# Chemistry 101 - The Math Behind the Fertilator



## BryceM (Nov 6, 2005)

For good or ill, fertilizing involves a lot of math. That's a pretty foreign concept to some people - just like much of the artistic side of the hobby is a pretty foreign concept to me, and a few others from a science background. I'll try to throw out enough here so that anyone can be dangerous with a calculator.

*What is a ppm? What does it mean?*

PPM is shorthand for parts-per-million. The usual unit of aquarium water for calculations is a liter, since math is easier in the metric system. One liter of water weighs 1,000 grams. 1/1000 of a gram is one-millionth (1/1,000,000) of a liter. 1/1000 of a gram is also known as a milligram. One milligram of potassium, or phosphate, CO2, or anything else, dissolved in a liter of water is said to be 1 ppm.

*How much KNO3 do I need to add to 1 liter of water to get X ppm of nitrate?*

Sounds like an easy question doesn't it? To answer it, you need to know that KNO3 is made up of two parts, which separate when dissolved in water. Potassium (K+) has a positive charge and is known as a cation. Nitrate (NO3-) carries a negative charge is known as an anion.

Next, you need to know that not all atoms are created equal. Each has a specific atomic weight. From the periodic table you can see that K has an atomic weight of 39.10, N (nitrogen) is 14.01, and O (oxygen) is 16.00.

The total for the whole molecule is 39.10 + 14.01 + 16.00 * 3 = 101.1
The proportion of potassium is 39.1/101.1 = 0.387 or 38.7%
The proportion of nitrate is 62.0/101.1 = 0.613 or 61.3%

That means if you have 100 grams of KNO3, you really have 38.7 grams of potassium and 61.3 grams of nitrate.

If you have a bag full of KNO3, and you know that you'd like to add 10 ppm of NO3 to 100 liters of water you'd figure it out like this:

You want 10 ppm which means you need 10mg of NO3 per liter. But you don't have a bag of NO3, you have a bag of KNO3. Since only 61.3% of what you're adding is actually NO3, you'll need to add more than 10mg of dry KNO3 per liter. In equation form:

mass(NO3) = mass(KNO3) * 0.613
rearanging:
mass(KNO3) = mass(NO3) / 0.613
fill in the variables:
mass(KNO3) = 10 mg / 0.613
which equals 16.3 mg KNO3 per liter

Since you want enough for 100 liters, multiply by 100 for 1,630mg or 1.63 grams.

If you have an electronic scale, it's easy. If not, you'll need to convert to some other unit like teaspoons. People have determined that a teaspoon of KNO3 weighs about 5.2 grams. We need 1.63/5.2 = 0.31 or a little more than 1/4 of a teaspoon. Since KNO3 comes in different forms (powder, granules, pellets) with varying densities, the conversion of grams to teaspoons can introduce some pretty big errors.

BTW, you can also figure out how much potassium comes along for the ride. You added 1.63 grams of KNO3. 38.7% of this is potassium. 1.63 x 0.387 = 0.63 grams. Divided into 100 liters = 6.3 milligrams / liter = 6.3 PPM potassium.

One thing to be aware of: Some dry chemicals attract water. MgSO4 (epsom salt) only readily exists in a hydrated state. On a molecular level this means that 7 molecules of water are 'attached' to each molecule of MgSO4.

If you have 1 gram of epsom salts you actually have:
24.31 (Mg) + 32.06 (S) + 16.00*4 (O) + 1.00*7*2 (H) + 16.00*7 (O) = 246.37

24.31/246.37 = only 9.87% Mg. Of the original gram, there is only 0.0987 grams of magnesium which will give 99 ppm Mg if dissolved in 1 liter of water or roughly 1 ppm if dissolved in 100 liters of water.

*Seachem's Flourish lists 0.32% soluble iron, Seachem's Flourish Iron lists 1% soluble iron. What does this mean in PPM?*

Let's assume you dose Flourish per their recommendations (5 ml per 250 liters per week).

5 x 0.0032 / 250 = 0.000064 grams/liter or 0.064 mg/liter or 0.064 ppm Fe per week.

Let's assume you dose Flourish Iron per their recommendations (5 ml per 200 liters):

5 x 0.01 / 200 = 0.00025 grams/liter or 0.25 mg/liter = 0.25 ppm per dose, about 3 times as much.

