Salinity determination by density

Discussion in 'Reef Chemistry by Randy Holmes-Farley' started by JimWelsh, Mar 4, 2016.

  1. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    The subject of various alternative means of determining salinity previously came up in this thread where I dabbled (in what I now see was an amusingly over-simplified way) with the idea of using a couple of simple tools to determine salinity by calculating the density of your tank water.

    I have recently revisited this idea, and have some interesting things to report.

    The method I describe in this thread appears, after some initial testing, to be able to provide salinity results that can be accurate to +/- 0.3, or SG results that are +/- 0.0002, requiring only a few simple tools, provided sufficient care and attention to detail is given to certain steps of the process.

    The density ρ of a substance is equal to the mass m divided by the volume V: ρ = m/V. If you know the mass of a given volume of your tank water, then you can determine the density.

    Salinity is frequently expressed in terms of specific gravity, which is the density of a substance relative to the density of water at the same temperature. So, in order to determine specific gravity from density, then the temperature must also be known.

    If the mass, volume, and temperature of the sample are known with sufficient accuracy, then the specific gravity can be determined, and salinity can also be determined.

    The basic idea that I floated in the previous thread is that one might be able to take, for example, a 100 mL volumetric flask, weigh it empty to establish the tare, fill it with tank water to the graduation line, weigh it a second time, and subtract the tare weight to determine the weight of the sample. In the example I gave, I did the test with everything at 20C, which greatly simplified everything. I also attempted to estimate the method uncertainty, to see what sort of confidence I could have in my result.

    Since then, I have spent more time thinking about and reading about the process I was attempting and I am now humbled, amused, and embarrassed at how many things I got wrong in that thread. I believe that the approach to the subject I am positing in this thread is more well thought out, and more correct, in terms of both the science and the math. I also have recently had the good fortune of being required as a part of my job to develop a custom interface between numerous Anton-Paar DMA5000 densitometer instruments and our LIMS (Laboratory Information Management System). As a necessary part of this work, I am required to run samples on the densitometer while testing the interface I am developing, providing me an excellent opportunity to run as many samples as I desire on this instrument, which can determine the density and specific gravity of liquid samples to six decimal places!

    More to come.....
     
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  2. redfishbluefish

    redfishbluefish Stay Positive, Stay Productive R2R Supporter R2R Excellence Award Reef Squad NJRC Member Article Contributor

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    I'm liking this Jim.....it reminds me of my educational days where we used pycnometers (highly accurate little volumetric flasks) to determine density. This was late 60's/early 70's. The volume was extremely accurate, where the glass stopper had a thin tube that also needed to be filled right to the tippy top. Had to also adjust the temperature of the sample (I want to say 20C) before carefully weighing the flask.

    [​IMG]
     
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  3. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    If I understand correctly, pycnometers are used to determine the density of substances like granular or powdered solids. A preferred method of determining the density of liquids is the buoyancy method, where a "plummet" of known volume is immersed in the liquid being measured, and the negative difference in the weight of the apparatus holding the plummet before immersion and the weight after is the weight of the displaced liquid. TMI about density measurement can be found here.

    The approach I propose uses more readily available and more practical tools.
     
  4. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    As stated above, there are only three basic variables to this salinity calculation: The mass, volume, and temperature of the sample. The accuracy and precision of the resulting salinity calculation will depend directly upon the accuracy and precision with which we can determine those three variables.

    Before we delve into the details of the method, perhaps we should look at what kind of accuracy of these three measurements is necessary to achieve a particular degree of accuracy in the final salinity result.

    The following errors in each of the three input variables will cause a 0.5 (or -0.5, as shown) error in the resulting salinity value as PPT (based on the flask being 100 mL):

    Weight: 0.038 g
    Water Temperature: 2 degrees C
    Volume: 0.038 mL (-0.5)

    Similarly, the following input errors will result in an error in salinity of 0.1:

    Weight: 0.0075 g
    Water Temperature: 0.37 degrees C
    Volume: 0.0075 mL (-0.1)

    So, this should give the reader an idea of how practical it is to be able to do this salinity test with the desired degree of accuracy. I realize that that the requirement that the volume measurement accuracy be within 0.038 mL in order to calculate salinity to within 0.5 PPT sounds pretty restrictive. This is especially true when you realize that the Class A tolerance for a 100 mL volumetric flask is +/- 0.08 mL! But, bear with me, because I will show that this requirement may be more achievable than it may appear at first glance.
     
