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Author: Subject: Volumetric glassware, proper use and calibration by water weight.
semiconductive
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Volumetric glassware, proper use and calibration by water weight.

I did a very basic water volume experiment with precision glassware and it surprisingly failed expectations. That's when I began to realize that I had no idea how far "off" naively using water as a volume standard could be. I'd like to share my results for other amateurs. Hopefully, I will raise the communities awareness of typical amounts of error in using water as a volumetric calibration standard. Rule of thumb data can be used to make estimates or help calibrate common kitchen glass-ware with confidence. I am also interested in collecting measurement and modification techniques/ideas for improving the precision/usefulness of glassware. This is especially important for glassware that has been damaged or is defective.

I purchased a 50ml volumetric flask on ebay that was "refurbished". It cost $12 instead of$40 new (and I didn't have to buy six of them). The flask was still optically clear with no haze, Pyrex grade A, T.C. 50ml @ 20C. My initial assumption was that even though it might not be perfect, it looked like it was well cared for and it's error would still likely be less than a grade B flask. The flask was marked with a maximum error of +-0.05mL.

According to NIST, the density of water at room temperature ought to be 0.99821 g/mL. ( My house is 71F ~= 21.5C ; so, 0.99789 g/mL ) According to physics sites, water pressure causes negligible density changes unless 10's of atm are involved. Therefore, I ignore atm and expected to weigh 49.894+-50mg of water.

That's not what I got.

After weighing the flask (AKA Tare weight); I filled the flask with R.O. (Reverse osmosis) water to the inscribed line and reweighed. I also have calibration weight set so I know that nothing was wrong with my scales, but the net water mass was light by over 200mg (~4mg/mL). Even cheap jewelry scales can pick up this large an error, let alone my precision scale.

There are two things I noticed, mirco-bubbles were forming on the glass of the flask, and there was a small lump of something on the inside of the flask behind a scratch mark on the outside. That's what got me to thinking about repairing damaged flasks. And I realized that I didn't have any idea how much dissolved gas is in water (I assumed it's negligible but it isn't). Those bubbles took up noticeable space. Even using a teflon stir bar (without the stirrer) and neodymium magnets to drag it around getting rid of bubbles was hard. I realized that I could heat the water, drive out the gas, and then let it cool ... (which works to get rid of bubbles); but during the cooling period it would re-absorb gas.

This is when I decided to consider various ways to enhance the usability of flasks, and recalibrate them.

 Quote: Originally posted by DraconicAcid I think your best best would be to re-mark the volume with a very thin piece of electrical tape or duct tape. It's easy, close enough, and not going to come off under normal washing conditions.

