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Topic: Ionic bonding and variable valency confusion  (Read 3442 times)

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Offline PicturesOfLilly

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Ionic bonding and variable valency confusion
« on: July 23, 2017, 09:28:59 AM »
Why do the elements with a partially filled d sublevel gain/lose different amounts of electrons from what we'd expect? Merely saying that there's a small energy difference between 4s & 3d, does not properly explain why transition metal have variable valency. Not to mention the fact that iron doesn't even have a 4s energy level! One might even think that iron would prefer to gain 2 electrons to attain a complete 3d10 energy level.

And why is the 4s energy level lower than the 3d energy level. Is the 4s further away (distance) from the nucleus? I mean why else would it be denoted '4'?

It seems to me that any electrons in the 3d enery level would be considered to be in the 4 shell by beginner scientists. And that would seem to imply that there are (3d10, 4s2, 4p6, 4d10, 4f14) 42 electrons in the 4 shell!

If the answer to my question is a complicated one, let me know. I haven't thought of this in term of Heisenberg's uncertainty principle, because I'm afraid that would confuse me more!

Thanks

Offline mjc123

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Re: Ionic bonding and variable valency confusion
« Reply #1 on: July 24, 2017, 08:22:56 AM »
Quote
Merely saying that there's a small energy difference between 4s & 3d, does not properly explain why transition metal have variable valency
Better, perhaps, to say there's a relatively small difference between dn and dn-1 states. You don't "hit a wall" as you do with s and p block elements at a noble gas configuration.
Consider e.g. the first few ionisation energies of Mg and Fe:
Mg 738, 1451, 7733, 10540, 13629 kJ/mol
Fe 759, 1561, 2957, 5287, 7236
It takes energy input to get from Mg+ to Mg2+, but this is more than compensated for by the increased lattice energy with a divalent ion, so Mg prefers to form divalent rather than monovalent compounds. However, the extra energy required to go from Mg2+ to Mg3+ is very high, and not compensated by the extra lattice energy, so formation of Mg(III) compounds is unfavourable.
With Fe, however, the ionisation energies increase, but there is no such big step from one to the next (at least as far as we have gone). The energy balances are more subtle, and compounds in different oxidation states may be of comparable stability.
Quote
Not to mention the fact that iron doesn't even have a 4s energy level!
Who says it doesn't? Every element has a 4s level.
Quote
And why is the 4s energy level lower than the 3d energy level. Is the 4s further away (distance) from the nucleus?
Have you heard of the concept of orbital penetration? (Google it)
Quote
I mean why else would it be denoted '4'?
Because it has a principal quantum number of 4. Have you studied quantum mechanics, the Schrodinger equation etc.? Without this it's hard to answer your question.
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It seems to me that any electrons in the 3d enery level would be considered to be in the 4 shell by beginner scientists.
I don't mean to sound dismissive, but that's why they're called beginners. It is more complicated than that - for multi-electron atoms, the levels in the same shell (same principal quantum number) have different energies, and levels from different shells can overlap, like 3d and 4s. In science, we don't go by "how it seems to beginners", but listen to those who know what they are talking about.
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And that would seem to imply that there are (3d10, 4s2, 4p6, 4d10, 4f14) 42 electrons in the 4 shell!
Wouldn't 4d be in the 5th shell, and 4f in the 6th, by your logic?
Quote
If the answer to my question is a complicated one, let me know
Unfortunately, it is. There's no real way of explaining it properly if you don't have at least a basic knowledge of quantum mechanics.

Offline PicturesOfLilly

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Re: Ionic bonding and variable valency confusion
« Reply #2 on: July 26, 2017, 05:32:55 PM »
Thank you for your straight answers on this.

It'll be nice to my head around this, perhaps by first reverting back to quantum mechanics, Schrodinger, etc.
« Last Edit: July 27, 2017, 12:33:42 PM by Arkcon »

Offline PicturesOfLilly

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Re: Ionic bonding and variable valency confusion
« Reply #3 on: July 27, 2017, 08:21:20 AM »
Unfortunately, it is. There's no real way of explaining it properly if you don't have at least a basic knowledge of quantum mechanics.
But for the sake of comprehending organic chemistry and covalent bonding, can I assume that the beginner's understanding is true?