  5. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    Let's tackle the volume issue first. A 100 mL Class A volumetric flask has a tolerance of +/- 0.08 mL. That uncertainty translates into a little more than 1 PPT salinity. On the face of it, this might sound like a deal breaker in terms of the hope of a salinity determination with the accuracy stated in the original post.

    If we take a closer look at what this tolerance actually means, we discover that it describes the accuracy of the placement of the calibration mark. That is a different thing than the precision that can be achieved when using the flask. Perhaps I should take just a brief detour to discuss accuracy vs. precision, since these terms are often used interchangeably, but really do mean different things.

    Accuracy describes the degree to which a determined result agrees with the "true" value. It is how close you are to the bullseye.

    Precision describes the degree to which you get the same result every time. Think of it as tight grouping.

    The accuracy of any given 100 mL Class A flask may be off by as much as 0.08 mL. This is true. But the precision that can be accomplished when using one can be much tighter than that. The precision of this tool is largely up to the user. With proper technique, and attention to just a few details, great precision can be achieved. My experience is that I can reliably fill a 100 mL volumetric flask to within 0.007 mL with 95% confidence (2 standard deviations of repeated measurements). With this kind of precision, one can easily determine the accurate volume of the flask by calibrating it using a method to be described later. Armed with this information, we will know the true volume of our flask, regardless of what it is. For the purposes of our salinity determination, it doesn't matter exactly what our flask's volume is. It only matters that we know the correct value with sufficient accuracy.

    So, with sufficient user attention to detail regarding precision, the volume can be accurately determined to well within the tolerance listed above for 0.5 PPT, and can even approach that for 0.1 PPT.
     
    Last edited: Mar 5, 2016
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  6. French27

    French27 Excitedly New to the Hobby

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    Loving the thread as I have worked in the pharma lab environment for a number of years now. Wish I had the Anton par density meter at home. What are your thoughts on balance precision for the home aquarist? Do you feel this will be your limiting factor?
     
  7. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    Possibly. But, that depends on how careful the aquarist is regarding precise, repeatable meniscus reading, as I alluded to above. In other words, if they are careful with the balance, but sloppy with the flask, then the flask usage could be the limiting factor.

    I have two different balances: one very inexpensive 300g x 0.01g balance that cost me about $30.00, and also a 200g x 0.001g balance that was more like $300.00. The first has a stated repeatability of 0.01g, which I find to be quite true. The second has a stated repeatability of 0.003g, but in practice I find it to be more like 0.002g. Just like with the volumetric flask, the performance of balances can be significantly affected by the skill of the user. And like the volumetric flask, the accuracy and precision of the weight determination using even an inexpensive balance can be significantly improved by attention to a few simple details and correct usage.

    Just as I have not yet elaborated the details regarding the meniscus, I will get into the details of how to eek better performance out of the balance later. For now, suffice it to say that I believe that with proper technique, even the 300g x 0.01g balance I have would suffice for this purpose.
     
  8. redfishbluefish

    redfishbluefish Stay Positive, Stay Productive R2R Supporter R2R Excellence Award Reef Squad NJRC Member Article Contributor

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    Jim, pycnometers are for liquids. There is no reading of a meniscus. You fill the flask completely, including the capillary-like stopper, right to the top of the stopper. This eliminates the error of reading a meniscus. Out of curiosity, I just looked up to see if they are still available for sale....and the answer is yes! Found them on both eBay and Amazon...from 1 ml to 100 mls. I use to use 25 ml pycnometer when in school.
     
  9. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    I should have said "primarily used", rather than simply "used" in my comment about pycnometers above. I got that idea because in the Sartorius document I linked, while they mention in passing using them for homogenous liquids, the only detailed discussion about them is in association with granular or powedered solid material and liquid suspensions. I do see that they can be used for liquids, too.
     