Incidentally, these calc's don't agree with what Seachem posted a while ago:
http://www.aquaticplantcentral.com/forumapc/seachem/14410-seachem-flourish.html?highlight=iron

I can only assume they made a math error in their calcs or that their labels aren't accurate. You can use this to figure out ppm's of other ingredients listed as a percentage of dry or liquid ferts.

Two free pieces of advice:

1) Please double check your calc's. Missing a decimal and overdosing nitrate by a factor of 100 will cause problems .
2) Remember, chemicals come in different forms. Incorrect assumptions about what is in that little brown bottle can lead to big problems.

The fertilator is a wonderful resource for most of the necessary calcs that we do. It has a few bugs in it though and is incomplete in other areas. Once we find a person with the programming skills needed to update it, the needed changes will be made. Any volunteers?


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## RoseHawke (Jan 4, 2005)

Thank you *guaiac_boy*, but it's still a foreign concept  . . .

I'm sure it'll help somebody though. . .


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## dennis (Mar 1, 2004)

You made that sound so simple, well done!


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## acbaldwin (Nov 3, 2005)

All I can say is that this is definitely sticky material.
...ummm... Wait I don't mean it like that!


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## Mnemia (Nov 23, 2004)

One question:
Is it actually true that mg/L == ppm? That definition seems problematic to me, since you are comparing two things that don't actually measure the same thing (mass and volume). If you assume that the definition of "part" is actually "weight" then it seems like you can't compare ppm measures of different substances, since they weigh different amounts per mole. So under this definition, a "phosphate ppm" is different from a "nitrate ppm". Now that's fine for most of our purposes since we only compare concentrations of each of these to concentrations of the same but it seems misleading to me to have a unit that means different things in different contexts.

A measure of concentration like molarity (mol/L), molality, or normality would allow us to actually use the same units for everything. I know that when I took chemistry some years back that it was a lot easier to deal mol/L in complicated formulas and stoichiometry. So under this definition ppm would actually mean something like the ratio of the number of ions of solute to number of water molecules in the tank * 1,000,000.

Advantages/disadvantages to each method?


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## BryceM (Nov 6, 2005)

Mnemia said:


> One question:
> Is it actually true that mg/L == ppm? That definition seems problematic to me, since you are comparing two things that don't actually measure the same thing (mass and volume). If you assume that the definition of "part" is actually "weight" then it seems like you can't compare ppm measures of different substances, since they weigh different amounts per mole. So under this definition, a "phosphate ppm" is different from a "nitrate ppm". Now that's fine for most of our purposes since we only compare concentrations of each of these to concentrations of the same but it seems misleading to me to have a unit that means different things in different contexts.
> 
> A measure like molarity (mol/L) would allow us to actually use the same units for everything. I know that when I took chemistry some years back that it was a lot easier to deal mol/L in complicated formulas and stoichiometry. So under this definition ppm would actually mean something like the ratio of the number of ions of solute to number of water molecules in the tank * 1,000,000.
> ...


I agree that molarity is a much better unit of measurement for all things chemical. The problem is that all of our test kits measure ppm. We'll probably never get away from that.

Regarding ppm...... As I understand it, the definition is based on mg solute per kg H2O, so it's a measurement of mass/mass. You are correct in the statement that it isn't a very good unit, since it certainly doesn't work to compare # of molecules of small ion vs # of molecules of a larger ion. The fact that K and NO3 from KNO3 exist in a 1:1 ratio, yet have different ppm concentrations is just one example of this. Oh well.


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## Mnemia (Nov 23, 2004)

Well, it's just a (different) constant conversion factor for each type of ion between the "ppm" unit and the molarity units. Obviously this is what you are in essence doing in the math above. They are just both units of measure, after all. I personally think that there is something to be gained by using the more "scientific" measures, since it gives me more of a "feel" for the relative amount of phosphate vs. nitrate that my plants are actually using.

You're right though, asking people (and test kit makers) to convert is probably an analogous situation to asking most Americans to use the metric system. It makes a lot of sense, but people are set in their ways and resistant. I imagine some of the reason for the ppm unit is to eliminate the need to understand scientific notation, as well.


