How much do elements weigh?

[Rat]

On my work forum today, I saw this (initially) startling post:

A young chap in the office has asked me a question. This is good news. This is what I am here for. But the question he asks appears, at first sight , to be slightly bizarre. This is even better. I am flattered.
The question, as he put it, goes like this;

how light or small does something have to be in order to unaffected by gravity.

Now, in the great scheme of things there is nothing, not even light, that is unaffected by gravity. But it quickly emerged that what he was really after is something that is lighter than air. This is easy. Go to the periodic table.
All of the gases below are lighter than air.
Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen

Now, this was from our technical expert. So he should, in theory, have a full grasp of technical issues. Admittedly, these issues mostly relate to building regs and planning stuff. Still, I found this surprising.

But then, the more I thought about it, the more I confused myself. I realize, of course, that his first mistake is to confuse oxygen with air, and I replied to that effect. But if I look at the periodic table, obviously carbon (for example) does indeed have a lower atomic weight than oxygen. Therefore I wish I'd paid more attention to chemistry in school. Does atomic weight have any bearing on this? Would this make more sense to me had I actually grasped the notion of moles, or is that irrelevant?

 

[trvlr2]

Rat-I am confused. Lithium, Boron, Carbon,Beryllium are not usually gases. Lithium is a metal, ditto beryllium, boron, carbon, semi metal.
Been a lot of years, but gravity affects everything in the universe-except things smaller than a Planck length, and imaginary stuff, like thoughts.
But, what was the question?

 

[Rat]

That was exactly the problem I had. It seemed to be wrong in so many ways that I just confused myself answering it. In short, if carbon has a lower atomic weight than, say, oxygen, can you say in any meaningful way that carbon is lighter than oxygen? I realize that carbon doesn't float in oxygen, of course, but, well...no, I don't know what I'm asking either.

 

[Graham Jackman]

That was exactly the problem I had. It seemed to be wrong in so many ways that I just confused myself answering it. In short, if carbon has a lower atomic weight than, say, oxygen, can you say in any meaningful way that carbon is lighter than oxygen? I realize that carbon doesn't float in oxygen, of course, but, well...no, I don't know what I'm asking either.

Provided that each element is compared at the same atomic density i.e. atoms per unit volume, then yes such comaprisons can be meaningfully made. This usually applies to gases under normal conditions, so that is why helium and hydrogen make good gases for balloons. Just remember that not all gases are monatomic, so that while He has a mass of 4 , hydrogen as H2 has a mass of 2, oxygen as O2 has a mass of 32 and nitrogen as N2 has a mass of 28.

 

[Whack01]

That was exactly the problem I had. It seemed to be wrong in so many ways that I just confused myself answering it. In short, if carbon has a lower atomic weight than, say, oxygen, can you say in any meaningful way that carbon is lighter than oxygen? I realize that carbon doesn't float in oxygen, of course, but, well...no, I don't know what I'm asking either.

Uh yes you can say that oxygen is heavier than carbon. The reason why carbon does not float in oxygen is a question of volume & resulting displacement. You're being thrown by Mass versus Density.

The notion of a mole comes in to play here, a mole is simply a fixed quantity of 'things', and is equal to avagardo's number approx 6.02*10^23. If you have 6.02*10^23 carbon atoms, and O atoms, the oxygen atoms will weigh more. However, the oxygen atoms will tend to spread out more and occupy more space (unless you cool it to extreme levels, at -218C oxygen becomes a solid).

eta: Also you can have carbon that weighs more than oxygen, however it would be radioactive. This is because an elements type is determined by protons, but a particular element may have more neutrons than protons. So a raw sample in the wild of a particular element may weigh more than a raw sample of a 'heavier' element, but if that's the case drop it and run cause you'll be glowing in the dark soon.

 

[Jeff Corey]

Then there's the question of whether or not a mole can float in oxygen. If so, she's a witch.