But before I did that, I wanted to make sure I was really measuring water density and not some kind of systematic error due to my R.O. water. I've decided to look for a common (systematic) error among the flasks before fixing my first flask. I bought two more flasks, one which looked perfect ... paired with one that had been scrubbed too hard during cleaning and showed a patina. (Pair price $34 delivered. ) After researching I learned that Pyrex flasks are calibrated so that the scribe line should be at the BOTTOM of the meniscus. https://en.wikipedia.org/wiki/Meniscus_(liquid) But even after re-measuring carefully with bubbles knocked off I still got 49.652 grams on my original flask. It's off by over 240mg. The other two flasks (same Pyrex brand, etc.) measured 49.697g and 49.789g. Both of them are closer, but both are off by over 100mg, and out of spec. I'm concerned about heating the pyrex flasks to de-gass the water,and have only removed bubbles mechanically so far because ...  Quote: Originally posted by WGTR Also, as an FYI, don't ever put volumetric glassware in an oven. It'll go out of calibration. Looking at the bottom of the flasks, the method Pyrex(TM) used to calibrate them was obviously some kind of robotic press that adjusted it. It's not like smooth Earlenmeyer flasks or other glassware I've seen. Stressed glass can be annealed and change shape as it relaxes. At some temperature, the calibration would change. I'm going to ruin a flask on purpose to test that, soon. But, the error I'm measuring is obviously systematic, as I can't believe three Pyrex flasks would all be off on the "light side". This bolsters my suspicion: @Artemus Gordon Quote: Originally posted by Artemus Gordon  Quote: Originally posted by Actinium Would Deionized water be better? and is there infact a good way to calibrate your Cylinder? I know that the top has T.C. (to contain) and T.D (to deliver) and at 22c. but if density is relevant to T.D.S. than the measurements are not absolute, so how infact to measure accurately? Thanks. -Ac- I always use steam-distilled water rather than DI water, mostly because I am more familiar with the process, but for home lab use I don't really think it makes any difference. As Blogfast25 said, the dissolved solids are very, very low for both types. Yes, you can calibrate your volumetric vessels. ** snip ** [Edited on 7-10-2014 by Artemus Gordon] So, I bought steam distilled water from the store, but ended up letting 50mL set out over night. It weighed 49.76 g and no mirco bubbles formed in the flask. That's a weight 100mg heavier than the reverse osmosis water in the same flask. Unfortunately, distilled water from the store is ozonated so I didn't bother doing an immediate measurement it wouldn't be NIST quality or repeatable. In order to truly check calibration of a flask, I've realized that I need to control three sources of error. I would welcome thoughts on how to do it/constructive criticism as this would probably be useful to other experimenters. 1. Total dissolved solids (which as a general rule increase the density of water and are not found in distilled / R.O. water); 2. Temperature expansion. ( Can be computed for water via. NIST tables and glass. ) 3. Dissolved gasses. ( Use a known gas at a given barometric pressure to calibrate. ) Glass has a linear coefficeint of expansion; for borosilicate glass (Pyrex) it's 3 ppm/*C and I'm using a 20*C flask at 21.5*C. ( 100% + (T2-Tc)*Coeff)^3 * RefVol = NewVol ( 1.0 + (21.5-20)*3e-6 )^3 * 50mL = 50.000225 ( Negligible. < 1 micro L ) For normal household glass, coefficient is 8.9e-6, ( 1.0 + (21.5-20)*8.9e-6 )^3 * 50mL = 50.0006675 ( Still Negligible < 1 mirco L. ) I don't think the flask size change is important as I can only measure to +-1mg. That leaves only dissolved gas as an explanation why my measurements are so far off. I found this: http://iopscience.iop.org/article/10.1088/0026-1394/19/2/002... Running the computation, for 21.5*C, I come up with: ( -4.612 + 0.106 * Tc*C )= delta mass. ( -4.612 + 0.106 * 21.5 ) = -2.333 mg/mL --- 50mL ---> -116.65mg That means, after equilibriating in air at approximately 1atm, 22.5C, water should have a density of: 0.99789 g/mL - 2.333 mg/mL = 0.995557 g/mL -- 50mL --> 49.778 That's very close to the volume I measured in the best looking pyrex flask I have with no scratches, or blemishes. 49.789g - 49.778g = 11mg error. (That's within the flasks spec). So, indeed dissolved gasses are a real problem for calibration of volumetric flasks. There's often Ozone in distilled water from the store and there's always a tiny amount of uncontrolled air under the cap, too. Although air is a mixture who's composition is fairly constant around the world since 1985 (when the linked above article was made) there's no guarantee that it will remain so in cities with smog. I'd like to figure out a calibration gas which is easy to get and relatively pure. For example, CO2 can be bought as dry ice, soda water, or butane lighters will produce butane gas if not struck. Unfortunately, Henry's law's constants are only good at a fixed temperature and I don't know how to compensate it; nor does Henries law tell me how much a volume will change, only how many moles of gas will dissolve. Does anyone know if the volume displaced per mole dissolved is approximately constant? Or does it follow a totally nonlinear formula even when at low part/million? Dr.Bob International Hazard Posts: 1989 Registered: 26-1-2011 Location: USA - NC Member Is Online Mood: No Mood I sometimes use volumetric flasks at work, and have also seen some errors in the volume, based on weight. If you are being very critical on concentrations, then you can use the volume as a starting point and then adjust by weight, but you will need a 4 place balance to get much more accuracy. But it is rare that we have to go to that extreme, except for special projects. Most cases the volume in a volumetric is within 1% and rarely are the chemicals involved that pure, often organics contain 1+% in solvent/water weight so that is much worse than the volumes involved. And if you want volumetric flasks, I have some used ones and a few smaller new ones as well.$12 is way too much to pay for a 50ml one.
semiconductive
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 Quote: Originally posted by Dr.Bob Most cases the volume in a volumetric is within 1% and rarely are the chemicals involved that pure, often organics contain 1+% in solvent/water weight so that is much worse than the volumes involved. And if you want volumetric flasks, I have some used ones and a few smaller new ones as well. $12 is way too much to pay for a 50ml one. The ones I bought were lifetime-red, Pyrex class A. So the extra price is in part because of the name and coloring. I know I overpaid, but I like the red line for visibility. I bought it as a reputable brand, in hopes of not having any problems to start with. But I already have three of them, so there's not much point in buying more unless there's an advantage in quality. You're right about most chemicals; However, I eventually have a goal of making semiconductors from liquid baths. Extreme purity will eventually be required; although that's mostly achieved with recrystallizations and electrical voltages; none the less, I want to make my lab as precise as I can with low cost equipment. Right now, I'm more concerned about getting used to making measurements (I'm a newbie); figuring out measurement errors and where they come from. The second thing I want to know is how calibration can be ruined and flasks repaired or improved. I have time, more than money. One of the things I've noted with flasks is that they all have randomly varying tare weights. Two 50ml flasks won't measure the same mass, let alone a mass that's an even number of grams, or tenths of a gram. Are your flasks different from Pyrex? I would like to either get or make a volumetric flask with a uniform tare weight that can be reproduced. A uniform mass on multiple flasks would allow me to leave my scales zeroed rather than doing multiple tare weight compensations. ( It's also harder to make mistakes and that's worth time and$\$ )

Right now, I'm thinking of two ways that I can modify a borosilicate flask's weight and volume. I can sand the outside of it, or boil the inside of it with sodium hydroxide (or fluorides) to slowly etch glass into sodium silicate. I can also heat it to soften the glass on the bottom of the flask to make bigger changes in volume.

But if I etch the glass using sodium hydroxide, (or a fluoride acid), the surface will become hazy and silicic acid will become embedded in the glass. I'm unsure if I can flame polish the inside of a flask because it's hard to get a brazing tip inside.

I know heating silicic acid to a few hundred degrees C can turn it back into silicon oxides; but I'm unsure if the I can smooth the surfaces out.

Another problem that I discovered is that some of the flasks I have (with a ground glass stopper) will leak a drop or two when I turn them upside down. That's when I was trying to dislodge bubbles in the liquid I was trying to measure. So, I'm interested in techniques to make ground glass stoppers seal tighter. eg: maybe silicon carbide dust and a lapping technique, I'm not sure.

