Challenge Questions

Why does Tom think the volume will be too small?
I can only imagine, but see below!
Is he right?
Assuming John is careful to transfer all the water, I think any systematic down-sizing is likely to be less severe than if he used the jug directly - but I'm open to persuasion

Why Tom might anticipate John gets too little mercury
Evaporation of water during pouring (should be insignificant if "precautions with regards to temperature" includes that the temperature is low enough);
Liquid left behind in the measuring cup;
Meniscus of water wetting the surface of the test-tube and causing the measurement reference to be too low down. If the tube [assumed glass] is clean and he uses pure water the meniscus should strike at an angle; although the angle and thickness may change with tube diameter, I believe that for moderate diameters the total volume above the surface reduces as the tube diameter reduces; in that case the change would result in a smaller error than using a measuring jug of similar material. But perhaps the measuring jug is not wetted by water, in which case there will be a small additional error;
Gap between meniscus of the mercury and the tube means tube is not filled (see comment on water meniscus);
He believes the measuring cup is itself inaccurate...

A reason Tom might think John will get too much mercury
On the other hand, any water meniscus will reduce the water pressure, which will increase the height of the water in the test-tube; then the test-tube will expand due to the weight and meniscus pressure of the mercury - so you'll have too much mercury (also insignificant, for a reasonable shape of test-tube capable of holding 10-ml, but I am clutching at straws here).

Anyone here got any better straws?

Well, whether the mensicus is concave or convex on water or mercury, with mercury, it will also be opaque, so there is room for error there!

I would guess the greater mass of the mercury is not going to swell the vessel appreciably or significantly more!

I think he would be better off with a scale!

Actual thermometer makers slide the tubes up or down to calibrate them, at least on the Discovery? Channel documentary series of stuff being made, so I doubt that any inaccuracy will be too big to calibrate out.

"It would be better to weigh it".
I agree entirely.
(The swelling was meant to be somewhat whimsical - an antidote to your previously stated requirement to evaluate all interactions before rejecting them)

I think I sort-of fell for the red herring - the apparent implication that the narrow test-tube was the problem. Of course using a standard measuring-jug directly would be worse, because of it's (presumed) larger diameter (unless of course the jug includes corrections for different fluids).

Returning therefore to the question, what might be the shortfall in volume? Well, I suppose a normal test-tube for a volume of 10-ml would have a diameter in the order of 1.5-cm (giving a depth of about 6-cm); in which case a "narrow" test-tube would have a diameter of 1-cm or less.
Based on the shape of mercury puddles, if the test-tube was 0.5-cm in diameter the lost volume would be (very roughly) 0.03-ml³. At a diameter of 1-cm it could be as much as 0.15-ml.

There would be some compensation due to the greater volume of meniscus in the water jug as compared with the test-tube, Because of the relationship between the density of water and its surface tension, the height of a 40^O wetting meniscus would be slightly greater than the mercury . However, my understanding is that the volume would be relatively small - so it's probably sensible to assume that the mercury meniscus dominates the effects.

So the question is whether a maximum 1.5% error is important in this case. If the scale is determined by use of a single practically-determined set-point (say pure freezing water), you'd have a 1.5-degree error at boiling temperature. That's actually appreciably better than I would expect from a home-brew single-point-calibration thermometer - and it could easily be improved by using two point calibration.

I still think Tom is worrying too much.

I agree - Tom is right. It pretty much has to be due to the positive meniscus of the mercury, which leaves a small void around the circumference of the tube; when the vertex of the meniscus is at the mark, part of the volume is filled with air. The water has a negative meniscus which means the mark slightly understates the volume of the liquid present because of the small quantity clinging to the glass.

I fear communications problems.

If the water meniscus is of any significance the amount of water in the measuring jug will be slightly more than 10-ml. Assuming sufficient care (possible impractical?) John will transfer all of the water to the test-tube (or at least substitute for what he cannot transfer). So the volume of water transferred to the test tube should be slightly more than 10-ml. The meniscus in the test-tube will reduce the height of the flat surface, but (assuming the surface area of the jug is greater than the tub's) not by enough to compensate for the excess.
But this increase in reference volume is unlikely to be significant, even compared with the small reduction in the volume of the mercury.

We are talking volume here, not weight.

Sorry, the scale would be useless.

The density of mercury is known and very consistent, so you can easily calculate the weight required. A mass balance would be fine. (In practice you would need to calibrate anything else)

"Hilda, it's so good to see you! How long has it been since we've had a mercury get together?"

