63.57 +2
Ag Silver 107.88 +1
Au Gold 196.97 +1


[ Calculations on the chemical equivalent based on the above data ]

This will give us:

Cu copper 63.57/2 =31.785 ( one chemical equivalent)
Ag silver 107.88/1 =107.88 ( one chemical equivalent)
Au gold 196.97/1 =196.97 ( one chemical equivalent)

The quantity of electricity to liberate *one chemical equivalent*of a substance can be found this way. We will keep two physical constants in mind as we do this:

1. A coulomb of electricity will deposit 6.25x10+18 atoms in one second of time.
2. Avogardo`s constant states the number of atoms in a substance is always 6.06x10+23 atoms in a * gram-atom* of the substance. This means that there will be:

6.06x10+23 atoms in 107.88 grams of silver. (one chem. equiv.)
6.06x10+23 atoms in 196.97 grams of gold. (One chem. equiv.)
6.06x10+23 atoms in 63.57 grams of copper. (two chem. equiv.)

To liberate the 107.88 grams of silver will require: 6.06 X 10+23 divided by 6.25x10+18 = 96,500 coulombs of electricity.

Remember that 6.25x10+18 is a *coulomb* or *one ampere* of current. To reduce 107.88 grams of silver will require 96,500 amps of current over a period of time. 96,500 coulombs of electricity will liberate one chemical equivalent of any substance, or in our case, 107.88 grams of silver ,or 6.06x10+23 silver atoms.

Now we will make a table of currents vs * chem. equiv.* :

A current of TEN amps for ONE hour will be 36,000 coulombs and we need 96,500 coulombs to reduce *one chemical equivalent*.  Observe:

10 amps for one hour
=
0.373 chem equiv (36,000/96,500)
5 amps for one hour   0.186 chem equiv
1 amp for one hour   0.0373 chem equiv
.5 amp for one hour   0.0186 chem equiv
.1 amp for one hour   0.00373 chem equiv
.01 amp for one hour   0.000373 chem equiv
.009 amp for one hour   0.0003357 chem equiv
.008 amp for one hour   0.0002984 chem equiv
.007 amp for one hour   0.0002611 chem equiv
.006 amp for one hour   0.0002238 chem equiv
.005 amp for one hour   0.0001865 chem equiv
.004 amp for one hour   0.0001492 chem equiv
.003 amp for one hour   0.0001119 chem equiv
.002 amp for one hour   0.0000746 chem equiv
.001 amp for one hour   0.0000373 chem equiv

Remember that the chemical equivalent of a substance equals the ratio of atomic weight in grams divided by valence number, and the chemical equivalent for silver is 107.88 .
If we ran 7 ma of current for one hour we would liberate 107.88 x 0.0002611 =0.02816 grams of silver in our water.

Keep this number in mind ( jot it down ).

Now we will look at the Faraday Laws of Electrolysis.

The one which concerns us says that The Mass of a substance liberated in an electrolytic cell is proportional to the quantity of electricity passing through the cell.

The amount of material liberated for each coulomb is called the *Electrochemical Equivalent* of a substance.

This is also the *Chemical Equivalent* divided by 96,500 or = the Electrochemical Equivalent.
The electrochemical equivalent is called *k*

k for silver is 107.88 /96,500 or =0.001118
k for gold is 196.97 / 96,500 =0.002041
k for copper is 31.8 / 96,500 =0.0003295

Faraday's equation for electrolysis is m = kIt

That is, mass in grams = electrochemical equivalent times current times time.
m = k x I x t or
m = k x coulombs , I x t = coulombs
Now we have m= mass in grams
k= electrochemical equivalent (atom weight divided by valence times 96,500)

I= current in amps
t= time in seconds

Now for 7 ma of current for one hour we have: 0.001118 x 25.2 coulombs =0.028159 grams of silver. Round 0.028159 to 0.02816 gm of silver ( now look at the number you jotted down before) . Viola ! We have done it!

We ran a current of 7 ma for one hour and produced 0.02817 gram of silver in the water we are using. Now if it we used 8 ounces of water, this silver is in the 8 ounces of water. That's 0.02817 gram in 8 ounces of water. There are 48 teaspoons in 8 ounces of water, so we divide 0.02817 by 48 and get 0.0005868 gram of silver in one teaspoon of CS. This is also 0.5868 milligram (mgm) of silver.

[ Note: see the page on the EPA toxicity report for further information ]

If we had a current of 3 ma for one hour it would be 0.01207 gram in 8 ounces of water or 0.0002514 gram in one teaspoon or 0.2515 mgm of CS - a little over 1/4 mgm of silver.

But my current starts low and slowly gets higher as it goes. The way I do it is to read the current every 5 minutes and add up the readings and take the average. If my current started at .5 ma and stopped at 7 ma after an hour the average would be about 3.5 ma.

As we recall there were 6.06 X10+23 atoms in 107.88 gm of silver. Let us find the atoms in 100 grams of silver, for that will make things easier later on.

100 is 92.69558 % of 107.88, so we have 5.61735 X 10+23 atoms in 100 grams of silver.

We now can make the following table:

5.61735 X 10+23 atoms in 100 gm of silver.
5.61735 X 10+22 atoms in 10 gm of silver.
5.61735 X 10+21 atoms in 1 gm of silver.

Remember we had determined that there was .02817 gram of silver (Ag) after running 7 ma for 1 hour ( average current ).

5.61735 X 10+21 times .02817 = 1.5824 X 10+20 atoms in .02817 gram of silver in our 8 ounces of water.

Divide that by 48 (teaspoons in 8 ounces) and we have 3.29666 X 10+18 atoms of silver in the teaspoon .

Let's do this for an average current of 3 ma for 1 hour, which was .01207 gram of silver in 8 ounces of water.

5.61735 X 10+21 atoms times .01207 = 6.78014 X 10+19 atoms in the 8 ounces of water. Now, divide by 48 ( teaspoons ) and we get 1.41252 X 10+18 atoms in the teaspoon of CS.

Really now ,who cares how many atoms are in the teaspoon we drink? What's it to us? Later I will post about CELLS and ATOMS because that's what we are made of. I will talk about viri and bacteria and proteins and other stuff!

Some times it's real hard to visualize things like atoms and all those big numbers, so I have made some calculations and will show you what it looks like. I`ll skip the 3 pages of numbers and just help you visualize the silver in your spoon!

We will now make a small square which will be the amount of silver in your spoon at 3 ma ( average ) for 1 hour in 8 ounces of water - and consider that you took one teaspoon of it!

Take some tin foil (or aluminum foil) out and some scissors. Cut a thin sliver of foil about 1/16" thick ,hold it in one hand and snip a small piece off the end also about 1/16". You now have a little tiny square of foil about the size of this o (o). Imagine that little square melted into your water (dispersed) and now its invisible. That little square represented a volume of 62.5 X 62.5 X 2 thousands of an inch or 7812.5 cubic thousands of an inch . Take a piece of scotch tape and pick up the little tiny foil square and stick in where you can look at it when you take your silver. It really helps to visualize by looking at it.

That 7812.5 cubic thousands of an inch is the volume of 1.41252 X 10+18 Atoms of silver. For those of you who like to put names on numbers 10+18 is called quintillion or 1000 quadrillion! Just thought I`d stick that in.

Bless all of you, keep up the good CS making and be well.

Bless you Bob Lee

[ We have added an Excel Spreadsheet that automates the calculations involved in Faraday's Law - See the document entitled "Herx's" Faraday's Law Calculator ]


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