[Edited on 9-12-2017 by semiconductive]
semiconductive
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Ok. I discovered that butane gas has a well known water solubility over temperature and yields precise measurements. Propane is even better, but I'll experiment with butane first since a lighter is easier to handle than lugging a propane tank into the lab.

https://sites.chem.colostate.edu/diverdi/all_courses/CRC%20r...

Std. dev. = ±0.012%
Temp. range = 273.1 to 347.15
Mx = 58.123 g/mol
moles( butane/water ) = exp( -280.525 + 14604./T + 38.7599*ln(T) )

From the mole fraction, I can compute Henries "constant" at all temperatures of interest.
Now, If I the volume of water displaced per mole of butane is reasonably linear, I will have everything I need to test flask volumes precisely.
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Rather than risk irreversible damage to your volumetric flasks
you could add weight rather than remove it
to make all of your volumetric flasks tare the same,
e.g. different lengths of stainless steel wire wrapped around the neck,
or match each flask with a stopper, and modify the weight of the stoppers, or ..........

BUT why do you want to use volumetric flasks at all ?
It is much easier, and more precise, to WEIGH your liquids
... no need for temperature compensation.

IF you intend to use burettes for titration etc.
then it may be worthwhile checking their calibration
as I find that weighing in this situation is more difficult.

P.S. I have not yet come across a situation where the precise concentration of a solution is important, e.g. 3.000M
it is only important to be near the target concentration
and to know the actual concentration precisely, e.g. 2.935M +/- 0.1%

P.P.S. For me, maintaining 0.1% accuracy is not easy,
When I titrated my acids vs. bases vs. diy reference I was unable to maintain 0.1% accuracy, even in such a simple situation.
You may want to try such an exercise;
e.g. Dehydrate sodium bicarbonate to sodium carbonate and make up a c1M 'reference' solution.
Use the reference solution to titre your acids,
then use each of your acids to titre your bases.
This requires a lot of work and a lot of reactants,
but if you get consistent results then you know that your techniques are good.
IF you do this, note that some useful reactants will be produced and may be worth saving (if not too contaminated with pH indicator)
(ammonium nitrate, potassium chloride etc.)
or you could economise by using 0.1M solutions ... (I've not tried)

[Edited on 9-12-2017 by Sulaiman]

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 Quote: Originally posted by semiconductive There are two things I noticed, mirco-bubbles were forming on the glass of the flask, and there was a small lump of something on the inside of the flask behind a scratch mark on the outside.

If the flask isn't full of water then it won't have the right volume of water in it.
Clean it and try again.
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I wish all same sized glassware weighed the same as well, but not only can manufacturers not easily make things all weigh the same, but every time you handle the flask, wash it, scratch it, or, worse yet, wash it with base, you will alter the weight slightly. I see the weight of my rbfs, which are tared in pencil on the white spot, change slightly over time, mostly going down. Scraping a solid from a flask, soaking in a base bath, or microscopic chips on ground glass joint edges all slowly erode glass from the flask, and the weighs go down over time.

Or worse yet, stuff can deposit on the glass and not come off, like Pd metal from Suzuki RXN, polymers formed, and more. Most of my rb flasks at work have pale circles etched into the bottom where a stir bar was left stirring for days, and if any solid is present, that will grind off some glass. So keeping a constant weight is nice, but not practical.

Sulaiman is correct that you could bring them all up to a common weight. Standardized weights are often made by grinding off material until the weight is lowered to a set point, but that is not easy for glass items. Using weight to make volumetric standards is very common, we do that routinely, the density of many compounds is known to 4 digits or more at set temperatures. Or making an approximate solution and then titrating it or evaporating a known sample and weighing, that is also fairly accurate. You can then even recorrect the conc. and re-test it. That is how most commercial solutions are made.
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Fundamentally, if you want to know how much stuff you have, you measure the mass- because it's relatively straightforward to measure that to good precision (don't for get to allow for air buoyancy- and you haven't mentioned that so I wonder if you were aware of it).

Measuring volume is fine- but the volume of a given amount of stuff varies with temperature.
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 Quote: Originally posted by Sulaiman Rather than risk irreversible damage to your volumetric flasks you could add weight rather than remove it to make all of your volumetric flasks tare the same, e.g. different lengths of stainless steel wire wrapped around the neck, or match each flask with a stopper, and modify the weight of the stoppers, or ..........

Modifying the weight of stoppers is one of the things I am doing. But, if there are two different stoppers that have different weights ... they look the same; so it's easy to put the wrong stopper on the wrong flask. I'm hoping to reduce errors, so making all stoppers the same tare is a must.

The first thing I'm doing is marking the flasks with sharpie markers with the tare weight. Sharpie can be washed off with acetone, but otherwise is relatively permanent.

Adding weight with wire is a reasonable measure.

 Quote: BUT why do you want to use volumetric flasks at all ? It is much easier, and more precise, to WEIGH your liquids ... no need for temperature compensation.

The first reason was to accurately measure the density of a liquid, so I could calculate the approximate molar concentration. This allows me to decide how much liquid to use to produce mostly copper I chloride, rather than copper II chloride. ( I realize now, that it could have been purely done by mass; but I didn't realize that before. )

Of course, the original purpose would be affected by air as well ... (and the mass is affected by air) and since air can make 50ml of water weigh wrong by more than 100mg ... it's important to figure out how to at least estimate the error in measurement that is likely. Most liquids, no matter what they contain, will obviously be affected by air saturating them.