"Hi Marge. Seems ages. Have you met my children? Bobby! Mary! Come away from that glass this very minute! There's no telling what you'll get if you touch that. Yech!"

I think that this question is merely looking at the difference in the way that water and mercury behave in a glass tube. Because water has a significant adhesion with the glass it can overcome the cohesion between its molecules with the result that it is pulled up the glass resulting in a concave meniscus (higher at the glass lowest in the middle of the tube). The mercury on the other hand does not have the same degree of adhesion with the glass and so the cohesion between its molecules is stronger resulting in a convex meniscus (highest in the middle lowest at the sides).

Now clearly if John is drawing his line on the tube at the bottom of the water meniscus and then filing the tube until the top of the mercury meniscus reaches it he will have less mercury volume in the flask. It should be pretty obvious to John, however, that the meniscus is different so he may draw his line at the top of the water meniscus and then fill the mercury until the top of its meniscus reaches this line. If he does the filling in this way any difference in volume between the two is due to the difference in shape between the two meniscuses (menisci?) such that if the mercury meniscus had a larger difference between its max and min than the water miniscus (which I think is the case) then the mercury volume will still be lower (but not by much).

I agree with BobD - The question is merely probing the difference between the water meniscus and the mercury meniscus at the tube surface.

However, I do not agree that John should draw his line at the top of the water meniscus nor even half way between top and bottom as this will give him much more than the required volume of mercury. The correct marking line would need to be slightly higher but only by an amount which would counteract the loss of the triangular cross-sectional area of the two meniscii multiplied by a circumference slightly less than the tube circumference- quite a difficult calculation.

Water meniscus against glass is highly variable, as it not only depends on the composition of the water but also on the cleaning method for the glass. I believe that "well-cleaned" (but unetched) Pyrex can have contact angles to deionised water between 0^O and 30^O.
John's best strategy is to ignore the water meniscus and make the mark at the height of the water surface. He can then see the height of the mercury meniscus and fill so that the mark is the appropriate position between the flat surface and the contact point of the meniscus. The additional difficulty is that although the contact angle will be close to 140^O (according to convention), the lost volume will be rather more than that indicates - and that difference will depend to an extent on the diameter of the tube.

The water will climb the inside of the tube causing the surface to be dished. The mercury will not wet the tube and it will have a surface that is domed in the center. This is the reason that the water mark will not work accurately for mercury.

The question states John needs 10ml. Tom seems to think John needs 10.00ml. Hopefully John will calibrate his 'homemade thermometer' after adding the mercury, so anywhere from 9.9 to 10.1 would be fine.

I agree that the concave/convex meniscus seems the most likely answer.

The meniscus of water goes up the glass, but the meniscus of mercury goes down the glass. Hence the small volume difference. I'd just weight out 135.5 grams of mercury and be done with it.

Because of the shape of the meniscus. This goes up the sides with water, down with mercury. So he marks the test tube a little lower than if there were no meniscus. Then when filling to the mark with mercury he loses approx same again.

Cheers.......Codey

i even knew that one but i did not knoe it was called meniscus in english, i thought that word had something to do with (bad) knees

Going around in circles.

The only significant factor is the temperature,and if you want to nit pick the purity of the water. go to http://www.simetric.co.uk/si_water.htm.

so one cu cm is equal to 1 cc of water at 25degrees C. and this will be the same as mercury at 25 degrees. So long as the temp is the same 1 cc of any liquid is the same as 1cc of any other liquid.

I know all about all the hazards of playing with mercury (after all, I was reasonably normal before I began turning pennys into "dimes" to impress the other kids), but this is one that really cries out for trying. And, the key word is "thin".

Regardless of difference in volume due to the meniscus, whether water or mercury, the DIY thermometer will need to be marked with a scaled and calibrated.

If the object of the exercise is to make a thermometer then why not go straight to the calibration process.

I think everyone nailed this one right away as being a meniscus problem -- but if John uses an eyedropper (or pipette) to fill the test tube, he might be able to avoid the problem. If he slightly over-fills the test tube with mercury, past the mark he made, then uses the eyedropper to carefully remove some of the mercury, the falling level of mercury will take-on a concave mensicus similar to that of the water. It might take a few tries to get it just right, but he should be able to match the line he marked using water.

THE MENISCUS STORY IS A RED HERRING!!!

Again density which is temperature related is the ruling factor.

While we are at it does everything disappear at -273 degrees?

