7.1 Overview of Trends and Atomic Radius
Chad's General Chemistry Videos
- 19.1 Oxidation Reduction Reactions and Oxidation States
- 19.2 Balancing Oxidation Reduction Reactions
- 19.3 Galvanic Cells
- 19.4 Standard Cell Potentials aka emf or Voltage
- 19.5 Nonstandard Cell Potentials the Nernst Equation
- 19.6 Reduction Potentials and the Relationship between Cell Potential, Delta G, and the Equilibrium Constant
- 19.7 Electrolytic Cells
- 19.8 Electrolysis Calculations
All right, let's have a little fun. First thing we're gonna talk about is periodic trends. They call them periodic because they relate to the periodic table. And they just show you different trends of different things and how they increase or decrease from one side to another on the periodic table. But it is a periodic trend, matching up with the periodic table. First one we're gonna talk about about is atomic radius. So if you look at atomic radius this is the overall size of an atom. So have you ever been to France? No France. So if you did go to France what you would find in France is that you'd eat too much cheese, too much bread and drink too much wine and you'd get really fat. So the fattest element on the periodic table is indeed francium. So- and if you look francium is in the lower left corner of the periodic table. And so your atomic radius trend increases in size going down towards francium. Now that meaning: it increases going down and it increases going to the left on the periodic table. So that is the general trend for atomic radius. We'll dive into more specifics here in a second. The second term we'll talk about: ionization energy. First of all do you know what it is? Like technical definition? Other way around. Yeah, so it's the energy it takes to remove an electron. So energy it takes to remove an electron. Notice, an electron is on an atom because it's attracted to the nucleus. The nucleus has protons in it. And so the atom likes-I'm sorry- the electron likes being a part of that atom. It's attracted to the nucleus. Plus-minus attraction. So to pull that electron off the atom it costs energy, and so ionization energy is typically endothermic, it requires the absorption of energy. So that's what it is: energy to remove an electron. And in this case we'll find that it follows the exact opposite trend of atomic radius. It actually increases all the way up into the upper right-hand corner towards helium. So it increases going to the right, and it increases going up. And we'll talk a little more about the specifics of that trend in a little bit as well. So I kind of wanna establish all four trends here and then we'll dive in into details about each one. So again ionization energy is the energy to remove an electron-now, what's electron affinity? Yeah, this is the energy change associated with gaining an electron, adding an electron. So in this case whereas it's typically endothermic when you want to remove one- it costs energy- so typically there's a release of energy when you actually gain an electron. Not always, there's exceptions, but most of the time it is a release of energy when we add an electron. So in this case the general trend increases going towards the halogens. And when we say it increases going towards the halogens- so going towards the right in the periodic table- we mean that it gets more negative. So it gets more negative. So it releases more and more energy. And again that's the general trend, we'll see some exceptions here in a little bit but I just want to establish this trend. One thing to note though, the noble gases are not part of the trend. It stops at the halogens before you hit the noble gases. Okay the last one on the list is electronegativity. Electronegativity. Now a lot of students confuse electron affinity and electronegativity. So- and if you look ionization energy and electron affinity go together. This is energy of losing an electron, this is energy of gaining an electron. Notice, if I gave you an electron. You'd gain one, I'd lose one. You would undergo electron affinity, I would undergo ionization energy and as a result: you gaining an electron you'd now be an anion: have a negative charge. I would be a cation: have a positive charge. And the bond between us would now be an ionic bond I'm a positive ion, you're a negative ion- ionic bond. So these really are often associated with ionic bonding. But this guy, electronegativity, is associated with covalent bonding. It talks about sharing of electrons. And specifically it's what we use to kind of determine unequal sharing. So who's the most electronegative element on the periodic table? Any ideas? Fluorine. So and it turns out second place is oxygen so I'll say that because typically the further you go to the right and the further you go up towards fluorine in the upper-right corner, the more electronegative it gets. Again, the noble gases are not included as part of this trend either. But if you look oxygen and chlorine are both equidistant