 Quote: IF you intend to use burettes for titration etc. then it may be worthwhile checking their calibration as I find that weighing in this situation is more difficult.

I'll keep that in mind, and the experiments you suggest with pippets.

[Edited on 9-12-2017 by semiconductive]
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 Quote: Originally posted by unionised Fundamentally, if you want to know how much stuff you have, you measure the mass- because it's relatively straightforward to measure that to good precision (don't for get to allow for air buoyancy- and you haven't mentioned that so I wonder if you were aware of it). Measuring volume is fine- but the volume of a given amount of stuff varies with temperature.

Buoyancy ... now that you use that word, I realize I partially overlooked it. I was thinking that butane gas in the flask would have to be compensated for mass since it has a different mass than air; but otherwise the pressure from air would be the same on flask as on the mass scale, and therefore cancel out; but now I realize that's wrong. The volume of the object determines the uplifting force experienced due to air pressure and the mass inside the object determines the downward force on the mass scale.

When my scale sits for hours, I notice the tare weight will drift from zero by up to 3 milligrams. At first, I thought that was because of electronic drift and heating; but now I wonder if it might be due to changing barometric pressure.

Dry air has an approximate density of 1.2041 kg/m^3 = 1.2041 mg/mL at 20C. ( And who knows how much more CO2 there is in the air since the value was measured... )

Therefore, 50mL of volume displaces ~60.205mg of air. So anything with less than 60.205mg mass/50mL will want to rise in air like a helium baloon. (I'm ignoring the tare weight of the flask).

However, the mass standard using water assumes measuring at STP so that 60.205mg is already accounted for in the mass definition of water??

I'm unsure of what's going on, but I'm going to assume that the definition of mass includes buoyancy at sea level. (Makes me wonder about rocket calculations I did in physics years ago for getting a rocket into space based on the mass....)

I assume we're only really interested in pressure changes from STP affecting buoyancy.

In a typical day, random barometric / air pressure can change by around 2millibars. or ~0.2% of average pressure at sea level. Since PV=nRT, is a linear equation in P,n ; then the mass of air per mL would change by 0.2%. That's a variation of around 0.12041mg. So, in reality normal drifts in buoyancy due to air pressure can't be measured on my milligram scale.

The 3 to 4 mg drift I am seeing over several hours really must be related to the electronics drifting.

I don't know how much humidity changes the density of air, but I doubt it's a 100% increase; so even that's not going to be a factor. It would be barely measurable on a 500mL flask....

However, this does raise the question of how much altitude will affect the buoyancy of 50mL of water. https://en.wikipedia.org/wiki/Pressure_altitude

Reworking the equation to compute decimal fraction percentage change in pressure from STP:
dfpct=(1 - (1 - AltFeet / 145366 )^5.255303)

I'm at around 75 feet above sea level, so I can expect a pressure change of: 0.0027
60.205mg * 0.0027 = 0.1625 mg error in mass due to altitude. (insignificant.)

But someone at mile high 5280ft, boulder Colorado, would find:
60.205mg * 0.1767 = 10.638 mg error in mass due to altitude. significant.

Unless I've made a mistake in my thinking ... air pressure will in fact affect the gram mass standard based on water for some experimenters !!!

This is something that physics fourms people essentially told me would not be a factor, since air pressure doesn't change the denisity of water significantly. But apparently buoyancy is a different issue.

[Edited on 9-12-2017 by semiconductive]
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 Quote: Originally posted by semiconductive However, the mass standard using water assumes measuring at STP so that 60.205mg is already accounted for in the mass definition of water??

I believe that this assumption is incorrect,
(e.g. what would be the density of oxygen ?)
.. that has a significant effect when working to high precision.

[Edited on 9-12-2017 by Sulaiman]

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semiconductive
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Quote: Originally posted by Sulaiman
 Quote: Originally posted by semiconductive However, the mass standard using water assumes measuring at STP so that 60.205mg is already accounted for in the mass definition of water??

I believe that this assumption is incorrect,
(e.g. what would be the density of oxygen ?)
.. that has a significant effect when working to high precision.

[Edited on 9-12-2017 by Sulaiman]

A mass scale has to have a reference (calibration mass) at a known density.

Consider, if you took a balance beam and operated it under water. Now, take two 1 gram weights, one of which has a density of 0.5gram/mL , and the other which has a density of 2.0gram/mL. (high precision isn't important). Even if they "magically" both contained exactly 1 gram of mass ... one of them will clearly float, the other will sink.

The balance arm, then, will claim that the mass that "sunk" has more mass than the one that "floated" away and is rendered useless because of the difference in density.

The same is going to happen in air, but the problem will be much less obvious and show up in the final digits of a meaurement (milligrams or micrograms.)

All digital scales, including mine, have to be compensated or calibrated using a mass with some finite density ; otherwise, they are nothing more than a weight scale and not a mass scale. The gravitational constant of the earth actually varies depending on where you are. Mass scales are supposed to be immune to that...

I thought the idea of water, and volume, was meant to produce a repeatable standard value. I gram = 1CC at 4*C. There is, of course, a limit to how precise a mass standard water can be. I don't know how many digits of precision (mg) the definition of water for mass is accurate to; that's something I'd like to know.