 

[fuelair]

One average carbon atom has less mass than one normal oxygen atom. But carbon atoms can bond with bundles of other carbon or other atoms. Some of these bondings wil have the property of being gasses (CO2, CO, CH4, C2H6, etc.) because they have, as one of their properties that they are gases in normal conditions. Some are liquids at/in normal conditions (ethanol, gasoline, carbon tetrachloride) . Some are solids in normal conditions (graphite, coal, silk, skin (lots of carbon compounds there!). It's not the atomic/molecular mass, these are other property results. And, picking another property - flammability: CH4 and C2H6, ethanol and gasoline, and coal (are all pretty easy to set on fire - resulting in the production of CO or CO2. With some, also water. Properties not directly related to atomic mass. By the by, chemical reactions are dependant on one primary thing - the number of electrons in the outer "energy level "of
thethe atoms of that element (see periodic table Groups). (As are part of the properties!!!)) The periodic table is your friend!!!).
Enough chem for now!!

 

[Yllanes]

The square mean speed of the particles of an ideal gas is

[latex]
\[
v^2 = \frac{3kT}{m},
\]
[/latex]

where k is Boltzmann's constant and m the atomic mass. This can be much higher than the escape velocity for light gases, so in that sense some gases are not bound by the gravitational field of the Earth.

 

[Mojo]

Would this make more sense to me had I actually grasped the notion of moles, or is that irrelevant?

What you need to know is that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (Avogadro's Law). This means that the mass of a given volume of gas depends on its molecular mass. So he was sort of right, apart from not realising that not all elements are gases and that not all gases are monatomic.

 

[Rat]

Good, I was a bit wrong, as I thought I might be. I realized as soon as I wrote my rebuttal that I might be misunderstanding. He is still a little slow for failing to observe that carbon (among others) is not a gas at rtp, and that oxygen≠air.

Hmm, I remember the Avogadro's law thing now you mention it. I can see that it doesn't work with solids, and indeed why it doesn't. I'm a little less clear on why it doesn't with liquids.

Thanks for elucidations, anyway.

 

[Southwind17]

Good, I was a bit wrong, as I thought I might be. I realized as soon as I wrote my rebuttal that I might be misunderstanding. He is still a little slow for failing to observe that carbon (among others) is not a gas at rtp, and that oxygen≠air.

Hmm, I remember the Avogadro's law thing now you mention it. I can see that it doesn't work with solids, and indeed why it doesn't. I'm a little less clear on why it doesn't with liquids.

Thanks for elucidations, anyway.

I'm just intrugued to know why you assumed that a guy who seems to be versed in where and how to erect a building should be qualified to comment on atomic physics! Tip: If you ever need a dripping tap fixing suggest you don't waste your time calling a florist!

 

[Rat]

I understand the concern, but they don't seem to me as if they should be entirely unrelated. When I trained in engineering, some basic chemistry was part of the courses I had to take (even if I've forgotten a lot now). While I don't know for sure, I suspect training as an architectural technician, which I assume he has, must cover at least enough basic science to do better than that. I don't especially expect him to know about comparative atomic weights, but I'd expect him (along with any school leaver) to know that carbon is not a gas, and that oxygen isn't air. In fact, I would guess that at least science GCSEs must be required at the start of a career path to architecture.

 

[shadron]

Avogadro's number is a constant integer value. If you have that many atoms or molecules of any substance, they will weigh precisely the atomic weight of the atom or molecule in grams. That's a "mole" of that substance. So, a mole of average carbon is 12.01115 grams and a mole of oxygen is 15.9994 grams. A mole of molecular oxygen (O2, the way it normally goes about) is about 32 grams.

The property you are seeking isn't weight, but density. That depends on the weight, but also how much space the molecules take up. Gases take up considerable volume, and that's regulated by the pressure they are compressed to and their temperature. Liquids and solids are much more compact ("higher densities"), so a sample of carbon sinks in oxygen. The property of volume is very dependent on external properties (pressure and temperature mainly) and internal properties (molecular and atomic magnetic effects, van der Waals forces, physical state, etc, etc). So the whole picture is not easily predicted or determined.

Complication: measuring the weight of anything here on the planet must take into consideration that that substance, while being weighed, is displacing an equal volume of air, which will lighten the weight measurement by the weight of teh displacement. In the case of helium, which weighs 4 grams per mole, that displaced air weighs more then the heium, so there is a net negative weight measurement for it. For most weighings, the amount of displaced air is negligible.