from fluorine. Oxygen is just to the left and chlorine is just below. But you should not only know that ah- that fluorine is number one, but you should know oxygen is actually number two, not chlorine. Suffice it to say, after that though, the closer you get to the fluorine the more electronegative. And what this means is that when fluorine makes a covalent bond he pulls those shared electrons closer to him than say, maybe, the other atom he's bonded to-provided it's somebody less electronegative. So the more electronegative the closer that atom has a tendency to pull the shared electrons towards him. Okay, so these are the four general trends- they're on your handout- but I want to dive in a little more into the details around each trend. So the first one we're going to talk about is the atomic radius. So here's the atomic radius. So in here we said atomic radius increases towards francium. Both going down the periodic table and going to the left on the periodic table. So why do atoms get a larger and larger and larger radius as we go down? Because of the shells. So the radius is determined by the electrons, right? The protons the neutrons are in the middle but it's the electrons around it and specifically the outermost electrons that determine the outermost boundary of the atom. As you get more and more shells- makes perfect sense- the atom gets bigger and bigger and bigger. Now the one that doesn't always make sense is this one though, the horizontal trend. If we look as you go to the left the electron cloud actually gets larger. And it seems counterintuitive because as you go to the left, what happens to the mass? It gets smaller. So the mass gets smaller this way but the cloud gets bigger and so it seems backwards. And we what we use to actually explain this is what we call effective nuclear charge. So we have a calculation for effective nuclear charge, which we'll look at in a sec, but it turns out effective nuclear charge increases going to the right. Effective nuclear charge increases going to the right. At least that experienced by what we call the valence electrons. The equation we use to calculate this: Z effective equals Z minus S. So Z effective equals Z minus S. So Z effective- Z stands for charge in general and in this specific case it stands for nuclear charge. So Z effective is effective nuclear charge. Z is then just plain old nuclear charge. Why does the nucleus have a charge? why is there a charge in the nucleus? What's- what's in there that's charged? Protons! And so the number of protons since they're each plus one, that is the Z the effect or sorry in this case just the nuclear charge. And then S stands for shielding or screening- use either one-electrons. So we'll talk about what that means here in a sec, but shielding or screening electrons. Okay so if we look for example, we're going to look at sodium. So sodium electron configuration is 1s2 2s2 2p6 3s1. And so if we look in the first shell of electrons, there are two of them. Two electrons in the first shell. In this second shell they're a grand total of eight. Cool and then in the third shell just one. And so which electrons actually determine the outermost boundary? The valence for sure. And so we're talking about the outermost boundary we are gonna be talking about this guy right here. Now this guy, he's attracted to that nucleus right there. What is the charge on sodium's nucleus? Well if we look he's atomic number 11, so he has a plus 11 charge. And so this electron looks at that nucleus and says *catcall whistles* so good-looking nucleus over there. But then he sees like these electrons right here and how does he feel about them? Yeah doesn't like em', he's repelled by them. So in this case it's attracted to that nucleus but any electrons that are closer than him are actually going to repel him the other way and so the Z effective here's the balance between those. So we've got a +11 attractive attraction right there- and so in the case of sodium our Z effective is equal to 11 for the Z number of protons in the nucleus, but how many electrons each with a negative 1 charge are closer than he is repelling him away? Ten. And so this-the S, the shielding, our screening electrons- is 10. And so we find out that the net effective nuclear charge he feels it's +1. That's a measure of how attracted to the nucleus he is. Now if we compare this to say, magnesium, on the other hand. So magnesium 1s2 2s2 2p6 3s2. So he's the next one in the series and again we got a nucleus. And we got three shells. How many electrons are in the first shell? Sweet. How many the second shell? How many? Good and so if we go to the same calculation for effective nuclear charge what is the Z on the nucleus? Well magnesium is atomic number twelve. So there are 12 protons in that nucleus, +12 charge. And so the Z here is 12. But how many electrons are- notice this is the outermost electrons and I can look at either one it does really matter- how many electrons