[James Lorden]

Can someone help with this question that came up on the water reports thread (not a lot of traction over there)

?

AJ deLange has a post on the Brewing Network forum about something he just found out about the Ward Labs report (if you don't know who he is, let me just say that when he writes about water chemistry I read it and hope I understand what he has to say).   If you look at the reports, SO4 is listed as SO4-S, which means the number reported is the sulfur.  AJ says to multiply by 3 to get the Sulfate as ppm.

Can someone explain why the multiplyer is three?

ppm SO4-S is ppm of sulfate in terms of the sulfur component of the sulfate only. The molecular mass of sulfur is about 1/3 that of sulfate so to get to SO4 as sulfate you multiply by 3. The latter is what is discussed in brewing texts, assumed in spreadsheets, etc.

So then parts per million is a measure of weight and not actual particles?  Don't know why this confuses me - it just doesn't seem logical.  I'm thinking sulfate is 1 sulfer surrounded by 4 oxygen so if I have 5 sulfate particles then I have 5 sulfers and 20 oxygens.

In that case assuming all sulfer in solution is part of a sulfate molecule then the parts per million of sulfer would equal the parts per million of sulfate.... I guess it doesn't work like that though... since AJ is saying multiply the sulfer by 3.

[SiameseMoose]

Parts per million is an antiquated measure of concentration. I truly wish it would go away, but that's not going to happen. My preferred use is milligrams per liter, or mg/L. With this nomenclature it's totally clear that it's weight per volume. They produce the same number, 1 ppm = 1 mg/L, but people prefer to say parts per million.

Disclaimer: I am an analytical chemist (retired) by trade. I've had to deal with ppm, ppb (billion), even ppt (trillion) my whole career.

[James Lorden]

Ok then as to the "multipy the sulfer by 3 to get sulfate" that AJ DeLange stated, is it because:

The atomic number of sulfer is 16

Sulfate is one sulfer and 4 oxygen

the atomic number of oxygen is 8

one sulfate has a combined count of (1 * 16) + (4 * 8 ) = 48

48 (sulfate)/16(sulfer) = 3

therefore the weight of the sulfate in solution is equal to 3 times the weight of the sulfer reported by ward labs (assuming all sulfer is in the form of sulfate)?


Or is that just coincidence?

[Kaiser]

James,

Thanks for breaking this out of the water report topic. I may want to do the same with the SO4-S vs. SO4 discussion since it is useful to have this as its own topic. I didn't know that either and had to add this info to my water report article.

Kai

[mabrungard]

No.  Its not atomic number that is used, its the molecular weights.

S = 32 grams per mole
O = 16 grams per mole  x4 = 96 g/mole

SO4 = 96 grams per mole

SO4/S = 96/32 = 3

So, there are 32 grams of sulfur in a mole of sulfate.  This is what Ward is reporting.  But to report the entire weight of the sulfate in the water, you have to multiply the SO4-S number that Ward provides by the SO4/S ratio (3) to arrive at the actual sulfate weight.
 

[James Lorden]

gotcha, thanks

The atomic weight is simply twice the atomic number so that is why my ratio worked, makes sense.

[mabrungard]

Its almost true that the molecular weight is twice the atomic number, but that analogy blows up as the atomic number and molecular weight go up.  For instance, pottassium is atomic number 19, but its molecular weight is 39.1 grams per mole.

It gets worse, mercury is atomic number 80 but its molecular weight is 200 grams per mole.  The good thing is that the molecules that we deal with in brewing are low weight and the roughly 2 to 1 ratio does generally hold up.  But it's best to use the weight instead of the number.

[Tim McManus]

I am enjoying this thread, although I am not as well versed in chemistry as the other folks on the thread.

Is the Relative Atomic Mass the same thing as the molecular weight?  I have a neat interactive periodic table and want to make sure I am aligning terminology properly.

[James Lorden]

per wikipedia - "Relative atomic mass is a synonym for atomic weight."  

I would say it seems logical that molecular weight is equal to the sum of the atomic weight of the atoms in the molecule... but that is just based on what seems logical to me.

[a10t2]

They produce the same number, 1 ppm = 1 mg/L, but people prefer to say parts per million.

Technically, that only holds true for low concentrations of the solute. Just an example I have handy: a 1% sucrose solution is 10,000 ppm, but 10,020 mg/L. It's a totally valid assumption at the concentrations we're talking about though.

I would say it seems logical that molecular weight is equal to the sum of the atomic weight of the atoms in the molecule...

That's the idea, although it also turns out to be not quite true. Due to mass-energy equivalence, some weight is actually lost in creating molecular bonds. The effect is several orders of magnitude below anything concerning chemists though, although it becomes measurable for some very large molecules, like transuranic compounds.

Ain't physics fun?

[James Lorden]

So to make it easy for CPA's like me that want to pretend that we're chemists on weekends (boy, life just keeps getting more exciting) when reading our brewing books it appears that:

ppm and mg/l are "relatively" equivalent units of measure....

And you could also say (and this is for extra credit) that 1 liter of water with 192 ppm of sulfate contains 1/500th of a mole of sulfate.

(sulfate = 96 grams/mole, 192 ppm = 192 mg/l, 96 grams / 192 mg = 500 (96*1000/192))

This didn't seem nearly as interesting in high school chemistry class!

[hopfenundmalz]

This has been a good discussion, and I have learned why AJ deLange's multiply by 3 works. 

Excellent stuff!

[hike20]

This didn't seem nearly as interesting in high school chemistry class!

I actually had a really good chem teacher in HS, but in college it was dismal. If my chem professor (or even TA's) would have made the attempt to tie into something real world many more people would have a better understanding of basic chemistry. Man, if knew how to apply it to things like beer I would have been all over it!

[punatic]

Expressing different chemicals as one common chemical material makes it easy to add their concentrations to get their total effect.  As an analogy, consider a wealthy person with bank accounts in several countries.  In order to calculate his total wealth, you must express each currency in terms of a common unit (such as ounces of gold).  

For instance, constituents that are often quantified as CaCO3 (calcium carbonate) are "hardness" species (divalent metal cations such as Ca 2+ and Mg 2+) and alkalinity species (hydroxide OH -), carbonate (CO3 2-), and bicarbonate (HCO3 -).

Expressing these species in terms of a single component (the common unit, in this case calcium carbonate) allows the individual species to be summed, indicating their eqivalant total reacting capacity.

Nitrate, nitrite and ammonia are often expressed as nitrogen - N
 
Sulfate, sulfite and other sulfurous compounds are often expressed as sulfur - S

[punatic]

In dilute solutions with a specific gravity of one, miligrams per liter is effectively equal to parts per million.
Not so for solutions with specific gravities other than one.

If the specific gravity of a solution is not equal to one, the conversion is as follows:
1mg/L = ppm (by weight) x specific gravity