# Newbie needs help calculating



## MrGuy (Apr 2, 2011)

Hi, I have started a nano tank. I've used a couple of different useful fertilator however all of them gives different measurements. So I decided to try to calculate this myself.

The formula I found online goes like this:

ppm = 1000000 x (mass of solute)/(Mass of solute + Mass of solution)

As an example I tried Flourish Nitrogen (1.5% Nitrogen) as my first try. 

Lets say the solution of water is 200 liters and if I were to put 5ml of Flourish Nitrogen, what would be the ppm of Nitrogen in the total solution?

So I followed the formula:

Assuming there is 1000g per Liter of water and 1g per 1ml of water....

ppm = 1000000 x (.015x5ml)/((200Lx1000g/L)+(5mLx1g/mL) = 0.384ppm

I compared the answer with APC fertilator it is far different result!

I'm new at this so sorry if this looks stupid but.... What am I doing wrong with the equation? or is it even the right equation?  I would appreciate it if someone corrects me...


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## Skizhx (Oct 12, 2010)

Double-posted while double-checking for errors.


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## Skizhx (Oct 12, 2010)

> ppm = 1000000 x (mass of solute)/(Mass of solute + Mass of solution)
> 
> ppm = 1000000 x (.015x5ml)/((200Lx1000g/L)+(5mLx1g/mL) = 0.384ppm


You've made some mistakes.

First... mL is a measurement of volume, not mass.

Second... You have assumed that flourish has the same density as pure water.

Third... You did not account for the mass of flourish added to the water.

So what I've done is I've taken my bottle of flourish nitrogen and measured out approximately 1mL. I say approximately because I don't have precise volumetric lab equipment, I just have a syringe I bought from the pharmacy. Playing around with it though I've found the margin of error is pretty decent when measuring distilled water. I should also mention a +-0.01g margin of error on my scale.

So what I found was that 1mL of flourish nitrogen weighs 1.20g.

Soooooo....

*Given*
5mL dose of flourish at 1.20g/mL = 6g @ 1.5% nitrogen content
200L of water @ 1.00g/mL

Now the first thing to note is that the solute you're calculating isn't the flourish nitrogen _solution_, it's the *actual* nitrogen content of that solution. So 6g of flourish @ 1.5% N = 6 * 0.015 = 0.09g of N in 5mL of flourish solution.

The second thing to note is that your mass of solution must account for the mass increase of the added flourish. So...
200L of water = 200 000g + 6g of flourish = 200 006g

Now for the math...

ppm = 1000000 x (mass of solute)/(Mass of solute + Mass of solution)

ppm = 1000000 x (0.09g of N)/(0.09g of N + 200 006)
ppm = 1000000 x (4.49*10^-7)
ppm = 0.450

Now to check our math we can go into a solution ppm calculator such as http://www.unitconversion.org/concentration-solution/grams-per-liter-to-parts-per-million-ppm-conversion.html

0.09g/200L = 0.00045g/L
If we convert 0.00045g/L to ppm we get 0.450ppm.

Hope that clears things up for you!


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## ray-the-pilot (May 14, 2008)

MrGuy said:


> Hi, I have started a nano tank. I've used a couple of different useful fertilator however all of them gives different measurements. So I decided to try to calculate this myself.
> 
> The formula I found online goes like this:
> 
> ...


You made a small mistake in your calculations but you get the same result as the fertilator

ppm = 1000000 x (.015x5ml)/((200Lx1000g/L)+(5mLx1g/mL) = 0.375 ppm (not .384 ppm)

The fertilator says 1.65 ppm but that is because the ferilator is calculating ppm of NO3 not ppm of N.

You need chemistry to make this conversion.
.375 x 62 g NO3/ 14 g N = 1.66 ppm

That little difference is probably due to the fact that the density of flurish is not exactly 1.00


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## Skizhx (Oct 12, 2010)

Heh, darn... So much for my scale... 

I suppose checking my answer with fertilator would have been the smart thing to do.


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## MrGuy (Apr 2, 2011)

Awesome! :high5: thanks for all the help guys this helps me a lot to try to calculate the fertilizers on my own... THANKS!!! artyman:

Now I need to post another thread question :angel: how to get rid of that damn string/web like algae that grows on one part of my dwarf baby tears... lol :typing:


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## MrGuy (Apr 2, 2011)

:wave: hey guys... one more question... am i doing anything wrong with this equation?

Tank size: 200L
Fertilizer: Flourish Potassium 5.8%
Dose size: 5ml

ppm = 10^6 x (.058 x 5 ml) / ((200 L x 10^3 g/L) + (5ml x 1 g/ml)(94.2/39.1) = 3.49 ppm


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## ray-the-pilot (May 14, 2008)

MrGuy said:


> :wave: hey guys... one more question... am i doing anything wrong with this equation?
> 
> Tank size: 200L
> Fertilizer: Flourish Potassium 5.8%
> ...


Yes but I don't have time to correct your mistake. This is one of those weird things that you just have to know. Potassium is expressed in percentages as percent of K2O not K so you have to divide 0.058 by the molecular mass of K2O and multiply by the atomic mass of K to find the percentage of K.


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## MrGuy (Apr 2, 2011)

ray-the-pilot said:


> Yes but I don't have time to correct your mistake. This is one of those weird things that you just have to know. Potassium is expressed in percentages as percent of K2O not K so you have to divide 0.058 by the molecular mass of K2O and multiply by the atomic mass of K to find the percentage of K.


That's what I thought I did...

ppm = 10^6 x (.058 x 5 ml) / ((200 L x 10^3 g/L) + (5ml x 1 g/ml)(*94.2/39.1*) = 3.49 ppm

94.2 = K2O Molecular mass
39.1 = K Atomic mass


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## ray-the-pilot (May 14, 2008)

MrGuy said:


> That's what I thought I did...
> 
> ppm = 10^6 x (.058 x 5 ml) / ((200 L x 10^3 g/L) + (5ml x 1 g/ml)(*94.2/39.1*) = 3.49 ppm
> 
> ...


I was very tired when I came home on Thursday and didn't really have time to look over your work.
It doesn't agree with the fertilator. 
but now that I look at it, check it myself and compare to the fertilator,there is a problem.

OK first your solution is wrong because the K and K2O are inverted. It should be:

10^6 x (.058 x 5 ml) / ((200 L x 10^3 g/L) + (5ml x 1 g/ml)) x 39.1 / 94.2 = 0.602 ppm

The fertilator says 1.25 ppm which is strange.


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## ray-the-pilot (May 14, 2008)

Here is the mistake:

There are 2 K’s per K2O so the calculation was off by 1/2:

10^6 x (.058 x 5 ml) / ((200 L x 10^3 g/L) + (5ml x 1 g/ml)) x 78.2 / 94.2 = 1.2 ppm which is close to the fertilator (1.25 ppm)

Flourish claims that the K formula is 50,000 ppm in K so:

50000mg/L x .005L /200L = 1.25 mg/L or 1.25 ppm which checks with the fertilator.

You really need to know some chemistry if you want to make your own fertilizers!


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## MrGuy (Apr 2, 2011)

oh WOW! as simple as that! Your help is greatly appreciated! Thanks! eace:


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