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## MatPat (Mar 22, 2004)

acbaldwin said:


> All I can say is that this is definitely sticky material.
> ...ummm... Wait I don't mean it like that!


Definately worthy of being a sticky but I think turning it into an article would be even better


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## averater (Dec 14, 2004)

very nice explination, but there are a few this that i think needs to be cleared further.

first there is a miscalculation in the proportion of kno3 that is no3, 62/101.1=0.613, not 0.683. if you add the proportion k with the proportion no3, it must be 1 (or 100%).

and i dont know how, but since you (guaiac_boy) explained everything else so nice, maybe you can clear out the folowing paragraph that i belive still is too complicated for a lot of people.



guaiac_boy said:


> 10 ppm = 10mg NO3/liter. But you don't have a bag of NO3, you have a bag of KNO3. To get 10 mg of NO3, you'd need to add 101.1/62.0 x 10 = 16.3 mg of KNO3. Since you need enough for 100 liters, multiply the answer by 100 = 1,630 milligrams or 1.63 grams.


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## BryceM (Nov 6, 2005)

averater said:


> very nice explination, but there are a few this that i think needs to be cleared further.
> 
> first there is a miscalculation in the proportion of kno3 that is no3, 62/101.1=0.613, not 0.683. if you add the proportion k with the proportion no3, it must be 1 (or 100%).


Thanks for catching the typo, you are absolutely correct. I've edited the initial post above to reflect the change.

I'll also try to clarify the paragraph that seems confusing.

- GB


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## Salt (Apr 5, 2005)

The way I do it...


```
[b]Potassium Nitrate - KNO3[/b]

Potassium = 39.0983 grams per mole
Nitrate (NO3) = 62.00494 grams per mole
  Nitrogen = 14.00674 grams per mole
  Oxygen = 15.9994 grams per mole
Potassium Nitrate (KNO3) = 101.10324

Potassium:
1 / (39.0983 / 101.10324) = [b][color=red]2.5858730431 mg[/color] to raise potassium 1 ppm in 1 liter[/b]

Nitrate:
1 / (62.00494 / 101.10324) = [b][color=red]1.6305674999 mg[/color] to raise nitrate 1 ppm in 1 liter[/b]
```
A very important point to remember... these calculations assume *100 percent pure chemicals* and *100 percent pure water*. Even Reagent ACS grade chemicals are not 100% pure, and most people use agricultural grade. In addition to that, there are many other factors that can affect the actual levels after you dose your tank. So while the formulas look very precise, you need to TEST using *QUALITY TEST KITS* to actually know what your levels are. From there, you can adjust your dosage using simple percent calculations.

For example, I use 5-stage filtered RO/DI water. Using the calculations from the periodic table (as above), I determine that if I change 15 gallons of water and I want a GH of 6 dGH with a 4:1 ca:mg ratio, I should dose 4.86 grams of CaCO3 and 1.02 grams of MgCO3. But with testing with LaMotte test kits, I find that it's more like 3.09 grams CaCO3 and .23 grams MgCO3.

Just to nitpick (sorry ),


> MgSO4 (epsom salt) only readily exists in a hydrated state.


Not true, MgSO4 is most _readily available_ as epsom salt in the hydrated form, but it is also available without the water molecules (which create the crystalline structure) as an anhydrous powder.


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## BryceM (Nov 6, 2005)

I should have said MgSO4-7H2O is the readily available form of Mag sulfate 

I will take issue with you about stating that test kits are more accurate than adding a known quantity to water. Sure, chemicals come in varying grades. Even so, even the poorest quality KNO3 out there is likely >95% pure. If that is the case, assuming you are using an accurate method of measurement (an electronic scale, not a bent, rusty teaspoon), the error between what you calculate and what is actually added to the water should only be 5% or so.

You are stating that your Lamotte kits are showing that you need to add 36% less CaCO3 than your calculations show. I'd assume that either your calculations are wrong, your reagents are old, the your Lamotte kit isn't all that accurate, you don't actually have pure water, or that your chemicals aren't really what you think they are.

People should not get the idea that they should use test kits to zero in on the math & chemistry behind it. Of the two methods, using a test kit is much less acurate than preparing a known solution. If you add 1 gram of KNO3 to 100 liters of water, you will have increased the concentration of nitrate by 6.13 ppm, every single time, regardless of what your test kits show.