are closer to the nucleus than either one of these? Ten still. Notice, the electrons that are in the same shell don't have really much of a repulsion on each other. It's this- turns out there's a little, but nothing we're going to account for here. And so we don't really count each other as shielding each other it's only the core electrons that shield the valence electrons. And so in this case the net effective nuclear charge is +2. And again that's a measure of how much that outermost electron is attracted to its nucleus. And so whose valence electrons, sodium or magnesium, is more attracted to its nucleus? Magnesium. And if it's more attracted it's going to get sucked in just a little bit tighter and end up being a little bit smaller and we see that magnesium is indeed smaller than sodium as a result. Because our effective nuclear charge will increase going across the periodic table. And so notice as you go from, say, sodium to magnesium to aluminum to silicon to phosphorus to sulphur to chlorine to argon all across the third row, that effective nuclear charge just keeps increasing because you as you go across that row you get another proton all along the way. And so the Z value keeps increasing. But because you're just adding more electrons into that outermost shell, you're not adding any more core electrons all the way across. And so as the Z value is going up the S value is not changing. And so here sodium's effective nuclear charge on the valence electron: +1, magnesium +2, aluminum +3, silicon +4, phosphorus +5, sulfur +6, chlorine +7, argon +8. And because it grows all the way across they get smaller and smaller and smaller and smaller because they're more attracted. One thing to know: how many valence electrons does sodium have? Ooo, those are core but valence is out here, just one. How many does magnesium have? Just two. How many aluminum? Three. So if you notice it's convenient that the number of valence electrons is equal to the effective nuclear charge on those valence electrons as well. We said sodium's effective nuclear charge +1, and he has one valence electron. Magnesium +2, and he has two valence electrons. Aluminum +3, he has three valence electrons. And so it's a quick way to remember that, oh yeah, the effective nuclear charge felt by the outermost electrons- the valence electrons- is the same as the number of valence electrons for your main group elements. Okay so, this is again why as the effective nuclear charge increases going from left to right, the size increases going the other way. Sodium's outermost electrons aren't as attracted to the nucleus and so they're further away. And so the size increase is going right to left opposite of the effective nuclear charge trend. So that's- that explains our funky atomic radius trend there. Okay one other thing to note, we took all this time to teach you about effective nuclear charge and because we did we used it to explain our atomic radius trend but we can ask you about effective nuclear charge about anything now. Notice it's only his effective nuclear charge that affects the overall outermost boundary of the atom. But what if I want to ask you about say his effective nuclear charge? The 1s electron. If I want to do this calculation for the 1s electron in sodium, what would the Z be? The number of protons at the nucleus. Well it's still 11- but how many electrons are closer to the nucleus than a 1s electron? None and so I'd have 11-0 and the effective nuclear charge he feels is +11. Now what does that have to do with the overall size of the atom? Absolutely nothing. But I can ask you that question now. The way this usually comes up is-let's say: compare sodium and magnesium. Now, instead of comparing the outermost electron let's just compare the 1s electron. Whose 1s electrons are closer to the nucleus? Well whichever one has more protons. Because if I compare any 1s electrons, is there an atom whose 1s electrons will ever have an S value? No, that always going to be 0 for a 1s electron. So I could ask you any elements of the periodic table not just sodium or magnesium but anybody and whoever has the greatest number of protons is going to have the S orbital that lies closest to the nucleus because it will have the greatest effective nuclear charge. And that's the other way you might see a question like this asked. You know sodium or uranium, and uranium is a huge element. Because it's so huge we think "oh it's electrons are far away". But if the question says whose 1s orbital is closer to the nucleus, uranium wins hands down because his effect-his effective nuclear charge on the 1s orbital is way way way more positive. So we can apply this idea of atomic radius to a couple other things as well first thing is bond length. So if we look at two atoms that are bonded together the length of the bond is defined as nucleus to nucleus. And so ultimately larger atoms form longer bonds. Longer bonds are weaker bonds it turns out. So you may