Does Dipole Moment Increase with Bond Length for the Same Charge?

[KYPOWERLIFTER]

Yeah, I know... pons asinorum

Polar covalent bonding/dipole moment:

If mu=Qr, where Q is the charge and r is the separation of charges, does it follow that as bond length increases that the dipole moment (mu) would increase in magnitude for the same charge? I do not understand this... If separation of charge refers to the slight neg. and slight pos. charge on say, an H and a Cl, respectively, then the more tightly bonded the molecule, the lower the "r" would be. It seems counter intuitive...

Suppose you have HCl and you want the dipole moment, aren't you contemplating the amount of charge incurred on H or Cl atom multiplied by the bond length? That is to say, H polarizes and Cl polarizes, then a polar covalent bond is formed.

 

[alxm]

If mu=Qr, where Q is the charge and r is the separation of charges, does it follow that as bond length increases that the dipole moment (mu) would increase in magnitude for the same charge?

Yes.

If separation of charge refers to the slight neg. and slight pos. charge on say, an H and a Cl, respectively, then the more tightly bonded the molecule, the lower the "r" would be. It seems counter intuitive...

I don't see why this is counter intuitive. Opposite charges attract. Charge separation costs energy.
The interatomic distance, r, is _not_ linear with charge. Chemical bond lengths and strengths can't really be explained in terms of classical electrical charge interactions.

Suppose you have HCl and you want the dipole moment, aren't you contemplating the amount of charge incurred on H or Cl atom multiplied by the bond length? That is to say, H polarizes and Cl polarizes, then a polar covalent bond is formed.

No, I think you might be misunderstanding the concept here. The dipole moment is a property of the molecule. It isn't the cause of the H-Cl bond. It's an effect of it. When you're talking about the dipole moment, you're talking about the amount of electrons (or really, density of electrons) around the respective atoms - relative their nuclear charge.

An atom by itself (H or Cl) is neutral and has no dipole moment (save for induced dipole moments, but that's another story). When they form a bond, it's a polar bond, an "ionic bond", that is to say that H lost its one electron and Cl has an extra one. So hydrogen has a net charge of +1, since it has no electrons left, and chlorine has -1, since it took hydrogen's electron when they formed a bond. (In reality, 'true' ionic bonds with integer charges don't usually exist. It's more like 90%-10% or something like that) So the resulting H-Cl molecule has a dipole moment.

 

[KYPOWERLIFTER]

Thanks for the reply. Yes, I was confusing two different concepts.

Is this a more appropriate way to think of the dipole moment:

In HCl the dipole moment refers to the separation of charge within an HCL molecule due to the polarizing effect of the difference in electronegativities of the two atoms involved, to wit: the H end tends to have a more positive charge and the CL end tends to become more negative (thus the electron density cloud is shifted toward the Cl end). The bond length in the molecule is taken into account because as it increases, the charges (at the H and Cl) which naturally attract, are separated further thus costing energy. So, they want to come together as the "Q" gets higher, but the bond holds them apart. This explains why that as the bond length decreases, the dipole moment decreases. The dipole moment is a product of how much charge is separated and the distance (bond length) of separation.

 

[alxm]

In HCl the dipole moment refers to the separation of charge within an HCL molecule due to the polarizing effect of the difference in electronegativities of the two atoms involved, to wit: the H end tends to have a more positive charge and the CL end tends to become more negative (thus the electron density cloud is shifted toward the Cl end).

This is all correct.

The bond length in the molecule is taken into account because as it increases, the charges (at the H and Cl) which naturally attract, are separated further thus costing energy.

Well, no. A dipole moment is simply defined as the product of a charge difference in two points and their separation distance. It doesn't matter whether or not there's a chemical bond directly along that line or not. It's a property that can be measured, without actually knowing anything at all about what the molecule itself looks like. If it has a dipole moment, then it must have two points which have a difference in relative charge, and are separated by a distance. For instance, H2O has a dipole moment, because the two hydrogens are electropositive relative the oyxgen. So the negative 'pole' is the oxygen atom, but the positive 'pole' would actually be a point in space between the two hydrogens!

Now look at CO2. It's O=C=O in a straight line. The oxygens are negative relative the carbon, but since there are two of them, at exactly opposite ends, they cancel out. CO2 is not a dipole. If it were at an angle, like water, then it would be.

Is it getting clearer?

 

[KYPOWERLIFTER]

Is it getting clearer?

Crystalline.

Well stated explanation. Cogent and coherent.

It seems I had convoluted a relatively simple notion.