Size of ion vs. atomic radius

[foxi]

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A practice problem had us decide which ion would fit through a membrane channel, based on size.

The ions of relevance were sodium and chloride, and I stated that chloride are smaller than sodium, based simply off of the trend of atomic radii. However, the answer was that sodium is smaller than chloride (which I understand based on more nucleons), and I don't understand if we should be looking at mass numbers or atomic radii...

 

[aldol16]

When referring to ions, we are most likely referring to the sodium cation and the chloride anion. (NOT the neutral atomic radii) Sodium has lost an electron to become a cation, while Chloride has gained an electron to become an anion. By gaining an electron, chloride's ionic radius is now larger than its neutral atomic radius. By losing an electron, sodium's ionic radius is now smaller than its neutral atomic radius. SO, the sodium ionic radius is actually smaller than the chloride ionic radius.

The ions of relevance were sodium and chloride, and I stated that chloride are smaller than sodium, based simply off of the trend of atomic radii. However, the answer was that sodium is smaller than chloride (which I understand based on more nucleons), and I don't understand if we should be looking at mass numbers or atomic radii...

Sodium's ionic radius is smaller than those of chlorine from simple periodic trends. Cationic sodium is a full row above anionic chloride. OP, perhaps you were thinking of potassium ion, which would be more difficult to tell but would still be smaller than chloride ion.

 

[BerkReviewTeach]

A practice problem had us decide which ion would fit through a membrane channel, based on size.

The ions of relevance were sodium and chloride, and I stated that chloride are smaller than sodium, based simply off of the trend of atomic radii. However, the answer was that sodium is smaller than chloride (which I understand based on more nucleons), and I don't understand if we should be looking at mass numbers or atomic radii...

I assume you are referring to one of our (that being BR's) general chemistry questions here. The purpose of this question is two-fold. On one level, you need to know that ionic radii vary from elemental radii. Sodium (element #11) and Chlorine (element #17) are in the same row of the periodic table, so as neutral elements they follow the size trend of descending radii moving left-to-right. This is due to the increasing effective nuclear charge, which contracts the electron could. So neutral sodium has an atomic radii larger than neutral chlorine (about 151pm to 79 pm). However, when sodium loses its valence electron from the third shell, it now has an an outer shell of n=2 coupled with a natural drop in size as the electron cloud loses and electron and does not repel as much. When chlorine gains an election to become chloride, the valence shell has a greater negative charge, which results in repulsion. This causes the shell to swell slightly, resulting in a larger ion. As such, sodium cation is smaller than chloride anion.

The second part of this question is to get you to realize that protein channels are held together by hydrogen bonding, so they are rather narrow. This is why single ions can easily migrate through, but polyatomic ions cannot.

This question really is helpful in fusing general chemistry with cell biology, something you need to be able to do on the MCAT.

 

[MekM]

So anions are bigger than their atomic counterparts which are (neutral) in charge due to the addition of more electrons . cations are smaller than their atomic counterparts due to having less electrons. Here the anionic chloride is bigger than the cationic sodium and thus would have a harder time passing the membrane

 

[aldol16]

So anions are bigger than their atomic counterparts which are (neutral) in charge due to the addition of more electrons . cations are smaller than their atomic counterparts due to having less electrons. Here the anionic chloride is bigger than the cationic sodium and thus would have a harder time passing the membrane

It's not so much due to having less electrons as having a greater or lesser effective nuclear charge. If you remove an electron and the proton count stays the same, then you now have more positive charge acting on each individual electron. If you add an electron and the proton count stays the same, then you now have less positive charge acting on each individual electron.

 

[MekM]

It's not so much due to having less electrons as having a greater or lesser effective nuclear charge. If you remove an electron and the proton count stays the same, then you now have more positive charge acting on each individual electron. If you add an electron and the proton count stays the same, then you now have less positive charge acting on each individual electron.

Yeah to be more specific I agree the effective nuclear charge is the foundation when talking in terms of how pulled the electrons are to the nucleus I wrote my explanation in such a rudimentary form lol thanks tho

 

[foxi]

Sodium's ionic and atomic radii are both smaller than those of chlorine from simple periodic trends. Cationic sodium is a full row above anionic chloride. OP, perhaps you were thinking of potassium ion, which would be more difficult to tell but would still be smaller than chloride ion.