get a question about just, which atoms, you know, you might be given you know a carbon- fluorine bond, a carbon-chlorine bond, a carbon-bromine bond, a carbon-iodine bond, and if you notice these are the halogens. This is increasing size of the halogens. And they usually give you a bunch of bonds to compare where one of the atoms is uncommon. And so if I look at these four bond lengths here, which one is going to be the largest? Which one's going to be the smallest? So and again carbon's the same size every time but notice the halogens, this is exactly how they look on the product table going from top to bottom. What happens to atomic radius' from top to bottom? Gets bigger, so which one of these bonds is the longest? Awesome. Which one is the shortest? So which one is the strongest? Good, shorter bond is harder to break. So this is the strongest and this guy the weakest. So you may get a question to ask for any one of those four: the strongest bond, the weakest bond, the longest bond, the shortest bond out of a given set. And bigger atoms make longer, weaker bonds. Smaller atoms make shorter, stronger bonds. Cool. The other place where you might use atomic radius, we have to relate this to ionic radius- to ionic radius. You know what I'm actually going to want a little more than this. So atomic radius is the radius of a neutral atom. What's an ionic radius then? Radius of a charged atom, an ion. So in this case I've got two ways you can look at this. So we first should just look at a comparison here. If I look at calcium and calcium 2+, what's the main difference between these two? Not size wise but I mean just in general sense, what it contains. So- would- yeah, so it's charges, the two less electrons. And so in this case we've lost two electrons to become calcium 2+. If the electron cloud has two less electrons, then what do you think has happened to the size of that electron cloud? It's smaller, and that's exactly it. So we got this guy here, we got this guy here. In the case of calcium 2+, the two electrons it lost represent the two valence electrons it used to have. And so it not only just lost a little bit of size, it lost the entire outermost shell. And it's significantly smaller as I've diagrammed here. And so what we learn here is that cations, positive ions, are smaller than their corresponding neutral species. Now, what if I were to ask you to compare say sulfur and sulfur 2-. A little more room here. Why is it bigger? Yeah, you've just added two extra electrons to its' electron cloud and so you've made the electron cloud bigger. More electrons to the electron cloud, it makes sense that it's bigger. And so in this case, we learn that anions are bigger than their corresponding neutral species. So let me ask you a question. What kind of elements typically form cations? What kind of elements typically are the ones that lose electrons? Metals, good. So if I asked you to find me an element whose ionic radius is smaller than his atomic radius then you should be looking for a metal. So they might wory that you might not know cations are smaller than their neutral species but if you didn't put it together that metals are what typically form cations you might not get that question right. If I ask you to find me an element whose ionic radius is larger than its atomic radius then, what kind of element would I be looking for? Well one that forms anions but, which elements form anions? Your nonmetals, awesome. So you should make that association. Metals typically form cations, nonmetals typically form anions. So metals typically have an ionic radius that is smaller than its' atomic radius. Nonmetals typically have an ionic radius that's larger than its atomic radius. Cool. You might have some other trends you need to do with ionic radius. So you might have to compare things of like charge. So let's say we compared magnesium, calcium, strontium, barium. Now these four, they're all the group two elements, right? Magnesium, calcium strontium, barium- right as you see them on the periodic table going down. So which of these has the largest atomic radius? Well atomic radius increases going which way on the periodic table? Down, so barium's the biggest. Cool so, I wrote them right as they show up on the periodic table. So barium is the biggest. Okay so, if these all were ions instead- with exactly the same charge then the same trend would apply. You can apply the atomic radius trend to ions provided they all have exactly the same charge. So, sweet, barium 2+ is still the largest out of these four as well. So the other trend you might have to do with ions is going to involve what we call an iso- electronic series. What does "iso-" mean? Not isolate. "Iso-" like: isotope, isomer, isotonic. Actually the exact opposite, it means the same, no change essentially, but the same. And so an isoelectronic series is a series of atoms or ions that have the same electronic configuration or the same number of electrons. So if we were to look at say sulphur 2-, Cl (1-), argon, potassium (1+), and calcium (2+). What you'd find out is that all five of these have the same electronic configuration as argon. Which means all five of these have 18 electrons. All of them. What's the difference then? If they all have 18 electrons then, how many protons does argon have, having no charge? Must have 18. How many elect- how many protons does sulfur have? Careful. 