  10. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    I have taken several days off from posting more on this because I've been gathering some more data and analyzing it. So far, the results are really encouraging!

    I have previously mentioned the accuracy and precision requirements for volume and weight. In this post, I'll touch upon the third variable: Temperature.

    Since we are dealing with density of water, and since water's density varies substantially with temperature, then it is important to know the temperature of the water being measured as a part of our measurements. There are plenty of inexpensive digital thermometers readily available to the hobbyist, but most of them will only be accurate to within +/- 1.0 C or so. Given the rather restrictive limit I described above of 0.37 degrees C in order to determine salinity to within 0.1 PPT, then this, too might appear to cast doubt on the viability of this whole idea. But many of these cheap thermometers are precise to within 0.1 degree C, and I intend to show that for this project, temperature precision is more important than temperature accuracy, and a thermometer that is off by 1 degree C or more is good enough, if it is precise enough.
     
  11. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    I have experimented with this method for a couple of weeks now, and so I have a small pile of data to draw conclusions from. I also have access to some very accurate and precise tools at the lab where I work, which enables me to compare the results of my experimentation with known "true" values. Those tools include an analytical balance with a readability of 0.00001 grams (0.01 milligrams), calibrated Class 1 mass standards used to verify the accuracy of that balance, a calibrated, NIST-traceable glass mercury thermometer with divisions every 0.1 degrees C, and the DMA5000 densitometer that can give the density and specific gravity of a sample at a given temperature to six decimal places with a temperature accuracy of 0.02 degrees C.

    I have determined that the basic requirements for this method are:

    1) A volumetric flask. I use a Class A 100 mL one. Class doesn't really matter, though, but if you're going to buy one, you might as well get a Class A. Capacity also doesn't really matter, but it should be the largest capacity possible that weighs less than your balance's maximum weight capacity when full.

    2) A balance with a readability of 0.01 grams, and enough capacity to weight the volumetric flask when full. It's OK if the balance has somewhat poor repeatability; imprecision of +/- 0.02 or so is not really a problem.

    3) Two "mass standards" that will be used to calibrate the balance: One with a mass roughly equal to the mass of the empty flask, and one roughly equal to the full flask. They do not have to be certified at all; it doesn't even matter if their actual mass is unknown. They just have to be constant weights that don't substantially change over time.

    4) A thermometer that can be read in increments of 0.1 degrees C (or 0.2 degrees F), and is also precise (reads the same number every time) to within that same tolerance. Accuracy doesn't really matter.

    5) The altitude of the place where the measurements are taking place must be known.

    6) A willingness to pay careful attention to a few simple details, and also to take the time to perform some initial calibrations of the flask and the thermometer. This willingness on the part of the user is one of the most important aspects to getting reliable results out of this method.

    7) The ability to do the necessary calculations, which I intend to provide in the form of a spreadsheet.

    For all of those things that might seem to be important, but I am saying they don't really matter, I am prepared to explain why those factors are not really important.
     
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  12. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    To give you an idea of the kind of accuracy I'm getting with this method, here are some numbers from the last week's worth of data from my display tank (diluted down by a random amount in one instance), my freshly made Instant Ocean saltwater, and a neglected QT tank where the salinity has been allowed to creep up over time, showing the date, the source of the water, and the salinity as shown by the DMA5000 densitometer, as calculated using my 0.01g balance, and as calculated using my 0.001g balance:

    Date Tank DMA5000 0.01g 0.001g
    03/07/16 Display 34.56 35.04 34.64
    03/08/16 Display 34.49 34.66 34.49
    03/09/16 Diluted 34.08 34.21 34.13
    03/10/16 Display 34.42 34.35 34.50
    03/11/15 QT 39.24 39.19 39.05
    03/11/15 IO 34.51 34.55 34.45


    The same data, expressed as Specific Gravity at 25C instead of salinity, to five decimal places:

    Date Tank DMA5000 0.01g 0.001g
    03/07/16 Display 1.02604 1.02641 1.02611
    03/08/16 Display 1.02599 1.02612 1.02599
    03/09/16 Diluted 1.02568 1.02578 1.02572
    03/10/16 Display 1.02594 1.02589 1.02600
    03/11/15 QT 1.02960 1.02956 1.02945
    03/11/15 IO 1.02601 1.02604 1.02596

    EDIT: I had the tables formatted nicely in the editor, but they don't display as nicely when posted. Sorry!:mad:
     
    Last edited: Mar 11, 2016
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  13. Habib(Salifert)

    Habib(Salifert) Well-Known Member

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    Jim, how did you calculate density? Was it by the formula you gave in the opening post: rho=mass/volume or did you make corrections to it? :)
     
  14. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    Well, I didn't change the definition of density. :D

    But your question is providing an excellent opportunity for me to segue to the importance of accounting for the buoyancy of air.

    The first step in this process is the calibration of the volumetric flask. The basic process is to weigh the empty flask, then fill it correctly and precisely to the graduation mark with very pure water of a known temperature, and then weigh the full flask. The difference between the two weights gives us the "apparent mass" of the water. Because the density of pure water at a given temperature is a well-known value, the volume of the water in the flask at that temperature can be very accurately determined from the "true mass" of the water. But the "apparent mass" is not the same as the "true mass". In order to calculate the "true mass" from the "apparent mass", the effect of the buoyancy of air must be properly accounted for.

    Now is a good time to provide some light reading for those inclined to delve deeper into these topics.

    When it comes to weighing things with a digital balance, there are a lot of things that can affect the reading. A detailed examination of some of these things that conveys the concepts without getting too deep into the nitty-gritty aspects of the subject matter can be found in this document: Weighing the Right Way. While there is some Mettler-Toledo specific marketing material to be found in that document, it still largely discusses the broader concepts that apply to any balance. Some of the issues discussed are of little relevance to the hobbyist with an inexpensive balance, but many of the concepts do still apply.

    The procedure I use for calibrating the flask is adapted with as little variation as is necessary to be practical from this document: Selected Procedures for Volumetric Calibrations. In particular, the calculations for Option B (two-point balance calibration) found on Page 39 of that document are used.

    Balances are generally calibrated using weights of a known mass, known as "mass standards". These weights are usually made of metal, and frequently stainless steel. Such mass standards typically have a density of around 8 grams per cubic centimeter. A given mass standard of, say, 200 grams has a "true mass" of 200 grams (go figure). Now, when the balance is calibrated using that mass standard, this doesn't usually happen "in a vacuum"; there is air present. That air has a density, too, of somewhere around 0.0012 grams per cubic centimeter (more or less, depending on temperature, humidity, and barometric pressure). Just like a heavy object feels lighter when submerged in water due to the Archimedes principle, the apparent weight of the mass standard is affected by the buoyancy of air. So, when the balance is calibrated using that 200 gram mass standard, what we are saying is that the balance knows how to accurately weigh substances with the same density as the mass standard in air of the same density as the air at the time the calibration was done. In fact, if you removed all the air from the room immediately after calibrating the balance, and then weighed the mass standard, you would see that its "apparent mass" is somewhat greater than 200 grams, because the buoyancy of air is no longer in effect, but the balance was calibrated to account for it.

    As long as you are weighing things with the same density as the mass standard used to calibrate the balance, and the density of the air remains the same as it was at the time of the calibration, then the "apparent mass" and the "true mass" of the weighed objects will be equal. But, when you are weighing things with a different density than the mass standard, and/or the density of air has changed, then there is a difference between the "apparent mass" (balance reading) and the "true mass" (the number we are really interested in). And even though it may be surprising, this effect is quite significant in the measurements involved in this method of determining the specific gravity of our tank water!

    So, to answer your question @Habib(Salifert), I did use the formula for density as stated above: ρ = m/V. But, the values for "m" and "V" have been corrected to account for the effect of the buoyancy of air, and also to correct for the thermal expansion/contraction effects when the measurement temperature deviates from 20C.
     
