Mass, density and weight...

[DyerWolf]

Are mass and density directly related?

I'm wondering if there any substance that has more mass per volume but less density than something else. I know that a cubic centimeter of uranium is much more dense, and much more massive than a cubic centimeter of lead - and that uranium is a hard metal, whereas lead is soft. But I also know that iron can cut lead, but lead cannot cut iron. Does this mean that a cubic centimeter of iron is more dense than than a cubic centimeter of lead?

[Jason Thompson]

I'm wondering if there any substance that has more mass per volume but less density than something else.

Density is defined as mass per unit volume, therefore the answer to your wondering is no, by definition. It reduces to wondering if there is a material that has more density but less density than another material.

Does this mean that a cubic centimeter of iron is more dense than than a cubic centimeter of lead?

Hardness and density are not necessarily directly related. Ice, for example, is harder than, but less dense than, water. Diamond is very hard, but less dense than most metals.

[Argos]

Iron density= 7.87 g/cm^3
Laed density = 11.36 g/cm^3

You think you´re talking about hardness. here´s a good link.

[01101001]

Hardness and density are not necessarily directly related.

DyerWolf, forget about the hardness. It's an effect at a whole different level than mass. It has to do with structure, organization of atoms, molecules, into crystals in the solid state. It's a bonding issue. There are many sorts of hardness as well, depending on what mechanical deformation is considered.

It has about as much influence in matters of mass as color does.

[mugaliens]

Are mass and density directly related?

Sometimes, the simplest answers are what we really need:

1. Yes, mass and density are directly related. As was mentioned, density equals mass per unit volume. One cubic centimeter of water, for example, weighs .998 grams at 20 deg C. Thus, it's density is .998 g/cm^3. When you freeze water, however, the organization of the molecules change, becoming crystalline, and the water becomes less dense, around .92 g/cm^3. This is why ice floats - because it's less dense than liquid water.

I'm wondering if there any substance that has more mass per volume but less density than something else.

No, as density and mass per unit volume are the same thing.

I know that a cubic centimeter of uranium is much more dense, and much more massive than a cubic centimeter of lead - and that uranium is a hard metal, whereas lead is soft.

While uranium is more dense than lead, whether or not it's more massive or not depends upon how much of each you have. For example, you could have a 1 kg weight of uranium next to a 1 kg weight of lead. Neither would be more massive than the other, as both have the same mass: 1 kg.

However, because it is more dense, the uranium would occupy a smaller physical space (volume) than the lead.

But I also know that iron can cut lead, but lead cannot cut iron. Does this mean that a cubic centimeter of iron is more dense than than a cubic centimeter of lead?

No. As someone said, density and hardness have nothing to do with one another. Titanium is much harder than lead, but it's a very light metal, whereas you can scratch pure lead with your fingernail, and you can scratch pure gold (a very dense metal) with most solid elements, even the lightest ones.

[DyerWolf]

Thanks for the responses.

Follow on questions:

Is there a difference in weight between polymorphs of the same element? I.e., would a cubic centemeter of diamond weigh the same as a cubic centimeter of graphite?

Relating to another thread, this question;

An atom of Nickel has 28 protons, 28 electrons, and 31 neutrons.
An atom of Barium has 56 protons, 56 electrons, and 81 neutrons.

Would 87 atoms of Barium weigh the same as 193 atoms of Nickel?

(Each would have a total of 16,791 protons, electrons and neutrons.)

[formulaterp]

Thanks for the responses.

Follow on questions:

Is there a difference in weight between polymorphs of the same element? I.e., would a cubic centemeter of diamond weigh the same as a cubic centimeter of graphite?

Relating to another thread, this question;

An atom of Nickel has 28 protons, 28 electrons, and 31 neutrons.
An atom of Barium has 56 protons, 56 electrons, and 81 neutrons.

Would 87 atoms of Barium weigh the same as 193 atoms of Nickel?

(Each would have a total of 16,791 protons, electrons and neutrons.)

1)No, diamond has a higher density than graphite, so for a given volume, it would have greater mass and weight.

2)Close, but No, protons and neutrons have similar mass, but are significantly "heavier" than electrons.

[DyerWolf]

Thanks - I should have read mugaliens post a bit more closely - he answered the 'polymorph' question when he described the ice/water density difference.

Still, regarding polymorphs: am I correct in assuming that if I placed a pure diamond on one tray of a scale and a pile of pure graphite on the other, that if I had a way to ensure that each had the same number of carbon atoms, both would weigh the same?

Using the water analogy, I assume that if I had a centiliter of water and froze it, it would still weigh the same - even though its volume would be different after freezing.

[Amber Robot]

Still, regarding polymorphs: am I correct in assuming that if I placed a pure diamond on one tray of a scale and a pile of pure graphite on the other, that if I had a way to ensure that each had the same number of carbon atoms, both would weigh the same?

Does the binding energy show up as mass?

[Grashtel]

Thanks - I should have read mugaliens post a bit more closely - he answered the 'polymorph' question when he described the ice/water density difference.

Still, regarding polymorphs: am I correct in assuming that if I placed a pure diamond on one tray of a scale and a pile of pure graphite on the other, that if I had a way to ensure that each had the same number of carbon atoms, both would weigh the same?