Secondly, substances have intrinsic mass, not weight. Weight is the net downward force exerted by the mass in a gravitational field. It is more difficult to measure mass than weight, so we often compute the mass from a weight measurement, using the average gravitational constant at the earth's surface as a conversion factor. As you move the substance farther from the center of the earth, the weight will recede, though the mass remains constant, because the gravitational "constant" varies with the strength of the gravitational field, which in simple cases varies with the distance from the center of mass, the center of the earth (coe). Most of our weight measurements, in fact, don't actually measure even weight, per se, but rather compare the weight to other, standard weights, and so the measurement of weight doesn't change with changes in distance from the coe, because both compared weights are declining in the same fashion. Those weighings that depend upon compressing a spring rather than balancing a scale, on the contrary, will decline.

Aren't you sorry you asked?

 

[shadron]

I'm just intrugued to know why you assumed that a guy who seems to be versed in where and how to erect a building should be qualified to comment on atomic physics! Tip: If you ever need a dripping tap fixing suggest you don't waste your time calling a florist!

From my point of view:

As it happens, there are people on the forum who are completely qualified to answer these questions by means of profession and educational credentials. However, this is a forum, open for the enjoyment of all. While I may not be as qualified to talk about physics as they are, I (for example) still do have a degree in Engineering Physics, before I ran off into that whore of a field called engineering. The depth of the question before the thread here is not so deep as to require a PhD to answer, so I feel qualified to do so; I feel it is my destiny, as Luke would have it. I am a frustrated teacher (errrr..., make that "lecturer"; my wife makes that distinction). The practical alternative, beyond the forum, is to hire out a Physics PhD's time, or make good friends with one and then just happen to drop over for a beer, if you can find him or her. The use of an internet forum, something not available to my parents at my age, is new, but is appropriate for exactly this sort of informal knowledge sharing, as long as you are cognizant of the drawbacks as well.

I also happen to know most of the rules and law (at least in selected counties in Colorado) for installing a tap. So, you can buy an engineer, or you can consult with me on the forum and then have the result checked by a local licensed expert for less money. That florist down the street may also know. I have, in my overly lengthy past, also consulted with florists about software to buy flowers from wholesale international distributors. I've helped land hardware on Mars, I've converted raw sunshine into electrical power in California with nothing more than mirrors, not even any smoke. I can create and sell computer applications, and have mapped the locations of every state-owned rest area in the continental USA. I know something about how train wrecks are handled, as one happened within sight of my house last winter. And I have the death sentence of 23 planets.

Now, what's your question?

 

[Elizabeth I]

I understand the concern, but they don't seem to me as if they should be entirely unrelated. When I trained in engineering, some basic chemistry was part of the courses I had to take (even if I've forgotten a lot now). While I don't know for sure, I suspect training as an architectural technician, which I assume he has, must cover at least enough basic science to do better than that. I don't especially expect him to know about comparative atomic weights, but I'd expect him (along with any school leaver) to know that carbon is not a gas, and that oxygen isn't air. In fact, I would guess that at least science GCSEs must be required at the start of a career path to architecture.

I think you're right, and that his general education should have taught him some of that. For example, my scientific and mathematical expertise would fit in a thimble and still leave plenty of room to cram an elephant in there, but even I know that "air" is mostly nitrogen, then oxygen, then a whole bunch of little bits of lots of stuff. And I learned that in my 7th-grade general science class.

 

[Southwind17]

From my point of view:

As it happens, there are people on the forum who are completely qualified to answer these questions by means of profession and educational credentials. However, this is a forum, open for the enjoyment of all. While I may not be as qualified to talk about physics as they are, I (for example) still do have a degree in Engineering Physics, before I ran off into that whore of a field called engineering. The depth of the question before the thread here is not so deep as to require a PhD to answer, so I feel qualified to do so; I feel it is my destiny, as Luke would have it. I am a frustrated teacher (errrr..., make that "lecturer"; my wife makes that distinction). The practical alternative, beyond the forum, is to hire out a Physics PhD's time, or make good friends with one and then just happen to drop over for a beer, if you can find him or her. The use of an internet forum, something not available to my parents at my age, is new, but is appropriate for exactly this sort of informal knowledge sharing, as long as you are cognizant of the drawbacks as well.

I also happen to know most of the rules and law (at least in selected counties in Colorado) for installing a tap. So, you can buy an engineer, or you can consult with me on the forum and then have the result checked by a local licensed expert for less money. That florist down the street may also know. I have, in my overly lengthy past, also consulted with florists about software to buy flowers from wholesale international distributors. I've helped land hardware on Mars, I've converted raw sunshine into electrical power in California with nothing more than mirrors, not even any smoke. I can create and sell computer applications, and have mapped the locations of every state-owned rest area in the continental USA. I know something about how train wrecks are handled, as one happened within sight of my house last winter. And I have the death sentence of 23 planets.