  15. Habib(Salifert)

    Habib(Salifert) Well-Known Member

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    I did 't go through your post yet, but wanted to be sure of that you would make corrections for the buoyancy effect because that would be significant in measuring the density to 4 significant numbers. :)

    FWIW, you can take a constant value of approx. 0.001 as a correction in the density calculated as mass/volume.
     
  16. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    I'd like very much to hear your feedback on it, should you choose to read it.


    Calculating the value rather than estimating it isn't all that hard, and with this application, I'm fighting various biases and uncertainties on many levels, so I'd rather do the work to eliminate them wherever I can. My data, based on a calculation factoring in altitude, barometric pressure at sea level, and air temperature, but assuming a humidity of 50%, shows a mean value for this adjustment of 0.00096, with an uncertainty (2 * SD) of +/- 1 0.000012. So, your estimate would work nicely, but I'm sticking with my calculation (since I've already done the work).
     
  17. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    I did another small experiment with this method today. I did five replicate measurements in a row, using both balances, to try to get an idea of the repeatability of the method. I then removed about 4.6 liters of water from my appx. 210 gallon total water volume system, and allowed the ATO to replace that 4.6 liters with RO water, which amounts to a 0.2 drop in salinity (PPT). I let enough time pass for more than 2 1/2 tank turnovers to happen in the system, and then did another five replicates at the lowered salinity, to see if the method could detect this 0.2 drop.

    Below is the chart of the data for this experiment. The darker and lighter blue lines are the data for the two balance before the salinity reduction, and the darker and lighter red/orange lines are for after the salinity reduction. I will mention that for the repitition #3 for the "after" pair of lines, I made a note that the meniscus had been set "slightly high" relative to the calibration line.

    While the method did detect the salinity change after the dilution well, and the average of the "Before" values would be roughly 0.2 more than the average of the "After" values, it is also clear that there is enough uncertainty to blur this distinction on any given individual measurement.

    To me, this chart shows clearly that the precision of the balance is not the most important factor; the 0.01g balance and the 0.001 balance track together nicely. The bigger factor affecting the uncertainty of the measurement is the setting of the meniscus. Temperature uncertainty is also a factor here, but a minor one, since it amounts to an uncertainty in the salinity value of only about 0.03.

    [​IMG]
     
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  18. Habib(Salifert)

    Habib(Salifert) Well-Known Member

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    I think it looks good Jim! :)

    I only wanted to know if you were making the "buoyancy correction" especially since you wanted to compare it to the Anton-Paar measurements. :)
     
  19. JimWelsh

    JimWelsh Well-Known Member R2R Supporter

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    The first steps in this method need to be done only once, when starting the method. It is important to know both the weight of the empty flask (tare weight of the flask) and its true volume at 20C (as opposed to the marked volume). Determining the true volume of the flask is "calibrating" the flask, and determining the empty weight is a part of that process. As mentioned above, the procedure described here is adapted from Selected Procedures for Volumetric Calibrations (2012 Ed).

    The calibration process is really very simple: The empty flask is weighed, then filled exactly to the calibration mark, using proper meniscus-setting technique, with pure water of a known temperature, and then the full flask is weighed. The difference between the full weight and the empty weight is the weight of the water the flask holds, and from that number, accounting for the buoyancy of air as @Habib(Salifert) mentions, and also the effect of thermal expansion on both the water in the flask and the glass the flask is made of, it is possible to calculate the volume that the flask holds at exactly 20C.

    In order to get the kind of precision described in this thread, it is important to reduce the uncertainty in the measurements as much as possible. To that end, certain techniques are used to help improve accuracy and consistency. One such technique is the use of a mass standard in the weighing process. Another technique to use the average of multiple weighings. Yet another is to address uncertainty regarding the amount of water that adheres to the neck of the flask above the calibration mark.

    The next posts will describe these techniques in more detail.
     
  20. Randy Holmes-Farley

    Randy Holmes-Farley Reef Chemist Staff Member Team R2R R2R Supporter R2R Excellence Award Expert Contributor Article Contributor

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    I'm going to post this as a sticky so folks can find it more easily. :)
     

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