# ppm by mass or by mole?



## BlueRam (Sep 21, 2004)

Vicker3000 said:


> When people refer to the doses of nutrients in ppm, is this parts per million mass or parts per million molar?


parts per million mass:
http://en.wikipedia.org/wiki/Parts_per_million 

The basics are ppm= mg per kg which just happens to also be mg per liter if you assume that 1L=1kg.


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## Vicker3000 (Aug 2, 2006)

That Wikipedia link basicly says that ppm can refer to parts per million mass, parts per million volume, parts per million molar, and parts per million mass/volume. I assumed it didn't mean ppm volume because that generally refers mixtures of gasses. When the solvent is water, as is our case, ppm mass is the same as ppm volume (as long as you're close to 4 degC), but that still leaves a choice between molar and mass.

In a more strict definition you're really supposed to specify which you're using, but within a certain branches of science one meaning is often assumed. A chemist like myself is more likely to assume molar, so that's why I asked.

My point is, ppm can mean many different things so I wanted to make sure I'm using the right meaning. From what you've said, it seems that aquariists assume ppm mass. Thanks for the reply! =)


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## KevinC (May 24, 2004)

Two things to point out/clarify/muddy the situation:

1. The base unit in the numerator and denominator are supposed to agree - milliGRAMS per kiloGRAM so they cancel out. As was stated, with water at a density of 1g/ml, it is OK to use mg/L. ppm by default in water chemistry is mass-based.

2. Things get a little more sticky with what comes after the ppm. For instance, nitrate concentration can be ppm NO3 (mg NO3 per L) or ppm N~NO3 (ppm N per L where the N is in the form of NO3). Same for phosphate. On this forum and in most test kits, ppm NO3 and PO4 are standard. Hardness and alkalinity are even more murky - ppm CaCO3 equivalent. In other words, the amount of CaCO3 you would need to dissolve in water to have the same effect on the water parameter (hardness or alkalinity) being measured. This is because the actual chemicals causing hardness and alkalinity can vary.


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## Vicker3000 (Aug 2, 2006)

Even if the units cancel out, ppm mass will give you a different number than ppm molar. A molecule of NO3 has a different mass than a molecule of H2O.

Let's look at an example:
NO3 has a molecular weight of 62 g/mole
H2O has a molecular weight of 18 g/mole

If you have an aqueous solution where you have one molecule of NO3 for every million molecules of solution, you have 1ppm _molar_.

Now let's take a look at the same solution, but with ppm _mass_:
1 molecule NO3 * 1 mole/N_A molecules * 62 g/mole = 62/N_A g
1*10^6 molecules H2O * 1 mole/N_A molecules * 18 g/mole = 18*10^6/N_A g
(For those who aren't familiar with the notation "N_A", this is Avogadro's Number. N_A = 6.022*10^23. A mole is a counting unit. There are 6.022*10^23 molecules in one mole.)

This leaves you with 62/N_A g NO3 for every 18*10^6/N_A g H2O. If you put this as a ratio, the N_A's cancel out, leaving you with
62 g NO3 / (18*10^6 g H2O)
which reduces to
3.444*10^-6 g NO3/(g H2O)

That's 3.444 ppm _mass_. A solution that is 1 ppm _molar_ NO3 is 3.444 ppm _mass_.

(Yes, I did round off slightly by saying that the solution is 1 million molecules of H2O instead of 999999 molecules of H2O and 1 molecule of NO3, but the error introduced by this assumption is on the order of 10^-6)

To summerize, ppm molar can not be used interchangably with ppm mass.

I'm not trying to argue; if ppm mass is what is assumed by aquariists then that answers my question. I just wanted to illustrate that there is a distinction between the two and that mass and molar are not equivalant.


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## KevinC (May 24, 2004)

Vicker3000 said:


> I'm not trying to argue; if ppm mass is what is assumed by aquariists then that answers my question. I just wanted to illustrate that there is a distinction between the two and that mass and molar are not equivalant.


OK - was your question answered or not? The above sure looks like arguing . . . I'm not sure who you are arguing with though.



KevinC said:


> ppm by default in water chemistry is mass-based.





BlueRam said:


> The basics are ppm= mg per kg which just happens to also be mg per liter if you assume that 1L=1kg.


I don't think BlueRam or I indicated that the ppm, ppmV or ppmM were interchangeable. Both of us do have advanced chemistry degrees and I also teach Quantitative Analysis.:thumbsup:


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## plantbrain (Dec 15, 2003)

Seems that it is more clarification and convincing themselves. 
I have to do that often myself

Regards, 
Tom Barr


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## Vicker3000 (Aug 2, 2006)

KevinC said:


> OK - was your question answered or not? The above sure looks like arguing . . . I'm not sure who you are arguing with though.
> 
> 
> 
> ...


I'm sorry if I sounded argumentative; that was not my intention. I was just trying to clarify. My words weren't aimed specificly at you. Not everyone on the forums is a chemist. My question has been answered, thanks for your help. =)


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## BlueRam (Sep 21, 2004)

Vicker3000 said:


> I'm sorry if I sounded argumentative; that was not my intention. I was just trying to clarify. My words weren't aimed specifically at you. Not everyone on the forums is a chemist. My question has been answered, thanks for your help. =)


Not everyone is a chemist but chemistry/engineering/technical is well represented here as fact checking  If you drop a decimal point beware!

Now it ppm has you thinking, the most accepted number of hardness (KH and GH) here is the German degree or drop count. Very easy to measure (like counting drops) and reasonable (roughly 0-15)....


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