What nonsense. The challenge says that "John is taking precautions about temperature". Even if he was really cavalier about temperature the problem would be smaller than the expected effect of surface shape. For a 10OC difference between reference temperature and actual temperature the error would be less than 0.18% (the volume expansion coefficient of mercury is 1.8x10^-4 /^OC, and the expansion of the measuring jug will provide a small amount of compensation).

And no, things do not disappear at -273.15^OC. The volume of a theoretical ideal gas would become zero, but ideal gases don't actually exist. Real gases also change state at much higher temperatures than that - and that reduces expansion/contraction rates by many orders of magnitude.

More rubbish. He just has to weigh out the mercury to get the volume he needs ! Meniscus is not a factor it is due to surface tension effects and bears no relation to the actual volume - it only matters in a barometer or a thermometer when thin tubes are involved but that would be a factor to consider in calibration - one always reads the top of the meniscus. It is related to the shape of the sample not the volume.

The main reason in a barometer is different - the surface tension actually drives the mercury down the tube.

But if you look at the shape of the meniscus and do the sums I think you should be able to confirm that the error if you measure from the top surface only (in a 1-cm diameter) would be about 0.15-ml. If you calculate a signifiacntly different value I'd love to see your sums.

Unfortunately that doesn't work in practice, because mercury "quite determinedly" maintains a near-constant meniscus shape against glass.

A more practical correction would be to push a rod that nearly fills the tube into the surface of the water so that it rises a known distance up the size of the rod, and mark the location of the rod. If you repeat this for the mercury you will have reduced the meniscus error.

But it's still easier and more accurate to use the test-tube as a container in which to weigh the mercury.

Au contraire.

From How to Read a Mercury Barometer:

"The barometer is said to be falling when the mercury in the tube is sinking, at which time its upper surface is sometimes concave or hollow; or when the hand of the wheel barometer or Aneroid moves to the left. The barometer is rising when the mercurial column is lengthening, its upper surface being convex or rounded, or when the hand moves to the right."

My comment was based on observations of mercury in air. The theory is that adsorbed gases prevent wetting of the glass surface, so it is likely that the situation will be different in a barometer where the gas pressure is very low. It is also probable that different glasses have different behaviours - test-tubes tend to use low-expansion glasses to minimise susceptibility to thermal shock, whereas I imagine that barometers would use glasses with relatively low melting points for controllability of manufacture.

I'm sorry to tell you, but mercury will not concave like water would, because it will not stick to the glass like water would. And water will not concave either if it is put in the tube without ripples. if you use a small tube to insert the water, keeping the end of the tube at the level desired and filling it very slowly. Just like filling a glass of water to it's limit, the water would go up and above the edge of the glass, as long as the rim stays dry.

I believe this makes the meniscus theory completely obsolete.

Time to look for something else.

Think guys, think.

There are heavy walled glass containers designed to hold dense fluids like mercury. Tom knew that thin walled test tubes would break when mercury was poured into them and that John would eventually run out of mercury, leaving him short.

Who the heck marked this "off-topic"? It's not 100%, but it's getting warm. Just cancelled that with a GA.

Test-tubes will withstand thermal shock and chemical freeze-expansion. The weight of mercury compared with such expansion should not be a problem - especially not in a narrow tube.
You surely don't think that diffusion into the tube could be significant in the sort of time the process would take? Note that even solutions (that can absorb the surface air that repels the mercury) take long periods before changes in concentration are significant

No, I don't think it will break. By the way, I assume the post didn't really mean a standard test tube? But, my point was the previous answer was not off-topic. It may not have been correct (though I think he's thinking in the right direction), but he wasn't off-topic. By the way, have you ever tried to put mercury in a thin tube? Interesting process.

"Have you ever tried to put mercury into a thin tube...."
Nice point

That depends how thin. I'm assuming it is only thin compared with the test-tube dimensions that you would normally use for a 10-ml volume - so probably around 1-cm in diameter. That is not too bad. Smaller than 5-mm diameter but capable of holding 10-ml would not (to my mind) be described as a test-tube. I think (not certain) that 5-mm is still doable - either using droplets or via a reasonably wide-based funnel - but would I be right in assuming that the depth left in the funnel at the end of pouring could be quite amusing?

Either way, for controllability I imagine John would need to overfill and then displace surplus liquid with a (glass?) rod.

I think the problem is getting too little water into the test tube. When the water is in the glass test tube, it is easy to see the meniscus but not so in the measuring cup if the measuring cup is not transparent. John may likely have put too little water into the measuring cup because the meniscus was not noticeable and he fill the cup only until the water touched the 10 mL mark. This would have been less than 10 mL. Any trapped air bubbles may also have not been visible until placed in the test tube where John would have seen them and tapped on the test tube until the released the surface.