Lots of newbies with horrible test kits use their tanks as little laboratories. They keep dumping the stuff in, waiting for the magic color change on the indicator. Before they figure it out they've got dead fish everywhere and nitrates up over 500 ppm.


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## Steveb (Oct 20, 2005)

I guess one other error we make is also assuming the size of our tank. We say it is a 20 gal tank, but does it really hold 20gal of water when we have the substrate, rocks, plants, heater, pumps etc in there?
I have a Hagen 20gal tank, but it only holds about 17.75 gals of water before I add anything (substrate etc) in there.

SteveB


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## Salt (Apr 5, 2005)

And I take issue right back at you.

What you say makes sense if you are talking about 100% pure chemicals and 100% pure water, with _absolutely nothing else happening_.

This is hardly the case with an aquarium. It's a dynamic environment. Lots of biological processes happening, with fish, plants, and bacteria, lots of other variables and unknowns, such as ions and other substances coming in to the tank through the substrate, fish food, and other factors such as other products with which the hobbyist might dose the tank.

My calculations are not wrong, the kits are brand new and I tested them and found them to be within 5 ppm accurate (very impressive IMHO), and the RO/DI water is pure (it's measured with a TDS meter which can detect less than 1 ppm of any conductive ion).

In my case, I add Seachem Flourish, Flourish Trace, and Fresh Trace throughout the week, as well as fish food and some other products. Then there's uptake by flora and fawna. This is likely where the difference is in test results versus amounts added.

There is absolutely nothing wrong with verifying what your levels are using test kits. There are plants which don't like high carbonates. There are plants which don't like magnesium levels higher than 10 ppm (41 ppm as CaCO3). Knowledge is power. Test kits give you the power to know what is going on in your tank and control it.

I think it's absolutely ridiculous in saying using a test kit is inaccurate. If you prepare a known solution, then verify it with a test kit, you will then have the power to know and better understand the dynamics of your tank, and every tank is unique.


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## averater (Dec 14, 2004)

most people that use test dont do standard solutions or standard added solutions (not sure bout the terms only know them in swedish).

i'd be very impressed if anyone can use one of these drop-tests and get a more accurate reading than 20%.

but of course, it is possible to get better values of whats in youre tank with tests performed by experienced laboratory personel, but those who does such testings probably dont use any olnline fertilizer calculator.


Salt: do you know how youre tests work? what are they actually measuring? i find it hard to belive youre big difference compared with the calculator. maybe is it problems with different forms of hydrations? if the calculator assumes some kind of hydrated form?


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## Salt (Apr 5, 2005)

LaMotte's kits are more expensive but they are more precise. GH is a standard EDTA chelation test which tests for calcium and magnesium cations using EDTA, magnesium chloride, sodium sulfide, sodium hydroxide, sodium borate, ethanol, methanol, and calmagite. Their calcium test is similar but includes an inhibitor which prevents magnesium from showing up on the test. The tests all read in a CaCO3 equivalent. GH reading - calcium reading = magnesium reading.

Laboratory personel? The tests are very simple and anyone can do them.

http://www.lamotte.com/pages/common/pdf/instruct/4482drli.pdf
http://www.lamotte.com/pages/common/pdf/instruct/3609.pdf
http://www.lamotte.com/pages/common/pdf/instruct/4491-dr.pdf

I don't use the calculator, I do my own calculations and am 100% certain they are correct.


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## Laith (Sep 4, 2004)

I think both views are correct and there isn't a fundamental difference.

*If* you are willing to test/calibrate your test kits, they will give pretty accurate indications of what's in your tank water. But testing the test kits needs to be done with each new kit and if you don't use it that often, also during the life of the kit to check that the reagents have not gone bad. And of course different test kits give best results at certain concentrations of what you are testing for and useless for other ranges (eg good at between 0-10mg/l but useless results at anything above that). So *ideally* when testing/calibrating you should test against several known concentrations and not just one.

The vast majority of people do not bother (and do not want) to test the kits. And as mentioned, many people use their tank to test their test kit ("wow, my plants are consuming 15mg/l of NO3 a day!"). And not many hobbyists will spend the money for high end, more reliable test kits.

