Doing the Math

Simple Math and Lots of It !

 There are about, 602,000,000,000,000,000,000,000 Atoms in one Gram Atomic Weight of a substance. (The atomic weight measured in grams.)

(Pennies made before 1982 were mostly copper, and weighed about 3.1 grams. Today's penny weighs 2.5 grams and is composed mostly of zinc. —Joe Riel—)

Find a penny made after 1982. It weights 2.5 grams. Now pretend that the penny is 100% pure copper.

Copper has an atomic weight of 63.54.
So, that means that a copper penny would contain about 23,685,867,170,290,000,000,000 atoms.

  • 63.54 grams of copper equals 1 gram atomic weight.
  • 2.5 grams is the weight of a penny.
  • 3.9345% of a gram atomic weight our penny is.
  • 6.02 X 1023 is the number of atoms in an gram atomic weight.
  • 23,685,867,170,290,000,000,000 atoms are present in the penny.

After that example, you should be happy to know that you won't have to do this type of calculation very often, when working with Hydroculture, except for fun.

The craft of mixing hydroponic salts, works very well just using the gram atomic and/or gram molecular weight of our samples.

Water soluble salts (Mineral Salts) contain more than one type of atom and often times, have a number of water molecules involved also.

So, we need to know the atomic makeup of our salt and its molecular weight.

Then, we divide the atomic weight of each type of atom present, by the molecular weight of the salt, move the decimal point. This gives you the percentage of each atom present. Often times, the presence and amount of an atom in a salt, is expressed as a percentage on the package.

A little addition gives you the parts per million (ppm) and you subtract to determine the actual amount of distilled water you'll need.

At this point, you shouldn't be suprised to learn that 100 grams of Magnesium Sulphate contains only 9.87 grams of Magnesium.

So, if you need, 10 ppm of Magnesium in your 1000 liter tank of solution, you would need to weight out 101.3 grams of Magnesium Sulphate.

That was pritty straight forward, wasn't it? But, what if you don't want to mix 264 gallions all at once, what if you need to use well or city water, and how are you going to measure the salts that only need to be present in the 0.010 ppm range?

Math, sweet math.   This is why Mother Nature invented spread sheets.

And, this is where we employ a few little "Tricks of the Trade" !

Dilution

Increasing the accuracy of your measurments is important. Your standard 2610 gram, Triple Beam Balance, chemical scale, has an accuracy of ±0.1 gram. That doesn't mean much if you are weighing 1000 grams of a chemical. However, if you need to measure 0.2 grams of something, using a scale with a ±0.1 gram error factor, your sample could have an actual weight somewhere between 0.1 to 0.3 grams. Since twice optimum is toxic, this will not be acceptable. 1000 ±0.1 g. results in a possible error of ±0.01%, while 0.2 ±0.1 g. has a possible error of ±50.0%

Happilly, it is not necessary to buy a more expensive scale, and then try to weigh samples virtualy too small to be seen. Instead, we can create a system of "stock solutions" and "dilutions".

Stock solutions are a convienent way to dispense and store the chemicals for making your hydroculture solution. Stock solutions can also increase the accuracy of your measurements by a considerable amount.

Lets look at our 0.2 g. sample with the ±50% error. What if, we weigh enough salt for 10 feedings instead of one. Our error factor would now be 2.0 ±0.1 g. or ±5%. Continuing, weighing 200 grams would yield an error of only ±0.5%. So, the accuracy of the scale measurement can be increased, up to a point, by weighing out larger quantities.

Now comes the solution, and again how accurately you can make your measurements. The list of items for measuring liquids is quite long. A liquid possess the properties of surface tension and capillary action. Surface tension will cause the liquid to "dome" above the top of a container and capillary action will cause the liquid to "climb" the walls of the container above the center of the liquid level.

It is quite important for you to determine how the calibration lines are referenced on your measuring device. Read the instructions that came with your device or play with it until you can accurately measure out a series of equal amounts from a unit quanity.

We now face the issue of Solubility. Each mineral salt has a maximum amount that can be disolved in a unit quanity of a liquid. When this point has been reached the solution is said to be saturated. If your stock solution system is to be uniform and consistant, the volume of water used must be greater than the amount needed, to disolve the least soluble of your trace element salts.

If you love math you can generate a set of equations to explore the various possibilities, if computers are your thing, a nice spread sheet will work or if you are like me, just look at the numbers, take a few notes, and do it off the top of your head. At this point I would like to thank the teachers who insisted I learn the following table.

Multiplication Table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128
9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176
12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192
13 26 39 52 65 78 91 104 127 140 153 166 179 192 205 218
14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224
15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240
16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256
There is a certain beauty in a table of numbers. The rhythms of the relationships, have a special charm all their own.

Memorizing this table will save you thousands of hours of math work!

It also, will allow you to quickly estimate the outcome of many events.

Having a natural feeling of knowing, "The Ball Park of Numbers", will help you know when it is worth getting out the calculator.

A System of Concentrates

Mole. — Mass numerically equal to the molecular weight. It is most frequrntly expressed as the gram molecular weight, i.e. as the weight of one mole expressed in grams.

Molal solution. — contains one mole per 1000 grams of solvent.

Molar solution. — contains one mole or gram molecular weight of the solute in one liter of solution.

Normal solution. — contains one gram molecular weight of the dissolved substance divided by the hydrogen equivalent of the substance ( that is, one gram equivalent ) per liter of solution.

30 milliliters is a convient quanity to use for dispensing stock solutions. 30 ml. is about an once, which is also a nice unit, if you care to use the English System of Numbers.

Getting back to our 0.2 g. sample. We chose to weigh enough salt for ten feedings at once, so, if our plan is to dispence 30 ml. of liquid for each feeding, we will need to add water to our salt sample to make 300 ml. of concentrate.

A quart is about 0.946325 liters, so a bottle of either unit will be large enough for our purposes.

" Note: – Add Water To Make ... "

One (1) in twenty (20), is Not the Same as one (1) to twenty (20) !

  • 1 in 20 = 5%   or   50,000.0 ppm
  • 1 of 20 = 5%   or   50,000.0 ppm

  • 1 to 20 = 4.7619047%   or   47,619.047 ppm
  • 1 + 20 = 4.7619047%   or   47,619.047 ppm

    This is a difference of 2,380.952 ppm !
    ( Some of our plant food elements, need to be present in our Water of Life, in the range of 0.010 ppm. )

In the first example there are twenty (20) total units of solution, whereas in the second example, there are twenty one (21) total units of solution. Always think through the wording that is used to define a solution.

With the Metric System and water, we can easily move our decimal point around to, rather accurately, measure any quanity of mineral salt, we need for our plant food.

(This is a work in progress)

Click Here to Continue Tour. Hydroponic Reference Center — Mixing the Solution

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