Now, what's your question?

Well, I didn't actually have a question, but you've now prompted one: What, exactly, is your point?

 

[blutoski]

On my work forum today, I saw this (initially) startling post:


Now, this was from our technical expert. So he should, in theory, have a full grasp of technical issues. Admittedly, these issues mostly relate to building regs and planning stuff. Still, I found this surprising.

But then, the more I thought about it, the more I confused myself. I realize, of course, that his first mistake is to confuse oxygen with air, and I replied to that effect. But if I look at the periodic table, obviously carbon (for example) does indeed have a lower atomic weight than oxygen. Therefore I wish I'd paid more attention to chemistry in school. Does atomic weight have any bearing on this? Would this make more sense to me had I actually grasped the notion of moles, or is that irrelevant?

The other thing is that it's a question about density rather than a question about atomic mass.

The equation you're looking for is the Ideal Gas Law PV=nRT, where P=temp, V=volume, R is a constant for all ideal gases, T is temperature.

You can't compare the density of carbon to the density of nitrogen directly by examining atomic mass, because you don't know how much the atoms are spaced out from one another. For example, carbon atoms will bind to one another and form huge lattices, and the different types of lattices will have different densities. There are tables that show the density of, say, diamond at room temperature and pressure. About 3.5g/mL, or 3500g/L. Graphite has a density of 2.09g/mL, or 2090g/L. Same element, different bonding pattern, different density.

And when an element forms a gas, its density drops quite low very quickly, because gas atoms tend to fill quite a bit of space compared to liquids or solids. Consider water: same molecular weight for H2O in all three phases, but you see that ice floats on water, and both ice and water will drop like a rock inside a steam-filled space.

In the case of gases, it's actually quite fair to compare gases to one another in terms of buoyancy because if they're at the same temperature and pressure, they will expand the same way, and this is the underlying principle of the ideal gas law. You solve for n/V to find density (n/v=P/(RT)) and so you're quite right that the densities are directly proportional to molecular weight. m/V = n/v*atomic mass.

But be mindful that nitrogen gas is N2, not N, oxygen gas is O2, not O, and carbon dioxide (not carbon) is CO2.

Example calculation: the density of nitrogen gas is based on an atom of N2 at RTP:

g/mol = 2 x 14 = 28 g/mol
g/L = (28g/mol)(mol/L)
= (28g/mol)1atm/(0.08205784(L*atm/(mol*Kelvin))*298Kelvin)
= .573 g/L

Based on the ratios of N2, O2, and CO2 in air, air should be about 0.7296g/L

Here's a copy-paste of a few gases from a quick-and-dirty excel sheet:

molecule mw density (g/L)
N2 14 0.573
O2 32 1.309
CO2 44 1.799
H2 2 0.082
He 2 0.082
F2 38 1.554
Cl2 70.9 2.899
Br2 160 6.543
CH4 16 0.654
O3 48 1.963

You can see why hydrogen and helium are so popular for floating stuff.


Also be mindful that gases mix due to brownian motion, and in the long run will be found somewhat mixed throughout a space regardless of their molecular weight. But if you're talking about balloons, it's safe to assume that the gas stored in them won't mix with the outside air too quickly, although we all know from experience that this happens in the long run. Also be aware that balloons have added mass of latex to add into the buoyancy equation. It's often heavier than the buoyancy gained by the lighter gas enclosed.

 

[Evilgiraffe]

Good explanation blutoski, just one small niggle.... Helium has an atomic mass of 4 g/mol rather than 2 g/mol.

[/pedant]

 

[MattusMaximus]

Just a point upon which I will, as a physics teacher, nitpick... please refer to the quantity in question as the atomic or molecular mass, not the weight. You wouldn't believe how hard it is to undo the misconception that mass & weight are equivalent when students get to physics after having had chemistry.

 

[blutoski]

Good explanation blutoski, just one small niggle.... Helium has an atomic mass of 4 g/mol rather than 2 g/mol.

[/pedant]

Totally correct. He mw = 4.00. So helium gas has about half the buoyancy of hydrogen gas.

That's what happens when I throw everything into excel, fire out a bunch of results mechanically, and skip the 'reality test' step before posting.