UG/L to MG/L

[flexbrew]

My water report lists Calcium at 2150 UG/L. It lists Chloride at 8.7 MG/L.

Down below the chart it says "UG/L = micrograms per liter = parts per billion" and "MG/L = miligrams per liter = parts per million".

I thought miligrams per liter were different than parts per million and micrograms per liter were different than parts per billion? It seems as they are interchangeable? If they can be used interchangably can i divide 2150 by 1000 to go from 2150 UG/L to 2.15 MG/L which would ultimately be 2.15 ppm for use in my brewing calculators.

 

[a_potter]

Correct.

 

[ajdelange]

They are different. If you put 10 mg (0.01 g) of some salt into 1,000,000 mg of water ( little over a liter) you would have a solution of strength 10/1,000,010 = 9.9999E-6 parts salt per part water. This is 9.9999 parts per million parts. So yes they are different but for the weak solutions we generally deal with it doesn't matter much. Even 1000 mg (about as high as it ever gets in brewing) in 1000000 mg water comes out to 999.001 ppm i.e. an 0.1% error. As we generally can't weigh and measure to 0.1% it's moot and you can safely interchage mg/L with ppm (and ug/L with ppb).

 

[horseinmay]

They are different. If you put 10 mg (0.01 g) of some salt into 1,000,000 mg of water ( little over a liter) you would have a solution of strength 10/1,000,010 = 9.9999E-6 parts salt per part water. This is 9.9999 parts per million parts. So yes they are different but for the weak solutions we generally deal with it doesn't matter much. Even 1000 mg (about as high as it ever gets in brewing) in 1000000 mg water comes out to 999.001 ppm i.e. an 0.1% error. As we generally can't weigh and measure to 0.1% it's moot and you can safely interchage mg/L with ppm (and ug/L with ppb).

Actually, the billion parts includes the ten. So ten parts per billion is 10/1,000,000,000, not 10/1,000,000,010. Ug/L is ppb and mg/L is ppm. They are directly interchangeable.

 

[beerkrump]

+1

When a lab is reporting concentrations as ug/L or ppb, it is read as, "in 1 liter of solution, X micrograms of compound was measured". Or, "in 1 billion parts, X parts were measured of this compound".

Not, "to make a solution of this concentration add X micrograms of compound to 1 liter of water to get this concentration."

 

[ajdelange]

-2.

What a lab does is compare the "signal" (voltage reading from an ISE, optical absorption of a spectral line in passing through a flame, strength of an emitted line from a plasma...) from the unknown to the signals from a set of standards of known strength. Ultimately comes down to the standard - the measurement will be in the same units as the standard(s). I have one on the desk labeled "Calcium, Total Hardness, Ampule, 10,000 mg/L as CaCO3". Everyone would call this 10,000 ppm but it isn't. It's 10,000 mg (a unit of weight) per 1,000 cc, a unit of volume. Thus it is actually 100*10/1000 = 1% (1 grams per 100 cc) w/v and this is a correct way to state it's strength.

To use ppm notation, the "parts" must be the same. Describing the portion of your apple harvest in terms of 4 Granny Smith Apples per 100 apples is meaningful. 4 Granny Smith Apples per 100 oranges isn't. The reason we use the 10,000 ppm notation so freely is because 1 cc of the solution weighs about 1 gram (in fact it weighs 1.008375 grams ± a few mg). To express the strength of this solution as 100*40/1008375 = 0.991695 (0.991695 grams of calcium per 100 grams of solution) or 9916.95 ppm is correct (and close to 10,000). As long as everyone understands what is really meant by 10,000 (and I hope the two previous posters will be on board after this) it is OK to use this approximation.

Now lets look at a 1 mg/L solution. We would call this 1 ppm. It is so weak that it will have the density of water (0.998203). So it's strength w/w is 1/998203 = 1.001,800 ppm. Thus even for very dilute solutions the mg/L are not equal to the ppm.