The surface tension of mercury is very much lower than that of water so the shape of the meniscus will give rise to an error resulting in a low reading.

Maybe John can just freeze a hunk of mercury and cut an appropriately sized cube. I don't fancy working out the size, but it might solve his meniscus problem. OK, I'm being silly, yeah yeah, but I'd like to know if you could freeze and cut the stuff.

As usual with these challenges, I'm stumped.

While reading the question, my first though was the meniscus too, but I did a little research on the internet and found that the meniscus of water in a test tube is typically a few micro liters (someone correct me if I'm wrong on this).

Basically what I'm getting at is that the meniscus seems negligible. I see everyone is discussing this in their response but maybe this isn't the right answer.

I would think human error would account for more than this.

Alright, I did a little more research and here's my guess.

Mercury doesn't adhere to glass surfaces and it's surface tension is more than 5 times greater than that of water. At the same time, water does adhere to glass surfaces so it would have a different meniscus than mercury (water's being concave).

So the 10 mL of water would have a concave meniscus resulting in a few micro liters difference and the mercury (convex meniscus and air in the tube) would most likely result in a few more micro liters difference.

I still think these differences are irrelevant though.

You can get the shape of a mercury meniscus from this reference (originally given in post #4). You just need to remove the part of the droplet that is below the point where the mercury reaches the contact angle (I'm told it is typically about 143^O for clean Pyrex that has been exposed to air). That is the origin of my estimate that the missing portion could be in the region of 0.15-ml (for a 1-cm diameter test-tube).

Excellent solution Kris. GA from me.

So long as you cover the base of the tube, wouldn't a couple of ml for the first mark reduce the error?

You'll have to explain - I haven't any idea what you mean

Proposed revised position for first mark:

Put enough water in the test tube so the surface is in the uniform part of the tube (no need to measure this volume, but it should require less than 2-ml), and make your first mark.

The remainder of the process is unchanged.

Less mercury, and needs a smaller tube.

Ah, I see what you mean now. Sure, that would work just as well, and there are probably lots of other varaiations. I'm still sobing because nobody answered my proposal to freeze + cut the mercury to size .

GA from me Kris. It's one thing to 'answer the question', but to solve the problem is worth more 'brownie points' any day.

This whole thing kind of reminds me of something I was told a long time ago when I was trying for precise measurement of a piece of steel I was about to cut with an oxy/acetylene torch: Measure with a micrometer; mark with chalk; cut with an axe.

compute the weight of 10ml of Hg - then weigh it out on an accurate scale.

Edmund

For those of you who do not think that this challenge is about the meniscus, please take a look at this link:-

http://en.wikipedia.org/wiki/Meniscus

Test tube A has water in it.

Test tube B has mercury in it.

It should be obvious that if John has managed to precisely obtain 10ml of water and uses the mark shown on A to measure out his mercury in B, he will be measuring out slightly less than 10ml.

A homemade mercury thermometer is only going to have an accuracy of about 1% at best, so the effect has to be that much or greater. The meniscus just doesn't do that, though the OP might not have realized that?

Hi TVP45,

I am of the opinion that the homemade thermometer bit is just part of the story that makes the challenge more interesting to read. I don't believe it has any relevance to the actual issue of the volume shortfall. This is why I believe the challenge setter is referring to the meniscus issue.

That is why you have to weigh it! the meniscus will be there no matter what the bore of the tube and the graduation mark will have to cater for it. The volume remains exactly what it is and the meniscus is a different problem and only relates to the use and bore of the tube.

The question was based on volume - perhaps the intended answer has something to do with weight versus volume in accuracy of measurement.

That is correct to get the right volume you can weigh it (using density & correcting for temp) They are interdependent. In the paint industry paint is packed by weight but sold by volume - it is easier and more reliable as weight is constant and volume is temperature dependant.

Due to the surface tension of the water, a small amount rides high on the edge sticking to the glass. Mercury, on the other hand, does not have this tension and instead the edge of the surface tends to repel the glass leaving what might be described as a small groove around the edge of the glass on the surface of the mercury. Thus there is less mercury than water when each is properly measured.

tomm

If proper measurement does not include correction for the meniscus, the larger diameter of the jug could mean that more water is poured into the tube in the first place.

Because Tom is not as bright as all of you. He thought that because mercury is heavier it would compress and take up less volume.

I think I misread this question (what else is new?) and started thinking about a thin thermometer tube rather than a thin test tube. So, I'll back up and try again.