Even LaMotte kits need testing. Though they are probably the best kits I've used, I have in the past seen LaMotte kits be completely off. Seachem kits are original in that they include a reference solution so that you can test the kit without mixing up your own calibration solution.

So for the vast majority of hobbyists a decent gram scale, along with keeping an eye on their plants will suffice. We're not dealing with rocket science here.

But I also like to know what is in my tank water so I do test from time to time. But through lessons learned the hard way, I test the test kits first.


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## BryceM (Nov 6, 2005)

I don't mean to be confrontational Salt. I just think we're talking about 2 different things. If you goal is to keep and maintain a certain level of a given nutrient in the tank, then that's different, and is the subject of hundreds of threads on this forum. I agree that aquariums are very dynamic and there are many more variables than we can account for. In practial application you can supply the nutrients in excess (EI method), test frequently to keep things where you want them (PPS method), or just keep an eye on the plants once you know what to look for.

If, on the other hand, you're trying to calculate how many grams of X is needed to increase the concentration by X ppm, then test kits aren't needed and, in fact, are less acurate than just doing the math. SteveB's input that we rarely know the volume of the tank is valid, but you can can make a pretty good guess. Laith is right - this isn't rocket science and we aren't trying to put a man on Mars here. Ballpark values are almost always close enough.

I just wanted to get the math 'out there' for people who lack the math/science background to do put it together on their own. What's the value in this? Well, the fertilator has a few errors in it, for one. One should have some background knowledge to understand when something doesn't seem right. Finally, for me, it's kind of fun to use my brain from time to time when playing around in the hobby.


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## Edward (May 25, 2004)

guaiac_boy said:


> In practial application you can supply the nutrients in excess (EI method), test frequently to keep things where you want them (PPS method), or just keep an eye on the plants once you know what to look for.


Most testing is done by people using EI. There are hundreds of posts to prove it.

Thank you
Edward


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## BryceM (Nov 6, 2005)

Yeah, most testing probably is done by people using some variation of EI methods. If they are testing, I assume it's becasue either they enjoy it, they don't understand the math behind the method, they have uncertainty about the exact quantities they're adding, or they simply aren't seeing the results they expected in their plants.

If you are a purist, you really shouldn't need to do tests if you use EI. As a realist, I look at my tank and realize that my tap water contains some nutrients. Other people's water is different. My fish load is different than other people's. How much I feed, and how much waste (read nitrate & phosphate) is produced by the fish is different. I test to keep an eye on my empirical dosing. I make changes to how much I dose only when things really get out of whack, since doing occasoinal large water changes tends to cancel out any errors that I make.

I simply thought that if people had access to an example of how to work out concentrations from quantities that it woulid improve their ability to predict how much they're actually putting in.

No offense, but I find PPS to be confusing, and I've never tried it. My understanding is that you make the assumption that once you get the needs of the tank figured out, then you can tailor a dosing program to keep things pretty close. I've always looked at my tank as more dynamic than this. My tap water changes with the seasons. My plant mass is consistently different, depending on how much I've trimmed. I'm continuously messing with different plant species and fish load. This seems to indroduce such a large variation in plant uptake needs that dosing slightly in excess of plant needs, and evening it out with big WC's makes more sense for my application.

If I've completely misunderstood the basic concepts of PPS then it's almost certainly due to my lack of reading about it and lack of experience with it.


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## Edward (May 25, 2004)

Basically what you are describing is a search for the right fertilizer. A fertilizer that is easy to use and flexible enough to fit any aquarium needs. It has already been done.

Look how simple it is, everybody can use it, PPS.Dosing.With.Water.Changes.pdf

*Solutions content, 4 bottles*
SS - 16 gram K2SO4, 20 gram KNO3, 6 gram KH2PO4
PF - 20 gram K2SO4, 20 gram KNO3
Mg - 169 gram MgSO4
TE - 24 gram TE or trace element equivalent

*Example for 50 gallon tank,*
Dose daily 10 ml SS, 22 ml PF, 3 ml Mg and 3 ml TE
Do 50% weekly water change
Never do any testing

You will never have to worry about having too little or too much fertilizer. Happy trimming.

Thank you
Edward


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## Laith (Sep 4, 2004)

I'm having trouble grasping what the discussion is about here. The initial post was a very clear and useful explanation of some basics re fertilizing.