As to the density of Oxygen, I just read a disturbing paper referenced by NIST. Apparently, due to some kind of interaction with CO2 ; Oxygen in the atmosphere vs. water have different isotope distributions. Is that what you are talking about, or do you mean something different? I haven't studied it yet...

https://srd.nihttps://srd.nist.gov/JPCRD/jpcrd104.pdfst.gov/...

[Edited on 9-12-2017 by semiconductive]
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I only meant that the density of oxygen is so similar to air that without bouyancy compensation a meaningless answer would result, hydrogen and helium for example would have negative mass, sorry for the confusion.

e,g, air is c784x less dense than water at sea level ... a 0.127% error if not compensated for.
A stainless steel weight would only need a 0.016% correction for bouyancy.

[Edited on 9-12-2017 by Sulaiman]

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 Quote: Originally posted by semiconductive I assume we're only really interested in pressure changes from STP affecting buoyancy.

No the other thing that matters is the density of the thing you are weighing.

Very high precision mass comparisons are done in vacuum chambers.
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Quote: Originally posted by unionised
 Quote: Originally posted by semiconductive I assume we're only really interested in pressure changes from STP affecting buoyancy.

No the other thing that matters is the density of the thing you are weighing.

Very high precision mass comparisons are done in vacuum chambers.

Right, but the thing I am measuring is a liquid inside a fixed volume. So, it's buoyancy is implicitly computed when measuring the mass. I purposely neglected the mass/buoyancy of the glass container because it's a tare mass and it's buoyancy is zeroed out. When I measure any mass inside a fixed volume container, the density is implicitly computed. So, the water density was already figured into my equations.

OTOH: Water can't really be put in a vacuum chamber. It will turn to ice, boil, etc.

My target purpose is to produce (and reproduce) the most accurate results I can given low cost equipment and easily accessible gasses.

Some (damn lucky) amateur's will be able to get access to 4 digit mass scales and dry nitrogen, but I seriously doubt most people can afford a vacuum chamber and a scale capable of operating in a vacuum.

When the metric system was adopted in the USA, one of the "selling" points described to me in grade school was that the mass standard of a gram or a CC of volume were supposed to be easily reproduced anywhere in the world by using basic equipment and water.

https://en.wikipedia.org/wiki/Kilogram

"The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice.[6] The final kilogram, manufactured as a prototype in 1799 and from which the IPK was derived in 1875, had a mass equal to the mass of 1 dm3 of water at its maximum density, approximately 4 °C."

So, the question is ... how was the IPK created since it couldn't be in a vacuum chamber ?
Secondly; how much does it vary in comparison to its "reproductions" ??

Pressure at sea level has changed since 1875 since CO2 is on the rise and 1atm is not the average pressure at sea level any more. The density of air has obviously changed.

Still, from the calculations I did ... these variations in standard conditions around the world are not enough to be measured by my milligram scale. Only gas entrapment in liquid water is measurable (and very significant!!!).

I think my equipment is good enough to make reproducible results to a degree of accuracy that is better than Pyrex flasks. I just need to control for gas dissolution in water using the NIST density corrections for water at 20*C to 21.5*C.

I think the original measurements for the gram were probably done in a sealed container with tared weight, or in air at sea level immediately after boiling water.

So, I've looked up the composition of air and how it might affect water:
https://en.wikipedia.org/wiki/Atmosphere_of_Earth

Common gasses have approximately the following solubility (mole fraction) in water at room temp (25C):
https://sites.chem.colostate.edu/diverdi/all_courses/CRC%20r...

The final number is a computed product of partial presure, etc. to show relative solubilities in grams.

N2: 78.084% 28.0134 g/mol solubility mol/mol= 1.274e-5 : 278.7e-6 g/mol
O2: 20.946% 31.9988 g/mol solubility mol/mol= 2.293e-5 : 153.7e-6 g/mol
CO2: 0.04% 44.098 g/mol solubility mol/mol= 6.15e-4 : 10.8e-6 g/mol
Ar: 0.9340% 39.948 g/mol solubility mol/mol= 2.519e-5 : 9.4e-6 g/mol

Everything else is only a trace amount.
If this gas mixture was stable, I would only need to do a saturation correction; but CO2 in the atmosphere has been increasing steadily, and it has over 20x the solubility of other gasses. So, a change of 0.05% CO2 is worth a change of 1% in O2. I'm uncomfortable with how far off the measurement might be (I'll check.); I also don't know when the wikipedia data was measured, or how any of the other gas percentages are changing.

http://www-das.uwyo.edu/~geerts/cwx/notes/chap01/co2_change....

Since 1958, there's been a: 355/315 ~= 12.7% increase in CO2 in the air.
So that's on par with a 0.1% change in oxygen. The solubility ought to still be accurate to almost four decimal places, assuming oxygen hasn't also changed noticeably.

That's consistent with me getting a result using the 1985 study on air solubility that was within 10mg of the ideal in a Pyrex flask.

But, if I measure water under a nearly pure gas, like butane, I'd be more comfortable that my experiment would be repeatable all over the world and in future years.

[Edited on 9-12-2017 by semiconductive]
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You can weigh water in a vacuum chamber- you need to use a sealed container.
The increase in CO2 is (from a pressure perspective) more or less cancelled by a decrease in O2.
The lump of platinum alloy in France is the kilogram- by definition- and they do use a vacuum chamber for their weighings.