The question asks for 10 ml of mercury to be measured. A good pedantic fellow (which I often am) would say that means anything between 5 ml and 15 ml since it has only one significant figure. But, common usage often gives 10 ml when 10. ml is meant, so let's assume that. That means anything between 9.5 ml and 10.5 ml is just fine.

So, he wants to measure 10. ml in a thin test tube. The smallest one that holds 10. ml is a 15 mm x 125 mm. Let's assume the wall thickness is 1. mm and the bottom is square, just to keep all the numbers simple. So, the ID is 13 mm, more or less.

The standard single meniscus correction for a 13 mm tube is 0.046 ml, so that would need to be subtracted from whatever reading he thinks he has.

We don't know how he measured the 10. ml of water. Presumably, he didn't use the aforementioned measuring cup since they have errors well over 1 ml. So, we'll give him a graduated cylinder. Parallax error is often as much as 0.5 ml, so we'll give him a nice mirror to hold behind. Even in a high quality cylinder, the dreaded line width error can run 0.2 ml, so we have to take that into account.

Further, we have the problem of getting all the water out of the cylinder and into the tube. Since a single drop of water ≈ 0.05 ml, it takes only a few drops left in to give us another 0.2 ml error. OK, we could use weight, so we'll do that.

Now, he made a line on the tube and we ought to account for that somehow, perhaps say 0.05 ml.

Now, when he pours the mercury into the clean glass tube, one of the big problems will be air that is invisible and trapped between the wall and the mercury. It's difficult to estimate that volume, but it screws up density measurements big-time and has to be eliminated by various means, especially vacuum. So, let's say he got all that out.

Now, he has a measurement that has perhaps a 0.5 ml uncertainity (I'm not clear on how to sum all the errors and I don't think it matters). The meniscus gives an additional error (which may add or subtract) of 0.05 ml, all for a measurement that has to +/- 0.5 ml to start with.

Nope, not the meniscus.

And, of course, Roger Pink could always pull out that little vial of mercury chloride he keeps to put in Penguins fans' beer , put a couple drops in the mercury and ZAP, no meniscus - flat as my wallet.

Does no meniscus also mean fewer bubbles?

I dunno. I never tried it; the stuff really is pretty deadly. But, apparently instrument makers used to use it in barometers. Makes you cautious about handling those pools of mercury.

I have nothing against penguin's fans. It's the penguins I don't like. Fortunately there are plenty of others slipping mercury in those penguins' food, I don't have to bother.

This is now an exercise in futility. Original entry lost !

I give up.

Goodbye.

The problem is that water wets the test tube and will have a concave meniscus, while mercury does not wet glass and has a convex meniscus. For the same height mercury will have a smaller volume equal to the difference due to this. Bioramani

I started to think about a "home-made" mercury thermometer - and I found that precise measurement of the amount of mercury was irrelevant.

Provisional method (several essential safety precautions are omitted): Get thick-walled capillary tube. Seal one end over Bunsen flame. Blow thermometer bulb. Bend tube about 90-degrees near bulb. Place bath of warm mercury (slightly below minimum operational temperature) in vacuum chamber. Evacuate to extract worst bubbles. Vent and cool everything to just below minmum operating temperature. Fix tube with open end under surface and the section of tube that is immediately adjacent the bulb pointing vertically upwards from bulb. Evacuate and let dry air back in. Adjust position of tube opening and repeat. Repeat whole cycle until tube is full to bend. Remove thermometer end from bath, maintaining orientation, evacuate once more and heat slowly (use old-fashioned lamp bulb?) to maximum operating temperature (to expel residual bubbles). If large bubble reaches bend, vent (if possible minimising cooling of the thermometer) and reorientate tubes so that the bubble can be extracted. Evacuate and heat slowly until you see bubble rise. You may need several cycles of reorientation and evacuation before you can reach maximum operational temperature. When you have, remove thermometer from vacuum enclosure, and calibrate.

In addition to the problem of the meniscuses (menisci?), there is the difference in the volumetric thermal expansion between water (207 x 10^-6 / C) and mercury (187 x 10^-6/C). But the effect here is small and would actually be to yield more than 10 mL of mercury.

If John is holding the thin test tube while he is filling it first with water and then with mercury, the 10 mL water will absorb heat from his hand and expand more than an exactly equivalent amount of mercury would. So if he is filling the tube with mercury up to a line established by water, the net amount of mercury will be slightly greater due to warming than he would have gotten if he had used a water bath to maintain a constant termperature for the water and the mercury.