Charge separation of O-H bond in water molecule?

[songoku]

Homework Statement

Please see below

Relevant Equations

p = qd

resultant vector

cosine rule

I thought by "charge separation" the question is asking about distance between H and H so I was thinking of using cosine rule to find the distance. It turns out the answer stated by answer key is 0.328e (which I don't know what that is)

Dipole moment has direction from negative to positive charge so by using formula of resultant vector:
$$6.18\times 10^{-30}=\sqrt{a^2+a^2+2a^2 \cos 104.45^o}, \text{where} ~ a ~ \text{is dipole moment of O-H}$$
$$a=5.04\times 10^{-30}Cm$$

I try to use formula of dipole moment $qd$ where $d$ is $0.9584\times 10^{-10} m$ and I get $q$ to be 0.328e, which matches the answer key, but I don't know what it is.

Is that the charge of O or H or something else?

Thanks

 

[Steve4Physics]

Answer deleted - sorry for any confusion.

 

[laser1]

Is "charge separation" the same thing as "separation of charge"? The latter was used in my lectures, which was a distance. I don't know about the former though. According to your answer key, it looks like "charge separation" is a charge?

Also, when you are using the formula of a dipole moment, I assume when you use $qd$, you are actually using $2qd\cos(\theta /2)$?

 

[Steve4Physics]

@laser1 spotted the problem. The term 'charge separation' here does not mean a distance. It means the effective charge at each end of an O-H bond. Shown as $\delta$ values in the image below:

https://i.ytimg.com/vi/kbn27lXQNYk/maxresdefault.jpg

Oxygen is more electronegative than hydrogen. In a water molecule, this results in a shift of the electron-distribution towards the oxygen. Read about polar molecules and electronegativity if you need to find out more.

 

[haruspex]

Way off my area of knowledge, but…
Seems to me the expression "charge separation" originally referred to the phenomenon of induced charge redistribution, not a quantity. I cannot find a reference that interprets it as a quantity.
In the context of a dipole of known magnitude, it could mean a distance if the charges are known or assumed, or a charge if the distance is known or assumed.
In this question, we can infer a magnitude of the dipole moment of each OH bond from that of whole molecule. The distance can then (arbitrarily) be taken to be the length of the OH bond, but the charge value that pops out has no physical meaning. Equally, the charge could be arbitrarily taken to be $e$, giving a distance, which also has no physical meaning.

 

[Steve4Physics]

Way off my area of knowledge, but…
Seems to me the expression "charge separation" originally referred to the phenomenon of induced charge redistribution, not a quantity. I cannot find a reference that interprets it as a quantity.

The original question appears to be incorrectly worded. The term ‘charge separation’ should not have been used. The correct term is (presumably) ‘partial charge’ – e.g. see https://en.wikipedia.org/wiki/Partial_charge.

In the context of a dipole of known magnitude, it could mean a distance if the charges are known or assumed, or a charge if the distance is known or assumed.
In this question, we can infer a magnitude of the dipole moment of each OH bond from that of whole molecule. The distance can then (arbitrarily) be taken to be the length of the OH bond, but the charge value that pops out has no physical meaning. Equally, the charge could be arbitrarily taken to be $e$, giving a distance, which also has no physical meaning.

From what little I know, bond length, bond angle and dipole moment can be measured experimentally – or calculated using suitable models. And the accepted values of these are supplied in the original question.

For some situations we idealise each water molecule as having a definite size and shape consistent with the accepted values. We can then assign unique values of partial charge: $\delta^+$ on each hydrogen atom and $\delta^-$ on the oxygen atom such that $2\delta^+ + \delta^- = 0$

 

[haruspex]

From what little I know, bond length, bond angle and dipole moment can be measured experimentally – or calculated using suitable models. And the accepted values of these are supplied in the original question.

Yes, I have no problem with that.

For some situations we idealise each water molecule as having a definite size and shape consistent with the accepted values. We can then assign unique values of partial charge: $\delta^+$ on each hydrogen atom and $\delta^-$ on the oxygen atom such that $2\delta^+ + \delta^- = 0$

Sure, but that is what I mean by its having no physical reality. It is not the case that a fraction of the charge of an electron has shifted all the way from the nucleus of one atom to that of another. It would be equally valid to think of the cause of the dipole moment as a whole electron charge having shifted part way.

 

[songoku]

Is "charge separation" the same thing as "separation of charge"? The latter was used in my lectures, which was a distance. I don't know about the former though. According to your answer key, it looks like "charge separation" is a charge?

Yes, it looks like charge

Also, when you are using the formula of a dipole moment, I assume when you use $qd$, you are actually using $2qd\cos(\theta /2)$?

Yes, this is the same as the method I use to find $a$ where $a$ is equal to $qd$

It means the effective charge at each end of an O-H bond. Shown as $\delta$ values in the image below:

View attachment 355326
https://i.ytimg.com/vi/kbn27lXQNYk/maxresdefault.jpg

So what does the value I have calculated represent? Is 0.328e the $\delta^+$ or $\delta^-$?

In this question, we can infer a magnitude of the dipole moment of each OH bond from that of whole molecule. The distance can then (arbitrarily) be taken to be the length of the OH bond, but the charge value that pops out has no physical meaning.

By "has no physical meaning", you mean we can't put 0.328e as either charge of O or H?

Thanks

 

[haruspex]

By "has no physical meaning", you mean we can't put 0.328e as either charge of O or H?

I mean that there is not an actual charge of $\pm$0.328e to be found anywhere in the molecule.

 

[renormalize]

So what does the value I have calculated represent? Is 0.328e the $\delta^+$ or $\delta^-$?
By "has no physical meaning", you mean we can't put 0.328e as either charge of O or H?

For more insight, take a look at this presentation: https://water.lsbu.ac.uk/water/water_molecule.html

 

[songoku]

For more insight, take a look at this presentation: https://water.lsbu.ac.uk/water/water_molecule.html
View attachment 355356

Based on this, the 0.328e is close to the charge of H. So I have to know/memorize that it is actually the charge of H in OH bond?

Thanks

 

[Steve4Physics]

So what does the value I have calculated represent? Is 0.328e the $\delta^+$ or $\delta^-$?

You have calculated the magnitudes of the partial charges at the two ends of each O-H bond. The two partial charges each have a magnitude 0.328e.

If you have done sufficient chemistry you will know that oxygen is more electronegative than hydrogen; consequently the O-end partial charge will be -0.328e, and the H-end partial charge will be +0.328e.

As already stated by @haruspex, these are not actual charges. They are effectively average values of charges arising from distortions in the shape of electron orbitals.

(It’s also worth noting that a water molecule consists of two O-H dipoles sharing the same O atom. The total partial charge on the O atom is 2 x -0.328e = -0.656e, but this is not what the question asks for).

Based on this, the 0.328e is close to the charge of H. So I have to know/memorize that it is actually the charge of H in OH bond?

No. You do not have to know/memorize this. In fact the values of bond angle and bond length (and hence partial charge) for water aren’t fixed; they vary slightly depending on the state (solid, liquid, gas), temperature and pressure.

 

[songoku]

I understand

Thank you very much for all the help and explanation laser1, Steve4Physics, haruspex, renormalize