From an amateur science point of view, practically none of this matters.
The 50 ml flask you weighed was underweight because it had air bubbles in it.

At work we had a QA system and one of the requirements was checking the analytical balances once a day with two test masses (which got re-certified every year).
They were 99.993 odd grams and 0.49965 or so grams (I haven't needed to use those numbers in 5 years or so, but I still remember them)

The data were carefully logged for years.
The apparent mass of the weigh went up and down a little, but the two balances readings of the weight were strongly correlated which suggests that there was some factor which affected both. My guess was that it was air pressure because it was about the right order of magnitude- something like a 1 in 10,000 change.

Unless you have access to materials that are 99.999% pure (and you don't) then the ability to weigh to more than 5 figures isn't useful.
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 Quote: Originally posted by unionised You can weigh water in a vacuum chamber- you need to use a sealed container.

And that creates it's own unique measurement problems... for the sealing of the container isn't trivial.

 Quote: The increase in CO2 is (from a pressure perspective) more or less cancelled by a decrease in O2.

I'm unsure. CO2 has a different molecular mass than O2, obviously. But the earths atmosphere is not a closed system. We loose a small amount of air into space every year (eg: in the tons of gas.) due to solar wind. If we didn't have a magnetic field, the losses would be far greater than they are. Also, the density of water (and sea water) changes depending on how much dissolved gas there is in it. O2 and CO2 are absorbed at different rates. But the ocean is rising by something like 2mm per year, which can be attributed to more water ... but also could be attributed to the water being less dense, or warmer water on average.

Long term barometric records are showing an increase in pressure in some locations, on average using 50 years of measurements. In other places, apparently, there is a decrease (which I wasn't aware of before looking it up, today.) The total air pressure needs to be a weighted average over the whole globe ... and I don't see a way to actually check that.

Also, even though the density of water due to pressure (not dissolved gas) is negligible in the lab, for experiments, the ocean is very deep. A few books I came across estimates that for every millibar the atmospheric pressure changes by, the ocean will rise by something like 1 cm. (I can't check this, with my limited knowledge of water's incompressability but it seems really high.).

But what I am certain of, is that average barometer pressures are not the same as they were in the 1700's. So, an individual trying to recreate the international kilogram at the same location as the original experiment ... would have a different set of conditions to work under when trying to remove dissolved gasses from water. It's not easy to do.

http://ccc.chem.pitt.edu/wipf/Web/Degassing_Literature.pdf

 Quote: The lump of platinum alloy in France is the kilogram- by definition- and they do use a vacuum chamber for their weighings.

That seems reasonable, given it's a solid. They are eliminating all sources of variation, except radiation/neutron bombardment and damage to the mass by handling which could change the mass over time by a very tiny amount.

Since they are comparing two masses in vacuum using a solid, the only known issue that could affect the measurement is a gravitational field gradient.

 Quote: From an amateur science point of view, practically none of this matters. The 50 ml flask you weighed was underweight because it had air bubbles in it.

I've made several measurements on different flasks and kinds of water. All were underweight. The physical micro bubbles, I am pretty sure, were a result of the the reverse osmosis system storing the water in a pressure tank with blue plastic pipe that uses air as a "spring" to re-dispense the water. Since water pressure is around 20 psi ... that means the RO water was exposed to around 2atm air pressure and had double the normal amount of dissolved air. When I get R.O. water from the tap into the flask; it's a super saturated solution with air. Therefore, micro-bubbles form on the glass when the pressure is reduced to 1atm. With time the bubbles coalesce into larger bubbles (right side of picture, hard to see.) But they are hard to dislodge.

Even after letting the flask equilibriate for a day, and then knocking the gas bubbles off the flask walls; the water still has a volume over 100mg lighter than expected from NIST data.

When I used the study of air solubility from 1985, I got a weight that's within 10mg of the expected value due to (not bubbles) but completely dissolved air in saturated solution. So, that means compensating for dissolved air is the right answer, not just bubbles.

That's why I'm thinking of calibrating my flask using butane gas. It has a low solubility in water, but can be used to remove entrapped gas by giving a headspace to dissolve in.
Letting water equilibriate for a day with butane over it, and then changing the butane could get the density of water far more repeatable than with air that could vary significantly from place to place; eg: Rather than using a vacuum pump to de-gas the water, I hope to figure out the ostwald constant (L) for butane gas.

If I can collect butane gas over water using an inverted volumetric flask, and have the saturation procedure down; I ought to be able to compute the molar mass of butane by ideal gas law to a fairly high degree. That would be an excellent check for the volume of the flask.

 Quote: At work we had a QA system and one of the requirements was checking the analytical balances once a day with two test masses (which got re-certified every year). They were 99.993 odd grams and 0.49965 or so grams (I haven't needed to use those numbers in 5 years or so, but I still remember them) The data were carefully logged for years. The apparent mass of the weigh went up and down a little, but the two balances readings of the weight were strongly correlated which suggests that there was some factor which affected both. My guess was that it was air pressure because it was about the right order of magnitude- something like a 1 in 10,000 change.

It depends on how your scale maintains it's calibration; but if you were using weight or force based scales, there is also the variance caused by the moon going over head on top of buoyancy. On a kilogram of mass, the moon would cause a force difference from one side of the earth to the other of around: 0.22 x 10-5 N per kilogram weighed.