In case this last example didn't make it clear the main source of difference between w/v and w/w is the variation of the density of the water with temperature. At 4 °C where water is denser the w/w strength of a 1 mg/L solution is 1/99972 = 1.002,800 ppm. OTOH at 50 °C it is 1/988031 = 1.001,973 ppm. If I want to measure out 10 mg worth of Ca++ from my 10,000 mg/L standard I need to do it at whatever temperature the solution was made up at (presumably 20 °C).

Again, the differences are small. My 10,000 mg/L standard at 20 °C is 9,898 mg/L at 50 °C.

Hope that clarifies.

 

[ajdelange]

+1

When a lab is reporting concentrations as ug/L or ppb, it is read as, "in 1 liter of solution, X micrograms of compound was measured". Or, "in 1 billion parts, X parts were measured of this compound".

Not, "to make a solution of this concentration add X micrograms of compound to 1 liter of water to get this concentration."

Just to be clear on this when a lab makes up a solution of desired strength the procedure depends on the way the strength of the solution is to be specified. If molar, normal or w/v solutions are being made up the appropriate amount of material is placed in a volumetric flask (one whose volume is accurately known) and dissolved in the solvent but the flask is not filled to the mark at this point. It is then placed in water bath and allowed to come to the temperature for which the flask is calibrated (20 °C). It is then carefully topped off to the mark. Then and only then is the solution of the desired normality or strength w/v. The label only reads correctly at 20 °C (or whatever temperature was used when the solution was compounded) because while weight of the material, w, doesn't change with temperature the volume of the solution, v, does.

If w/w solutions are being prepared the amount of material to be dissolved is placed in a tared flask and solvent added until the total weigh is correct for the desired w/w. The label is correct at any temperature (as long as it's not extreme enough to effect a phase change).

If molal solutions are being prepared the material is weighed out and the solvent is weighed out and the two are combined. The strength of molal solutions is also invariant with temperature.

 

[horseinmay]

The distinction may be in measurement of a solution vs. the creation of a solution in a lab. If you are making a solution, you are bound by equipment and materials to make it a certain way, in order to get as precise as possible. When measuring a solution, it is what it is, and that measurement is, "out of a million parts, x number of parts are of the component in question."

 

[ajdelange]

Please read #6. It explains in detail how measurements are made and why there is never a case in an aqueous solution (at atmospheric pressure) where the ppm w/v strength is equal to the w/w ppm and is illustrated with actual examples.

If you can't follow #6 try the Wikipedia article http://en.wikipedia.org/wiki/Parts-per_notation or the introductory chapters in a quantitative analysis text.

 

[Bmorebrew]

Sure, what ajdelange is describing is the difference between molarity and molality. At dilute concentrations they are effectively the same (though technically not). If you are looking for extremely high precision and accuracy, for example you are performing trace analysis of mineral or metal content in drinking water, your units do matter. For purposes here it is purely academic.

Your water report lists calcium at 2150 ug/L. That is an average most likely over the past year. Depending on your water source (river, reservoir, etc.) that number may change slightly or somewhat dramatically over the year depending on several factors, not the least of which are season, temperature . . .

We can get into a number of mathematical and statistical discussions over this number. Just one thing to consider is that the margin of error of 2150 ug/L is understood to be 5 ug/L - it is not being measured to the single ug/L - the next unit read would be 2160, 2170, 2180, etc.

Keep in mind that if you are looking to target a given city's water profile the distinction is meaningless. Let's say you are looking to emulate the water profile of Burton on Trent. Just a quick internet search reveals a wide Ca range. Depending on your internet source, you can find [Ca] anywhere from 275 to 350 ppm (mg/L). Work in all your error calculations and you'll quickly discover for brewing purposes there really is NO difference between mg/L and ppm (and ug/L and ppb).

 

[ajdelange]

Sure, what ajdelange is describing is the difference between molarity and molality.