Using the water analogy, I assume that if I had a centiliter of water and froze it, it would still weigh the same - even though its volume would be different after freezing.

Correct for all practical purposes, there would be a very slight difference in mass because of the different molecular binding energies though.

[Aiwe]

Does the binding energy show up as mass?

It will show up as a loss in mass.

Still, regarding polymorphs: am I correct in assuming that if I placed a pure diamond on one tray of a scale and a pile of pure graphite on the other, that if I had a way to ensure that each had the same number of carbon atoms, both would weigh the same?

Nope, if there is a difference in binding energy. The higher the binding energy, the greater the mass loss. Similarly, a lower bonding energy means less mass lost.
I can't see to find any reference to the actual binding energies for diamond and graphite. I'll keep searching, but can anyone recommend somewhere to look? I feel pretty confident that binding energy should be different for the two, because of the difference in atom structures and melting points, etc, but I'd like to look the numbers up and check. Also I'm just curious

[grant hutchison]

I can't see to find any reference to the actual binding energies for diamond and graphite. I'll keep searching, but can anyone recommend somewhere to look? I feel pretty confident that binding energy should be different for the two, because of the difference in atom structures and melting points, etc, but I'd like to look the numbers up and check. Also I'm just curious

The sp² bond in graphite is certainly shorter than the sp³ in diamond: 1.42Å versus 1.54Å, from my CRC Handbook.
If memory serves, that implies that graphite has the higher bond energy, which would fit with the fact that graphite is the more stable of the two, at standard temperature and pressure.

Grant Hutchison

[grant hutchison]

Oh. Here are the aliphatic and aromatic C-C bond energies from my ancient (1967) Three-figure Tables for Modern Mathematics and Science. (Log tables! Remember them?)

Aliphatic 83 kcal/g mole
Aromatic 121 kcal/g mole

This stuff's a fair way in the past for me, but recollection suggests that "aliphatic" should be a good guide to diamond and "aromatic" for graphite, if not right on the nail. Yes?

Grant Hutchison

[Aiwe]

The sp² bond in graphite is certainly shorter than the sp³ in diamond: 1.42Å versus 1.54Å, from my CRC Handbook.
If memory serves, that implies that graphite has the higher bond energy, which would fit with the fact that graphite is the more stable of the two, at standard temperature and pressure.

Grant Hutchison

Thank you Grant for looking up the bond lengths.

I agree that distance is probably a good estimate for relative bonding energies.
I was thinking heat of fusion would yield a good relative estimate also, but I’m not sure how to get a straight number out of that…
Actually, I’m probably making this harder than it is. I think I know where to look in my quantum book when I get back home. Thank you again for those numbers! They should prove very useful.

[Aiwe]

Oh. Here are the aliphatic and aromatic C-C bond energies from my ancient (1967) Three-figure Tables for Modern Mathematics and Science. (Log tables! Remember them?)

Aliphatic 83 kcal/g mole
Aromatic 121 kcal/g mole

This stuff's a fair way in the past for me, but recollection suggests that "aliphatic" should be a good guide to diamond and "aromatic" for graphite, if not right on the nail. Yes?

Grant Hutchison

Fantastic! Thank you!

Aliphatic implies the carbon atoms are in rings, or in straight or branched chains.

I wasn't too sure about Aromatic, but from what I can make out, it seems to be carbon in rings where the atoms are covalently bonded with alternating single and multiple bonds (so, a conjugated ring). Except, the ring has unsaturated bonds, which somehow makes the molecule stronger than usual. Neat!

[Swift]

I was thinking heat of fusion would yield a good relative estimate also, but I’m not sure how to get a straight number out of that…

In theory, I was thinking heats of crystallization, which should take into account the different crystal structures. But those are usually calculated from crystallization from solution. That data probably doesn't exist for diamond or graphite from aqueous solutions, though it might from molten metal solutions (which is one way synthetic diamonds are made). But I couldn't quickly google the info.

Dredging up things from my memory - the Born-Haber cycle might be another way to do it.

[grant hutchison]

I wasn't too sure about Aromatic, but from what I can make out, it seems to be carbon in rings where the atoms are covalently bonded with alternating single and multiple bonds (so, a conjugated ring).

Yes, the classic "aromatic" compound is benzene.

Edit: For completeness, the C=C bond is listed with an energy of 143 kcal/g mole, demonstrating how that aromatic bond hovers midway between a single and a double bond.

Grant Hutchison

[Aiwe]

In theory, I was thinking heats of crystallization, which should take into account the different crystal structures. But those are usually calculated from crystallization from solution. That data probably doesn't exist for diamond or graphite from aqueous solutions, though it might from molten metal solutions (which is one way synthetic diamonds are made). But I couldn't quickly google the info.

Dredging up things from my memory - the Born-Haber cycle might be another way to do it.

Thank you Swift for the Born-Haber Cycle recommendation!
At a first glance I don’t think it would work for this problem, since it seems meant for ionic compounds with a metal and nonmetal, but I’ll take a closer look.

Since carbon doesn't really form that way, heat of fusion is probably a better approach then crystallization.