Reef Chemistry Question of the Day #216 Seawater Barometer

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #216

Imagine you have a long glass tube, sealed at one end. You fill it with various liquids, and invert it with the open end facing down into a bowl of the same liquid, and the closed end straight up, without allowing any gas to enter.

In each case, the top of the liquid drops down from the end of the closed tube and stabilizes some way down the tube, leaving a gas/vacuum space between the top of the liquid and the sealed end of the tube. I'll call this the "gas gap".

Using the fluids below, rank order them from the one with the smallest gas gap at the top to the one with the largest gas gap.

A. Vodka < Tap water < Seawater < Mercury
B. Mercury< Tap water < Seawater < Vodka
C. Vodka < Seawater < Tap Water < Mercury
D. Mercury< Vodka < Seawater < Tap Water
E. Mercury < Seawater < Tap Water < Vodka

Good luck!




















.

 

[Brew12]

I'll go with E.

The correct answer is F.
Mercury<seawater<tapwater

The vodka would be mysteriously gone.

 

[beaslbob]

e

 

[beaslbob]

e

but then I kinda a dense guy.

 

[cypho]

I'm going to disagree with the others. I vote C.

But it feels like you should have specified the temperature....

 

[beaslbob]

e

woopsies. RTFQ

smallest to largest air gap would be

A.

 

[beaslbob]

I must be getting denser

 

[beaslbob]

am I allowed to think this question sucks?

 

[DLHDesign]

Imagine you have a long glass tube, sealed at one end. You fill it with various liquids, and invert it with the open end facing down into a bowl of the same liquid, and the closed end straight up, without allowing any gas to enter.

If the tube was full and no gas was allowed to enter, where is the "gas gap" coming from? I just tried what I envision this experiment to be and neither tap water nor salt water had any such gap at the top...

So either I'm confused (which is most likely the case), or the answer is "none of the above (they all have the same - no gap)"...

EDIT: Oh; it's right there in the title - you're describing a barometer. Gotcha.
I'll go with A. ;-)

 

[Brew12]

If the tube was full and no gas was allowed to enter, where is the "gas gap" coming from? I just tried what I envision this experiment to be and neither tap water nor salt water had any such gap at the top...

So either I'm confused (which is most likely the case), or the answer is "none of the above (they all have the same - no gap)"...

The weight of the fluid in the column will push down on the fluid in the container it is sitting upside down in and draw a vacuum in the top of the tube creating a "gas gap".

I may have to rethink this since the Vodka I would have drank may actually flash to a vapor at room temperature in a vacuum. . Initially, I thought E but now I am going with D. I believe the extra density of the mercury will cause the biggest gap. Some Vodka will vaporize making it number 2. Then the sea water and tap water.

 

[cypho]

Initially, I thought E but now I am going with D. I believe the extra density of the mercury will cause the biggest gap.

You are still suffering from the effects of drinking the vodka. Both D and E are votes for mercury having the smallest gap.

 

[Randy Holmes-Farley]

am I allowed to think this question sucks?

Yes. You can think whatever you want.

 

[Randy Holmes-Farley]

I'm going to disagree with the others. I vote C.

But it feels like you should have specified the temperature....

Room temp.

We can debate the effects if you live in a hot climate.

 

[DLHDesign]

790, 1000, 1029, 13560
Woot!

 

[Scorpius]

C.

 

[JimWelsh]

This is really a question about vapor pressure. The volume of the void will be determined by the vapor pressure of the liquid used. The lower the vapor pressure, the smaller the "gas gap" will be. From lowest vapor pressure to highest, Mercury < Seawater < Tap Water < Vodka. Answer is "E".

 

[SDchris]

Combined density and vapor pressure. Probably close to: C

 

[Reefersutherland_]

Trick question, they would all have the same gas gap

 

[Randy Holmes-Farley]

And the answer is...

A. Vodka < Tap water < Seawater < Mercury

Let's work through it, since it is not trivial.