Gravity is ~9.81N on a kilogram, so that's a force change of about 1:4.5e-6?
It would be +- 1/2 of the magnitude you are talking.

[Edited on 11-12-2017 by semiconductive]
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Unless I missed it, I'm surprised that nobody has posted this link yet, unless everyone already assumes this is common knowledge: https://www.nist.gov/sites/default/files/documents/2017/05/0...
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The balance had a built in calibration mass, so any local change in gravity over the course of a day or so would be likely to be cancelled out.

Trying to weigh gases is notoriously difficult; it was traditional to use mercury to check volumetric kit. A given "error" in volume gives rise to a bigger error in mass so it's easier to measure precisely.
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 Quote: Originally posted by DistractionGrating Unless I missed it, I'm surprised that nobody has posted this link yet, unless everyone already assumes this is common knowledge: https://www.nist.gov/sites/default/files/documents/2017/05/0...

Thank you. No, it wasn't mentioned anywhere in the thread.
I am a chemistry newbie, and didn't see it on NIST. This document is very helpful!!!

Ironically, it's using the same air density formula that I came across in the 1985 study; so that means I'm on the right track. ( re-inventing the wheel.) Although the study in 1985 is only good to 20C, NIST claims the formula works all the way to 25C.

I only had one thought about how carefully the manual wanted measurements done. but.. I didn't see them mention using gloves. A fingerprint probably weighs around 50 micrograms ... not enough to measure with my milligram scale, so it doesn't matter for me. But apparently that's about the amount of weight that the international kilogram has lost since it was originally stored a long time ago.

Removing oil looks difficult. Concentrated sulfuric acid is recommended. I only have regular battery acid from NAPA auto and hydrogen peroxide to make a weak piranah solution. I suppose I can get ROOTO from Ace Hardware which is much stronger.

Does anyone have any idea why NIST warns against letting acetone mix with ethanol?
Would 99% IPA be a possible alternative?

[Edited on 12-12-2017 by semiconductive]
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 Quote: Originally posted by DistractionGrating Unless I missed it, I'm surprised that nobody has posted this link yet, unless everyone already assumes this is common knowledge: https://www.nist.gov/sites/default/files/documents/2017/05/0...

Very nice document ... thanks

CAUTION : Hobby Chemist, not Professional or even Amateur
(suffering from separation of me and my chemistry stuff)
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 Quote: Originally posted by semiconductive Removing oil looks difficult. Concentrated sulfuric acid is recommended. I only have regular battery acid from NAPA auto and hydrogen peroxide to make a weak piranah solution. I suppose I can get ROOTO from Ace Hardware which is much stronger. http://www.sciencemadness.org/talk/viewthread.php?tid=3722&a... Does anyone have any idea why NIST warns against letting acetone mix with ethanol? Would 99% IPA be a possible alternative? [Edited on 12-12-2017 by semiconductive]

IPA isn't a great oil solvent, but it's better than ethanol.
Acetone is better. (And I think their concern for mixing chemicals is that it makes it more difficult to recycle them later)
You can use a cheap good oil solvent- like white spirit- and then wash the remaining white spirit off with IPA.

Conc sulphuric will remove the last traces of grease.
Strong alkali is also good, but attacks the glass. That's not likely to be a measurable effect in a home lab.

You may also want to consider boiling the water to remove dissolved air then letting it cool under cover. It will still pick up some air, but you would be approaching equilibrium from the other side compared to stuff stored under pressure.
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 Quote: Originally posted by unionised You may also want to consider boiling the water to remove dissolved air then letting it cool under cover. It will still pick up some air, but you would be approaching equilibrium from the other side compared to stuff stored under pressure.

I've had the same idea as you ... but the more I study the issue, the less it seems like a good idea.

You're correct, but I think it causes more uncertanty than it helps.
Consider the distilled water that I picked up, that's water that has been boiled but with some unknown amount of ozone allowed into it. I let it sit in an Erlenmeyer flask overnight before making the measurement in the volumetric flask. Even with >8 hours exposure to air, that water had only about half the density error as did air saturated R.O. water compared to NIST tables. However, R.O. water when allowed to equilibriate for either >8 hours, (or several days), measured the same uniformly. That's why NIST recommended that for calibration. So, it's clear that equilibrium is reached far quicker from over-saturation than it is from under-saturation. It's easier for gas to escape from liquid than to dissolve in it. (bubbles form anywhere, but gas only dissolves at the surface.)

This is a really deep question ... how to measure the most accurately (and precisely/repeatably). A known systematic error is better than a random one that nobody knows the source of. And gas that isn't subject to change with pollution is likely more precise than one that does....

There's obviously a number of subtle problems: the kilogram was originally defined as a volume of water a decimeter square at ~4 degrees C and 1 atm. Yet if you go to the NIST site and have it plot water density in g/mL or kg/decimeter ... it never reaches 1.0. The closest it gets is 0.99997, which is not even 5 digits accurate. There was obviously a subtle problem that not even the original chemists envisioned when defining the kilogram based on water. I probably won't be able to measure that accurately, but I want my result to be at least repeatable.

Another thing that I just noticed is that Oxygen, when it dissolves in water ionizes to OH- . So there is no free oxygen molecule dissolved in water, there's only hydroxide ions. But a hydroxide ion is a normal part of water. Chemical activity can affect water density in strange ways.