> Aldol: so a neutral sodium atom is larger than a neutral chloride atom, as predicted by the periodic trend of atomic radii, but a sodium ion is smaller than a chloride ion? As for why isoelectric cations are smaller than their respective isoelectric anions, I understand. But chloride and sodium are not isoelectronic... So how do we know that the ionic size is influenced so much that the order of their relative sizes switch?

 

[aldol16]

> Aldol: so a neutral sodium atom is larger than a neutral chloride atom, as predicted by the periodic trend of atomic radii, but a sodium ion is smaller than a chloride ion? As for why isoelectric cations are smaller than their respective isoelectric anions, I understand. But chloride and sodium are not isoelectronic... So how do we know that the ionic size is influenced so much that the order of their relative sizes switch?

Yeah - because sodium cation is a full row above chloride cation, i.e. it has one less shell of electrons. You should understand the reason why atomic radii trends are how they are and not simply memorize them because if you understand, then the reason becomes abundantly clear. The reason atomic radii decrease as you go right across the periodic table is because as you go right, the shell of electrons is still the same (same principal quantum number) but the nuclear charge increases. So you're increasing + charge without increasing shielding and so the effective nuclear charge is increasing.

But when you're talking about two atoms with an added shell of electrons, that argument no longer applies.

 

[foxi]

Yeah - because sodium cation is a full row above chloride cation, i.e. it has one less shell of electrons. You should understand the reason why atomic radii trends are how they are and not simply memorize them because if you understand, then the reason becomes abundantly clear. The reason atomic radii decrease as you go right across the periodic table is because as you go right, the shell of electrons is still the same (same principal quantum number) but the nuclear charge increases. So you're increasing + charge without increasing shielding and so the effective nuclear charge is increasing.

But when you're talking about two atoms with an added shell of electrons, that argument no longer applies.

> Sodium is in the same row as chlorine.. You're right, I shouldn't be following trends; I understand how the effective nuclear charge influences the size of the atoms. I still haven't exactly had my question answered, so I'll try to reword it:

Seeing how sodium and chlorine are in the same period, chlorine should be smaller based on it having a stronger effective nuclear charge (due to same size shell as sodium, but a greater number of protons). However, when considering their ionic forms, sodium becomes smaller because now it's effective charge has decreased, while chloride's effective nuclear charge has increased. So my question is: how do we know if the new effective charges compensated enough to reverse their relative sizes? It could still be that sodium's Zeff increased + chloride's Zeff decreased, but sodium is still larger than chloride.

 

[aldol16]

Seeing how sodium and chlorine are in the same period, chlorine should be smaller based on it having a stronger effective nuclear charge (due to same size shell as sodium, but a greater number of protons). However, when considering their ionic forms, sodium becomes smaller because now it's effective charge has decreased, while chloride's effective nuclear charge has increased. So my question is: how do we know if the new effective charges compensated enough to reverse their relative sizes? It could still be that sodium's Zeff increased + chloride's Zeff decreased, but sodium is still larger than chloride.

I answered your question - I don't think you're understanding my answer. First, sodium cation's effective nuclear charge is even bigger than sodium atom because you've removed an electron. By the same argument, chloride anion's effective nuclear charge is smaller than chlorine atom's because you've added an electron. Second - here's the part you missed - the argument that sodium atom is smaller than chlorine atom is predicated on the assumption that they're in the same row and have the same principal quantum number. Once you go down or up in quantum number, that assumption no longer holds. The implicit statement I'm making here is that when you're changing principal quantum number, you can no longer just say that effective nuclear charge wins because the predominating effect is the added shell of electrons.

 

[foxi]

I answered your question - I don't think you're understanding my answer. First, sodium cation's effective nuclear charge is even bigger than sodium atom because you've removed an electron. By the same argument, chloride anion's effective nuclear charge is smaller than chlorine atom's because you've added an electron. Second - here's the part you missed - the argument that sodium atom is smaller than chlorine atom is predicated on the assumption that they're in the same row and have the same principal quantum number. Once you go down or up in quantum number, that assumption no longer holds. The implicit statement I'm making here is that when you're changing principal quantum number, you can no longer just say that effective nuclear charge wins because the predominating effect is the added shell of electrons.

> That makes sense... Now I see what you mean by sodium ion is in a smaller shell than chloride (since Na+ is now functioning as if its n = 2), and chloride's additional shell makes it significantly larger than sodium. Thanks!

 

[aldol16]

> That makes sense... Now I see what you mean by sodium ion is in a smaller shell than chloride (since Na+ is now functioning as if its n = 2), and chloride's additional shell makes it significantly larger than sodium. Thanks!

Yes - exactly!