Offline PicturesOfLilly

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Offline Vidya

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Re: Ionic bonding and variable valency confusion
« Reply #5 on: July 27, 2017, 09:21:38 AM »
energy level.

And why is the 4s energy level lower than the 3d energy level. Is the 4s further away (distance) from the nucleus? I mean why else would it be denoted '4'?

It seems to me that any electrons in the 3d enery level would be considered to be in the 4 shell by beginner

Thanks
If you look at the Shape of the orbitals you will be able to Understand the difference.s orbitals are more compact and closer to the nucleus than 'd'orbitals which are more diffused and away from the nucleus.

Offline PicturesOfLilly

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Re: Ionic bonding and variable valency confusion
« Reply #6 on: January 30, 2019, 12:14:21 PM »
Quote
Merely saying that there's a small energy difference between 4s & 3d, does not properly explain why transition metal have variable valency
Better, perhaps, to say there's a relatively small difference between dn and dn-1 states. You don't "hit a wall" as you do with s and p block elements at a noble gas configuration.
Consider e.g. the first few ionisation energies of Mg and Fe:
Mg 738, 1451, 7733, 10540, 13629 kJ/mol
Fe 759, 1561, 2957, 5287, 7236
It takes energy input to get from Mg+ to Mg2+, but this is more than compensated for by the increased lattice energy with a divalent ion, so Mg prefers to form divalent rather than monovalent compounds. However, the extra energy required to go from Mg2+ to Mg3+ is very high, and not compensated by the extra lattice energy, so formation of Mg(III) compounds is unfavourable.
With Fe, however, the ionisation energies increase, but there is no such big step from one to the next (at least as far as we have gone). The energy balances are more subtle, and compounds in different oxidation states may be of comparable stability.
Quote
Not to mention the fact that iron doesn't even have a 4s energy level!
Who says it doesn't? Every element has a 4s level.
Quote
And why is the 4s energy level lower than the 3d energy level. Is the 4s further away (distance) from the nucleus?
Have you heard of the concept of orbital penetration? (Google it)
Quote
I mean why else would it be denoted '4'?
Because it has a principal quantum number of 4. Have you studied quantum mechanics, the Schrodinger equation etc.? Without this it's hard to answer your question.
Quote
It seems to me that any electrons in the 3d enery level would be considered to be in the 4 shell by beginner scientists.
I don't mean to sound dismissive, but that's why they're called beginners. It is more complicated than that - for multi-electron atoms, the levels in the same shell (same principal quantum number) have different energies, and levels from different shells can overlap, like 3d and 4s. In science, we don't go by "how it seems to beginners", but listen to those who know what they are talking about.
Quote
And that would seem to imply that there are (3d10, 4s2, 4p6, 4d10, 4f14) 42 electrons in the 4 shell!
Wouldn't 4d be in the 5th shell, and 4f in the 6th, by your logic?
Quote
If the answer to my question is a complicated one, let me know
Unfortunately, it is. There's no real way of explaining it properly if you don't have at least a basic knowledge of quantum mechanics.
Thanks,

But now I'm ten times more confused. You make me feel like I need to first go off any understand everything about particle physics before I can even begin to get my head around this!

Offline mjc123

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Re: Ionic bonding and variable valency confusion
« Reply #7 on: January 30, 2019, 12:30:22 PM »
Have you learnt anything in the past 18 months? That's not a sarky comment, but a genuine question. How have your studies in chemistry advanced your knowledge of quantum mechanics? You posted this in the undergraduate forum; is that where you are? If you were a 1st year undergrad in 2017, you should be a 3rd year now, and you should have covered the quantum mechanics at least to a level to be able to understand this question; say, to the level of Atkins's "Molecular Quantum Mechanics". If you haven't it's very hard to explain.

