Metrics of nutrients - Borgmann Aquaponik & Hydroponik

This concise overview serves as a guide to estimate the order of magnitude required for analytical techniques when analyzing and controlling the nutrients used for plant fertilization.

The analytical quality in chemistry has already reached a precision that is unnecessary for our purposes of controlled fertilization. To avoid using a sledgehammer to crack a nut when selecting different analysis methods and equipment, we have compiled a highly condensed overview of the necessary accuracies sufficient for monitoring individual additives. The chosen analytical technology has a significant impact on overall operating costs.

In addition to monitoring essential nutrients, control measures are also necessary to prevent over-fertilization. Nutrients from fish farming must not exceed certain concentrations, as this would otherwise impair optimal plant growth.

There is now a very large number of analytical methods on the market, which differ greatly both in the technology used and in on-site application. This overview helps you, even without our consulting services, to obtain quotes from various manufacturers that precisely meet your needs. Here is a random selection of manufacturers.

Here you will find the essential compounds required for plant growth. Depending on the plant and/or growth stage, the form of application, the chemical compound in which the desired "substance" is bound, may vary. In traditional cultivation (in soil), microorganisms and fungi facilitated the breakdown of necessary compounds. Since hydroponics lacks microorganisms to perform this task, this remains an ongoing area of fundamental research.

Compounds and Trace Elements / Orders of Magnitude in Nutrient Solutions

Conversion: mmol/L | mg/L | ppm

Element / Compound	Name	mmol/L	mg/L	ppm
Macronutrients
K	Potassium	3 – 8	117 – 313	117 – 313
Ca	Calcium	1 – 4	40 – 160	40 – 160
Mg	Magnesium	0.5 – 1.5	12 – 36	12 – 36
P	Phosphorus	0.3 – 1.5	9.3 – 46.5	9.3 – 46.5
S	Sulfur	0.5 – 2	16 – 64	16 – 64
Trace Elements
Fe	Iron	0.010 – 0.040	0.56 – 2.24	0.56 – 2.24
Cu	Copper	0.0005 – 0.002	0.03 – 0.13	0.03 – 0.13
Zn	Zinc	0.001 – 0.008	0.07 – 0.52	0.07 – 0.52
Mn	Manganese	0.001 – 0.008	0.06 – 0.44	0.06 – 0.44
B	Boron	0.010 – 0.045	0.11 – 0.49	0.11 – 0.49
Mo	Molybdenum	0.0001 – 0.001	0.01 – 0.10	0.01 – 0.10
Nitrogen Compounds
NO₃	Nitrate	0.8 – 3.2	50 – 200	50 – 200
NO₂	Nitrite	0 – 0.22	0 – 10	0 – 10
NH₄	Ammonium	0.06 – 1.11	1 – 20	1 – 20
Fertilizer Salts and Chelates
KNO₃	Potassium Nitrate	0 – 8	0 – 809	0 – 809
Ca(NO₃)₂	Calcium Nitrate	0 – 8	0 – 1312	0 – 1312
MgSO₄	Magnesium Sulfate	0.5 – 2	60 – 241	60 – 241
Fe-EDTA	Iron Chelate	0.010 – 0.040	3.5 – 14	3.5 – 14
H₃BO₃	Boric Acid	0.010 – 0.045	0.62 – 2.78	0.62 – 2.78
MnSO₄	Manganese(II) Sulfate	0.001 – 0.008	0.17 – 1.35	0.17 – 1.35
ZnSO₄	Zinc Sulfate	0.001 – 0.008	0.16 – 1.29	0.16 – 1.29
CuSO₄	Copper Sulfate	0.0005 – 0.002	0.08 – 0.32	0.08 – 0.32
KCl	Potassium Chloride	not common in nutrient solutions (chloride limited)
FeSO₄	Iron(II) Sulfate	chelated form (Fe-EDTA/Fe-DTPA) preferred
NH₄H₂PO₄	Ammonium Dihydrogen Phosphate	0 – 2	0 – 230	0 – 230
(NH₄)₂HPO₄	Diammonium Hydrogen Phosphate	0 – 2	0 – 264	0 – 264
MoO₃	Molybdenum Oxide	0.0001 – 0.001	0.014 – 0.144	0.014 – 0.144

Conversion Note: mg/L = mmol/L × molar mass (g/mol). For aqueous solutions, ppm equals mg/L. Values are based on current hydroponic standards (Hoagland, Sonneveld, Steiner).

