CS Calculations, Dan Nave.doc
When I started looking into how to make CS one of the main problems I encountered was how to
customize my setup for the materials I might have access to, how to tell when the CS was done, and
what concentration it was.
As a starting point Bob Lee, in his post of 4-11-98, gives a very valuable discussion of Faraday’s
equation for electrolysis which indicates how much silver is freed from the electrode during
electrolysis. Add to this Mike Monett’s experiments indicating that low voltage-very low current
setups allow one to make CS with a single 9v battery and a series resistor, providing for nearly
linear operation of the cell, and dispensing with the need for stirring. (Thanks Bob and Mike.)
Also, perhaps it is more correct to call this EIS (electrically isolated silver) rather than CS
(colloidal silver) since it is apparently much more ionic than colloidal.
This post is not essentially different from one of Mike’s but is put in a form where I can more
intuitively understand what is involved in the calculations.
For our purposes, there are three formulas that apply to the calculation of
this process.
The other equations are merely conversion factors which convert from ounces to grams to mg to
liters, etc.
*HOW MUCH SILVER IS LIBERATED DURING THE REACTION?
1. Faraday’s equation for electrolysis
m = k*I*t
where:
m = mass in grams
k = electrochemical equivalent = 0.001118
I = current in amps
t = time in seconds
This formula tells us exactly how much silver was liberated from the electrode (anode) and is
determined by k = a constant, I = current, and t = time.
[You can ignore this – just use the constant.
“k”, the electrochemical equivalent, is derived from the chemical equivalent for silver which is the
atomic weight in grams of silver divided by the valence number times the number of coulombs
(ampseconds) required to liberate this amount of silver:
k = atomic weight of silver/valence # *coulombs to liberate
= 107.88/1*96500
= 107.88/96500
= 0.001118
This is from Bob Lee’s post of 4-11-98]
Conversion factors:
Sec = hrs*3600 ;convert hours to seconds
I = ma/1000 ;convert milliamps to amps
So, the variables for this equation are the amount of current and the time of
the reaction.
*WHAT IS THE CONCENTRATION OF THE LIBERATED SILVER IN THE VOLUME OF DISTILLED
WATER?
2. ppm = mg/lt
where:
ppm = concentration of silver in parts per million
mg = milligrams of liberated silver
lt = liter of distilled water
The concentration is determined by the amount of liberated silver (from equation #1) per volume of
distilled water used.
Conversion factors:
mg = gm*1000 ;convert grams to milligrams
ml = 29.57*oz ;convert ounces to milliliters
lt = ml/1000 ;convert milliliters to liters
The variables for this equation are the amount of liberated silver and the volume of distilled water
used.
*THE CURRENT DENSITY AT THE ELECTRODES (ANODE).
3. den = I/sqin
where:
den = current density in Amps per square inch of anode surface area
I = current in Amps
sqin = surface area of electrode (anode) in square inches
Conversion factors:
[for wire electrode]
Sqin = pi*d*l ;surface area = pi*diameter of anode*length of anode
d = .08081 in ;for 12 gage wire
d = .06408 in ;for 14 gage wire
[For 12 gage wire, 1 square inch = approximately 4 linear inches.]
[For 14 gage wire, 1 square inch = approximately 5 linear inches.]
The variables for current density are the surface area of the electrode (anode)
and the current in Amps.
You can have any length of electrode you want. For equation 1 and 2 it doesn’t matter. What does
matter about the current density, as was shown by Mike Monett, is when the current density is very
low, about .080ma/sqin then the process can be made nearly linear and there are apparently few
losses of the liberated silver due to agglomeration or plating at the cathode. An additional
benefit is that stirring is apparently not required. Also, current limiting can be accomplished by
a simple series resistor of the correct value.
*TO CALCULATE THE CORRECT RESISTOR, OHMS LAW:
[OK, here’s a fourth equation to calculate the needed series resistor ;-]
4. R = E/I ;Resistance in ohms = Voltage / Current
Verify the current in circuit with a milliammeter or measure voltage across the
resistor and calculate:
I = E/R ;Current in Amps = Voltage / Resistance in ohms
I would recommend that one calculate the maximum amount of current allowable for their electrodes
for very low current CS where den = less than .08ma/sqin for example. Just don’t exceed that
current for your setup.
Special thanks to Bob Lee and Mike Monett.
Dan
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