Let me put this in perspective:

No gas should be less likely to ionize in water than a noble gas.
Argon is actually around 1% of air. So, Argon would be the gas most likely to not to undergo chemical ionization in water as it heats. If any gas would be expelled from water and not "stick" to it, I would expect argon based on what my teachers told me years ago. However:

http://www1.lsbu.ac.uk/water/material_anomalies.html#be

see graph 7. Clearly all noble gasses increase in solubility at a temperature slightly above 90*C. Some gasses were ALWAYS increasing in solubility at all water temperatures. Also: Graph 8, is qualitatively a 1/ inverse shaped function of graph 7. Note carefully: Both graphs agree, that at no temperature is the gas totally driven out of water although the solubility trend is harder to grasp in graph 8.

Argon is clearly in the air we breathe. ~1%.

There are water boiling charts which suggest that nitrogen and oxygen boil out of water.
However, no amount of boiling is going to entirely remove Argon, and it will selectively increase helium dissolution.

But that's not what's most disturbing to me ... for it's only 1% so .. it's a small error that could probably be calibrated out...

But from the mole data I gave a few posts back and the fact that ~50ml / grams of water is ~2.8moles; Something odd shows up when water is exposed to 1ATM air and the dissolved masses of each constituent is computed:

N2: 0.78mg
O2: 0.43mg
CO2: 0.03mg
Ar: 0.026mg
-----------------------
Total: 1.3mg (max). 25C, I'll assume ~15% lower dissolution than at 20C.
Round up: In my experiemnts, there was no more than 1.5 mg of air involved at 20C.

But that 1.3 .. 1.5mg of gasses displaces over 116mg of water (see my first post in this thread). In order to displace 116mg of water the effective (average) volume (length cubed) of the dissolved molecules to water molecules must be on the order of (116/0.99820...)^(1/3)=~4.89 x that of a water molecule. That's mind blowing based on physics, mass, etc. Oxygen and Nitrogen, are known to be diatomic molecules and the physical volume they occupy isn't much different than a water molecule. Their actual masses or sizes surely aren't 1/4 or 4x that of water molecules.

But the ratio suggests that even ~0.03mg of argon is causing almost 2mg of water mass error at 20C.

I know that rough estimates of size (in a gas, so corrections for collision) exist. These effective sizes are a baseline for physical size corrected for "average" random orientation effects of rotating and bouncing molecules; These sizes only neglect attractive forces like vander-wals. Here's the list of effective 'diameters' in kinetic situations that I found in picometers, with relative masses/molecule listed.

H2O 18g/mol 265pm
N2 28g/mol 364pm
O2 32g/mol 346pm
CO2 44g/mol 330pm
Ar 40g/mol 340pm

Note two things, none of the gasses is more than 1.5 times the kinetic diameter of water; and all of them are at least 1.5 times more massive (eg: slower moving for the same energy.) Not even the product of the mass and diameter can account for the volume displacement.

There is no way the volume the gas molecules are taking up due to kinetic motion are causing the massive displacement in water that is being measured experimentally if the gas is truly dissolved in water. (And not gas bubbles floating around with many molecules in it.)

I think it's likely that there is an attraction between water molecules that is being disrupted. eg: Every time there is a surface that water comes into contact with (whether or not it chemically interacts) there is a local density penalty in the vicinity of the disruption because the co-hesion/packing denisity of the water is disrupted. The penalty is a far larger effect than the displacement of volume by the thing that water comes into contact with. eg: Water will even likely measure a slightly different volume, if measured in a rectangular vessel rather than in a spherical one.

I have seen nothing in the literature which addresses this kind of problem, and how dissolved gas molecules likely affect water volume. But this seems to be a bit of a fundamental measurement in chemistry, and I'm probably just not looking it up right.

Each of the gas molecules is on the same order of size as a water molecule. Therefore, I would expect the amplified disruption in volume due to broken packing to be approximately the same regardless of the kind of gas interfering with the water. The actual molecules would not displace more than 2.0mg of water and their own mass would partially cancel the displacement; That would barely register on my scale but the disruption effect is going to be very large and (hopefully) regular regardless of gas doing the disruption. It depends on the total number of molecules (and likely ionizations) of gas present in the water more than the size of the gas or ion.

Notably, the density of water changes very non-linearly over the range 0-20C, according to NIST; but the volume of water displaced by gas in the 1985 study I cited earlier is very linear in temperature (and thus energy). The study gave 3 significant figures from 0 to 20C. For it to be that linear, there must be a reason why.

[Edited on 14-12-2017 by semiconductive]
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https://en.wikipedia.org/wiki/Henry%27s_law

 Quote: Henry's law solubility constant for many species goes through a minimum. For most permanent gases, the minimum is below 120 °C. Often, the smaller the gas molecule (and the lower the gas solubility in water), the lower the temperature of the maximum of the Henry's law constant. Thus, the maximum is at about 30 °C for helium, 92 to 93 °C for argon, nitrogen and oxygen, and 114 °C for xenon

So, even though some of the data I have seen on the web ( boiler maker data ) suggests that water totally looses oxygen at boiling... one of my suspicions is confirmed. It should have been obvious from Henry's law which does not depend on pressure, but only temperature. Since oxygen dissolves in water that is pressurized, when above 100C, then there is a finite solubility in water that is boiling; no matter how long it's boiled.

Boiling can not entirely remove air of any kind, and graphs which show it go all the way to zero at 100C are misleading.

[Edited on 14-12-2017 by semiconductive]

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