Conversion: Moles, mg/L, and ppm

When dealing with nutrient solutions, you will frequently encounter concentration values given in mg/L, ppm, or moles. Here is a brief guide on how to convert between these units. You will often find measurement ranges provided in a secondary citation format, e.g., nitrate as nitrate (NO₃) and as nitrate-nitrogen (NO₃-N).

Conversion: Moles and PPM

A Technical Definition of ppm

What is ppm? And how can something called "parts per million" be represented by mg/L? Parts per million indicates the number of "parts" of one substance in one million "parts" of another. The "part" can be any unit, but when mixing solutions, ppm typically represents units of weight. In this context, ppm indicates how many grams of a solute are present in one million grams of solvent (e.g., water).

1 g solute / 1,000,000 g solvent

When dealing with water at room temperature, it is common to assume that the density of water is 1 g/mL. Therefore, we can rewrite the relationship as follows:

1 g solute in 1,000,000 mL water

Then divide mL by 1000 mL:

1 g solute in 1,000 L water

Dividing both units by 1000 gives:

1 mg solute in 1 L water

Therefore, 1 mg in 1 L water is equivalent to 1 mg in 1,000,000 mg water, or 1 part per million (assuming room temperature and atmospheric pressure of 1 atmosphere).

How to Convert ppm to Moles

To convert ppm to molarity or vice versa, you only need the molar mass of the element or molecule in question. Here is a periodic table for molar masses (top left: atomic weight).

Take the molarity in mol/L and multiply by the molar mass in g/mol to obtain g/L. Then multiply by 1000 to convert grams to milligrams, and you have mg/L for aqueous solutions.

Example: Preparing a NaOH Solution

You have a stock solution of 1 molar NaOH. How do you prepare 1 L of a 200 ppm NaOH solution? NaOH has a molar mass of 39.997 g/mol.

1. Convert 200 ppm to molarity.

First, assume 200 ppm = 200 mg/L. Divide the result by 1000 to get g/L: 200 mg/L ÷ 1000 mg/g = 0.2 g/L.

Next, divide 0.2 g/L by the molar mass of NaOH (Na = 22.99, O = 16, H = 1) to obtain molarity: 0.2 g/L ÷ 39.997 g/mol = 0.005 mol/L.

2. Calculate the dilution recipe.

From step 1, we know the target molarity is 0.005 mol/L. To calculate the dilution, we use the dilution equation: m₁⋅v₁ = m₂⋅v₂

where:
• m₁ — concentration of the stock solution;
• m₂ — concentration of the diluted solution;
• v₁ — volume of the stock solution;
• v₂ — volume of the diluted solution.

We can input the numbers for all variables except the stock solution volume:

1 M ⋅ v₁ = 0.005 M ⋅ 1 L

Rearranging the equation gives the required stock solution volume:
v₁ = 0.005 M / 1 M ⋅ 1 L = 0.005 L

Therefore, we need to dilute 0.005 L (or 5 mL) of stock solution to a final volume of 1 L to obtain a 200 ppm NaOH solution.

How to Calculate ppm from Volume Concentration

To obtain volume-ppm:

Take the molar concentration of the solution in mol/L.
Multiply it by the molar mass in g/mol.
Divide it by the density of the solute in g/cm³.
Multiply everything by 1000 mg/g.
The resulting ppm volume unit is typically μL/L.

Here are more detailed examples for both conversion directions:

Conversion: Moles to Grams

Conversion: Grams to Moles

How-Tos and Measuring Instruments

Further Information:

https://en.wikipedia.org/wiki/Water_analysis (Local Copy)

SI Prefixes

Name	Yotta	Zetta	Exa	Peta	Tera	Giga	Mega	Kilo	Hecto	Deca
Symbol	Y	Z	E	P	T	G	M	k	h	da
Factor	10²⁴	10²¹	10¹⁸	10¹⁵	10¹²	10⁹	10⁶	10³	10²	10¹
Name	Yocto	Zepto	Atto	Femto	Pico	Nano	Micro	Milli	Centi	Deci
Symbol	y	z	a	f	p	n	µ	m	c	d
Factor	10⁻²⁴	10⁻²¹	10⁻¹⁸	10⁻¹⁵	10⁻¹²	10⁻⁹	10⁻⁶	10⁻³	10⁻²	10⁻¹

Context:

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