Offline PicturesOfLilly

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Re: Ionic bonding and variable valency confusion
« Reply #8 on: January 31, 2019, 07:59:10 AM »
Have you learnt anything in the past 18 months? That's not a sarky comment, but a genuine question. How have your studies in chemistry advanced your knowledge of quantum mechanics? You posted this in the undergraduate forum; is that where you are? If you were a 1st year undergrad in 2017, you should be a 3rd year now, and you should have covered the quantum mechanics at least to a level to be able to understand this question; say, to the level of Atkins's "Molecular Quantum Mechanics". If you haven't it's very hard to explain.
Thank you,

I'm actually graduated with an MSc in a bioscience field. I would have gotten through a few chemistry modules during my undergrad here and there.

I'd like to understand things from first principles upwards, so it's on my own accord that I'm studying chemistry, albeit with a lot of dead ends! That's why it's been so long.

Offline mjc123

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Re: Ionic bonding and variable valency confusion
« Reply #9 on: January 31, 2019, 08:51:01 AM »
Well, kudos to you for studying it for yourself. I don't want to discourage you. The problem if you haven't got a tutor is that you may not  know what's the best order to take things, what you need to know before going on to X, if you don't grasp something in the textbook there's nobody to explain it to you. So by all means make use of this forum, though it would help us if you made clear your limited chemistry background, so we know where you're at.

Let's try and have an approach at this. You have heard of the Schrodinger equation. Its solutions for the hydrogen atom (one electron) are characterised by four quantum numbers, n, l, ml and ms.
States with the same n have the same energy, which is proportional to -1/n2.
l (the orbital angular momentum quantum number) can take integral values from 0 to n-1. These are labelled s, p, d, f... So you get 1s, 2s, 2p, 3s, 3p, 3d, etc.
ml indicates the orientation of the orbital angular momentum vector with the z axis, and can take values -l, -l+1, ... l-1, l.
ms indicates the orientation of the electron spin vector with the z axis, and can take values -1/2 or +1/2.
One way of looking at this is to see that the energy increases with the number of nodal surfaces (surfaces where the value of the wavefunction is zero), which is equal to n-1.
n=1 has no nodes, only the spherical distribution (1s orbital) is possible.
n=2 has one node; 2s has a radial node; 2p has an angular node (separating the + and - lobes of the p orbital).
n=3 has 2 nodes; 3s has 2 radial nodes, 3p has one radial and one angular, and 3d has two angular nodes.
See e.g.https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_A_Molecular_Approach_(Tro)/07%3A_The_Quantum-Mechanical_Model_of_the_Atom/7.6%3A_The_Shape_of_Atomic_Orbitals

So much for hydrogen. Heavier atoms have multiple electrons, and the complexity of their interactions means that exact solutions to the Schrodinger equation can't be found, but they can be approximated to 1s, 2s, 2p etc. And an important point that emerges is that levels of the same n don't all have the same energy. For example, consider a 2s and a 2p orbital. The 2s wavefunction has non-zero amplitude at the nucleus, while the 2p has a node at the nucleus. That means that a 2s electron has greater probability than a 2p of being found very close to the nucleus, so it is less shielded from the nucleus by the 1s electrons, and therefore it has lower energy. This is called the "penetration" effect.
For higher shells, where the difference between the shell energies is smaller (remember it goes roughly as 1/n2), this splitting between the s, p, d... levels can mean that (for example) 4s is lower than 3d. This is reflected in the electron configurations of the elements, and the structure of the periodic table.

However, these things aren't fixed in stone. For example, though 4s is filled before 3d, in the transition elements it is usually the 4s electrons that are ionised first, leaving a dn configuration. Thus Ti is 4s23d2, but Ti2+ is 3d2, although the isoelectronic Ca is 4s2. It seems that although all the levels change in energy with increasing nuclear charge, some change more than others, so going from Ca to Ti2+, 3d drops below 4s. When an electron is removed from an atom, there is an adjustment in the energy of all the other electrons, so the configuration is not necessarily "the same with one less electron in the top level". Cr is 4s1 3d5 rather than 4s2 3d4, because of the special stability of a half-filled d shell. I don't expect you to remember all these, but it just illustrates the complexity of the situation where different orbitals are of similar energy, and a variety of effects are at work in determining the configuration.

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