16. 16. How many protons does calcium have? 20. So the electrons is not the difference now, Before these comparisons, it was about the number of electrons being different but that's not different here. They're all 18 electrons. The difference is whose nucleus has the most protons. Well the most positive one does. And so being the most positive, the valence electrons have the greatest attraction to the nucleus and makes the atom the smallest. and so in this case with an isoelectronic series like this, the most positive one will be the smallest, the most negative one will be the largest. Cool and these are the kind of general comparisons you'll see. You may just get a straight-up question on atomic radius. You may get a question that really is dealing with atomic radius but asked in the form of bond lengths. You may get a question comparing atomic radius to ionic radius. You may get a question that just deals with ionic radiuses that all have the same charge or you may finally get one dealing with an isoelectronic series. So in this case- again- it's not about a difference in electrons it's about a difference in protons in a nucleus. Most protons will be the most positive one in the series and will therefore attract the outermost electrons in the tightest and be the smallest. Most negative would therefore, opposite, be the largest. Cool. Those are all the comparisons you might need to make involving atomic radius.
In this lesson you will learn:
-The Periodic Trend for Atomic Radius
-The definition of Effective Nuclear Charge (Zeff)
-How Effective Nuclear Charge affects Atomic Radius
Atomic Radius Increases Down a Group
Atomic radius increases down a group on the periodic table. This is fairly intuitive as this increase in radius is explained by an increase in the number of shells of electrons as one moves down a group on the periodic table.
Atomic Radius Increases Right to Left Across a Period
Atomic radius increases right to left across a period on the periodic table. Initially this seems counter-intuitive as this increase in radius is accompanied by a general decrease in atomic mass. But if we keep in mind that the atomic mass is concentrated in the nucleus whereas the atomic radius is related more to the size of the 'electron cloud' it can be understood that these trends do not need to align.
This trend in atomic radius is best understood in terms of the effective nuclear charge experienced by the valence electrons. The effective nuclear charge (abbreviated Zeff) is measure of the strength of the attraction of a valence electron to the nucleus. It accounts for both the attraction to the protons in the nucleus and the repulsion from the other electrons in the atom.
The effective nuclear charge can be approximated by the following simplified formula:
Zeff = Z - S
where Z is the number of protons and gives the charge of the nucleus and S represents the number of 'shielding' or 'screening' electrons. For a valence electron the number of shielding electrons is simply equal to the number of core electrons. This methodology says that valence electrons don't experience repulsion from each other. This is not technically true but a decent approximation for our purposes as the repulsion from another valence electron should be considerable less than from a core electron. It turns out that not all core electrons will contribute the same repulsion either as described in Slater's Rules, but the rough approximation being used here will be sufficient to explain the trend in atomic radius.
Sodium and magnesium are a good comparison to demonstrate the trend. Sodium has 11 protons (Z = 11) and 10 core electrons (S = 10) and its effective nuclear charge is
Zeff = Z - S = 11 - 10 = +1
Magnesium has 12 protons (Z = 12) and 10 core electrons (S = 10) and its effective nuclear charge is
Zeff = Z - S = 12 - 10 = +2
Magnesium's valence electrons experience a higher effective nuclear charge which indicates a greater attraction to the nucleus explaining why it would have a smaller atomic radius (130pm for magnesium vs 154pm from sodium).
Overall, as one proceeds from left to right across a period there is an increase in the number of protons in the nucleus while the number of shielding electrons remains constant leading to an increasing effective nuclear charge. We've now established that effective nuclear charge increases left to right across a period and see how it explains the corresponding decrease in atomic radius. The atomic radii and effectively nuclear charges for the 2nd period elements is show below.