No, not really. I am talking about the fact that ppm (or ppb or ppt) is dimensionless and that mg/L is numerically equal to mg/kg only if the solution weighs exactly 1 kg/L which it only does at one (for a particular solute and that must be one that will increase the density of the solution) concentration for each temperature. A molar solution is a w/v solution. A molal solution is a w/w solution but it is weight of solute per unit weight of solvent. In neither case is ppm equal to mg/L.

At dilute concentrations they are effectively the same (though technically not).

Yes.

For purposes here it is purely academic.

That's the important thing.

Your water report lists calcium at 2150 ug/L. That is an average most likely over the past year. Depending on your water source (river, reservoir, etc.) that number may change slightly or somewhat dramatically over the year depending on several factors, not the least of which are season, temperature . . .

Just one thing to consider is that the margin of error of 2150 ug/L is understood to be 5 ug/L - it is not being measured to the single ug/L - the next unit read would be 2160, 2170, 2180, etc.

How do you conclude that? No information about number of measurements, precision of measurement, dispersion of measurements or any other statistical data was given by OP. The measurement instrument may or may not have read to 4 significant digits and even if it only read to 2 or 3 the mean (if it is indeed and average and it probably is) would certainly have more digits and if the standard deviation were small enough the SEM could be small enough that 3 or 4 digits could be significant. If your point is that a published value of 2150 ug/L does not mean that the water in question will contain exactly 2150 ug/L but rather some number close to that (with what "close" means unspecified) then it is valid.

 

[Bmorebrew]

Sure, what ajdelange is describing is the difference between molarity and molality.

Should say "is like the difference . . ." My bad - the point was to reinforce your point of technical difference vs. practical.

Curious to me also that the value would be reported as 2150 ug/L as opposed to 2.15 mg/L. I have it backwards in my initial response actually, purposely reporting in such a manner hints that the zero is significant. Reporting as 2.15 mg/L would obviously eliminate any ambiguity over the last zero if it were in fact not significant. However, my guess is that the measurement is made on an ICP/MS, and here minerals on drinking water are run using method 200.8 and done in mg/L.

even if it only read to 2 or 3 the mean (if it is indeed and average and it probably is) would certainly have more digits

One would not report more digits than those used in making the measurements.

 

[ajdelange]

However, my guess is that the measurement is made on an ICP/MS, and here minerals on drinking water are run using method 200.8 and done in mg/L.

My guess too. If the Standard Procedure or MOA or Practice or whatever calls for standards whose concentrations are expressed in mg/L then the result should be expressed in mg/L and in water analysis this is usually the case. The example standard I mentioned in #6 is labeled mg/L and any analysis I do using a calibration based on that standard is, thus, to be expressed in mg/L. I could, of course, do some math and convert that strength of that solution to equivalents per liter or moles per liter or % w/w or grains per gill or any other unit I wanted and report in that way but the reason the standard is labeled in mg/L is because the standard practice wants the reporting in mg/L.

One would not report more digits than those used in making the measurements.

Averaging finite precision data to get answers more accurate than the precision is one of the oldest tricks in the book but it must be done with care. In particular, the SEM must justify the carrying of the extra digits. As an example of this if I take 1000 numbers each equal to 2.600 plus a gaussian random variable of standard deviation 1 and then "measure" the value of the result to unit precision (i.e. I can have "measurements" of 0,1,2,3,4 etc and average these I get averages like 2.596, 2.573, 2.576, 2.622 for different "experiments". Clearly, I have been able to measure beneath the "quantizing noise" introduced by the finite precision of my measurement process. Given that the standard deviation in the raw sequence is about 1 count the SEM is 1/sqrt(1000) = 0.03 and so I am justified in reporting at least 1 and perhaps 2 additional digits. Thus my answers could be 2.6 for all four examples or 2.60, 2.57, 2.58, 2.62. The ability to do this obviously depends on assurance that one is free of systematic (bias) error, and that one has a large enough samples (1000 isn't reasonable for checking on the calcium content of ones water)and small enough SD to hold the SEM down.

All this is well and good but the extra significance may not be desired (in which case there is little point in doing all the extra measurements). The protocol often states the number of significant digits to be reported.