Yes, there was a typo and it was corrected. How did this turn into a "my system/method is better" argument?

As the old saying goes, "there are many roads to Rome". And they will all get you there... Once the underlying basics are understood, there are many ways to ensure that your plants have enough ferts. The original post helped make the basics better understood.

Take a deep breath everyone!


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## BryceM (Nov 6, 2005)

Yes, like many previous threads it has taken on a life of its own quite apart from the original intent.

Perhaps some redirection.... I thank MatPat for his kind words earlier. If this was made into a more formal article, and was made a little more readable are there any other calulations or topics that people would like to see included? Is it worth doing, or does the fertilator already do all the math that needs doing?

If people have questions / comments / ideas they could perhaps be incorporated into the writeup and/or added to the next re-vamp of the fertilator.

....... and a perfect opportunity to ask again if there is anyone 'out there' with the programming skills to polish up the fertilator a bit.


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## Salt (Apr 5, 2005)

Hey now, there's nothing wrong with debating, it's how new things are learned, all the world's professions have been doing it since the dawn of history. Even great philosphers have called each other names.


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## Edward (May 25, 2004)

Yes we need to fill up the missing grams in the *Conversion of tbs / tsp / Dash / Pinch / Smidgen* section of the Fertilator. I didn't have all the listed chemicals at home at the time of making the Fertilator. Any volunteer?

Thank you
Edward


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## BryceM (Nov 6, 2005)

I'm a little concerned about the variable forms of the chemicals. My KNO3 is finely powdered, while I understand other people use small pellets. That's sure to make a pretty significant difference in the conversion of tsp to grams.


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## Edward (May 25, 2004)

You are absolutely right. The form makes a huge difference in final quantity. Powder, pellets, crystals, fine powder and so on. The right way is to get a digital scale. They are so cheap today that it is not worth the trouble.


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## Laith (Sep 4, 2004)

http://users.ev1.net/~spituch/Chemicals/chemicals.html#List of Measuring Spoon Volumes


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## BryceM (Nov 6, 2005)

Who put all this together? Very nice resource!


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## standoyo (Aug 25, 2005)

great post guaic, 
dug out the experts to come forth with a healthy but informative debate for boneheads like me... :bump:


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## czado (May 26, 2005)

> *Seachem**'s Flourish lists 0.32% soluble iron,  Seachem's Flourish Iron lists 1% soluble iron. What does this mean in PPM?*
> 
> Let's assume you dose Flourish per their recommendations (5 ml per 250 liters per week).
> 
> ...


 Here's one that may be similar that I am learning with, just uses TMG.

Using a 55gal tank and 38mL dose (example from another forum), FertFriend gives 0.133ppm Fe. (Fertilator doesn't do TMG.)

I started the way you did, using percentage of mass over volume. I got %solution = grams/100mL from this site and this site (first on google).
http://antoine.frostburg.edu/chem/s...nt-to-ppm.shtml
http://homepages.gac.edu/~cellab/appds/appd-a.html

(Also, Steve Pituch's page linked by Laith above has a constant that multiplies percentage of solution by 10.)

So,
% solution = grams/100mL
TMG is .07%Fe = .070g Fe/100mL = .7mg Fe/mL

.7mg Fe/mL * 38mL dose / (55gal * 3.785L/gal) = .128mg/L Fe

FertFriend looks off but maybe it's a rounding error. Here's my online calc built on these assumptions, so its easy to compare to FertFriend if you want.

But I did not read that TMG says "W/W% (Gew./Gew. %, P/P%)" and gives density. So since thats probably weight over weight

From TMG bottle: 250mL = 260g
TMG = 1.04g/mL = 1040mg/mL

mL dose * 1040mg/mL * .0007mg Fe/mg TMG / (tank gal * 3.785L/gal) = Fe ppm

38mL * 1040mg/mL * .0007mg Fe/mg TMG / (55gal * 3.785L/gal) = .133ppm Fe

So the difference above was my error and FertFriend is correct.

(If this is confirmed, I will change the php for the above link. Anyone can use my code.)


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## czado (May 26, 2005)

(Corrected linked TMG Calc. Scroll down and there's a ppm from % mass/volume calc built on the formula above, so can still compare values by entering .07% for TMG's Fe. Please correct me.)


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