First, we must assume the tube is long enough to have a gas gap. If it is less than 760 mm long, none of them will, and if it is 800 mm long, only the mercury one will have a gap at the top. THe liquid will reach the top of all the others. We'll assume it is very long.

The gas gap will, in each case, be the total height of the tube interior minus the liquid height contained in it.

For the first pass analysis, we will assume that vapor pressure in the tube is unimportant. In that case, each liquid is pushed up by the 1 atmosphere of air pressure pushing down on the liquid in the bowl. The liquids are pushed up until the downward pull of gravity on the liquid in the tube above the level in the bowl exactly matches the air pressure pushing down in the liquid in the bowl and hence up the tube. This process is how a standard mercury barometer works.

Since the outside air pressure is the same in all cases, the weight (mass) of liquid inside the tubes is also the same.

If the mass is the same and we want to know the liquid volume in the tube, we can get that the from the density. The more dense the liquid, the less of it will be present inside the tube to attain the same mass.

Mercury has by far the highest density of the liquids chosen, so it creeps up the tube the least, and has the highest gas gap. That makes sense since it is super heavy, it moves upward less than the lighter liquids.

The relative densities are (~20 deg C):

mercury 13.5 g/cm3
seawater 1.025 g/cm3
fresh water 0.998 g/cm3
vodka ~0.92 g/cm3

So assuming no vapor pressure of any of them, the gas gap is:

Vodka < Tap water < Seawater < Mercury

And how much does the liquid rise in each case? Starting with the known value that mercury rises 760 mm at 1 atmosphere pressure, the relative heights of liquid are inversely related to the density.

mercury 13.5 g/cm3 -----> 760 mm (0.76 meters)
seawater 1.025 g/cm3 -----> 760 x 13.5/1.025 = 10,010 mm (10 meters)
fresh water 0.998 g/cm3 ----> 760 x 13.5/0.998 = 10,280 mm (10.3 m)
vodka ~0.92 g/cm3 ----> 760 x 13.5/0.92 = 11,150 mm (11.5 m)

The gas gap, of course, is the difference between these values and the top of the tube. If the tube is more than 12 meters long, there will be a gas gap for each.

OK, now to deal with vapor pressure. If gas enters the space above the liquid, it is no longer vacuum above the liquid, but a gas with the pressure of the vapor pressure.

This vapor pressure will depend on temperature. Let's just assume 20 deg C.

The vapor pressure tends to offset the outside atmospheric pressure pushing up on the liquid. If the liquid was just at its boiling point, the inside pressure of 1 atmosphere would exactly match the outside pressure and there would be no movement up the tube at all. It would be all gas gap.

If we determine what fraction of one atmosphere each of these liquids shows at 20 deg C, we will reduce the pressure differential between inside and outside by exactly that value, and so allow the liquid to travel less far up the tube to balance the pressure difference.

Mercury has almost no vapor pressure at 20 deg C, and so needs no correction and still has the largest gas gap.

Vapor pressures at 20 deg C:

http://www.laboceano.coppe.ufrj.br/ittc2011/documents/2011/pdf Procedures 2011/7.5-02-01-03.pdf
for ethanol/water (vodka = 40% ethanol by volume or 0.17 mole fraction ethanol)
https://www.researchgate.net/figure...ilibrium-total-pressure-data-as-a-function-of

mercury ~0
fresh water 0.0231 atmospheres
seawater 0.0226 atmospheres
vodka ~36 torr = 0.046 atmospheres (estimated from the second link above)

So how much is each rise reduced?

mercury (1-0) x 760 mm = 760 mm
seawater (1-0.0226) x 10,010 mm =9,784 mm
fresh water (1-0.0231) x 10,280 mm = 10,042 mm
vodka (1-0.046) x 11,150 mm = 10,637 mm

We can see that the vapor pressure brought all down except mercury, and brought down vodka the most, but not enough to alter the relative ordering of the fluids, and the answer for the relative size of the gas gap (tube height minus the liquid rise) still is...

A. Vodka < Tap water < Seawater < Mercury

Of course, I might have made a mistake or two somewhere, or the data I foud might not be correct. lol

Happy reefing.