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### Course: AP®︎/College Chemistry>Unit 1

Lesson 6: Periodic trends

# First and second ionization energy

An element's second ionization energy is the energy required to remove the outermost, or least bound, electron from a 1+ ion of the element. Because positive charge binds electrons more strongly, the second ionization energy of an element is always higher than the first. Created by Jay.

## Want to join the conversation?

• Would there be such a thing as third ionization energy? Also, if the third electron from Lithium would be pulled away would take the same amount of force as the second or would this in turn be even harder to pull away?
(23 votes)
• There is most certainly a third ionization energy, and fourth, and fifth....! The 3rd IE corresponds to the energy required to remove an electron from the gaseous M2+ species of any element, i.e. Na2+, Ca2+, or S2+. As you remove more and more electrons, the atom becomes progressively more positively charged, Hence, it becomes harder and harder to remove an electron, which is negatively charged.

Each successive ionization energy would be larger in magnitude than the previous one. The ionization energy that corresponds to removing an electron from the noble gas configuration would be substantially higher than those before. For example, for P, the 5th IE is 6,270, while the 6th IE is 21,200. For Al, the 3rd IE is 2,881, while the 4th IE is 11,600.
(43 votes)
• you stated that the first ionization energy for Li is 520 kj/mol and the second ionization energy is 7298kj/mol. how would you calculate those ionization energy values for Li and also take the value of the shielding constant into consideration. thank you.
(19 votes)
• What is z in the equation (meaning)
(0 votes)
• Does size of the atom have a relation between nuclear charge and ionization energy? Would it correct to conclude that larger the atom, lower the ionization energy (since distance from the nucleus is higher)?
(8 votes)
• Great question! The size of an atom does affect both the nuclear charge and the ionization energy. First of all, If an atom has more protons in its nucleus, then the nuclear charge will obviously be greater, so the ionization energy will be higher. But just as Jay said, you also have to take into account the distance between the electrons and the nucleus, as well as electron shielding/screening. A larger atom will have more distance between the nucleus and the farthest electrons, so it will be easier for that atom to lose an electron. Also, a larger atom will have more electrons, which will all repel each other and push the outer electrons away from the nucleus (at least, that's what I would think). Both of these factors will lower the ionization energy. So I believe you are correct in that the larger the atom, the lower the ionization energy will be. (Sorry, I know this answer is late in coming.)
(5 votes)
• I'm trying to understand the concept of joules in relation to pulling an electron away. I am used to using watts (and amps and volts) as measurement for energy and watts can be experienced through things like electroshock therapy, but something like 7 joules sounds like lightbulb that would be too bright to make a meaningful difference other than as a heat lamp.
So, can this instead be conceptualized as how many pounds a would be needed to pull an election away if you could clamp an atom down and tie a string to one election? or even better in terms of pulling one magnet from a 1 pound piece of mild steel? I'm a bit of a meathead coming from a blacksmithing background so please bear with me.
(1 vote)
• I think it would be helpful here to go over the fundamental definitions of energy and all the units you’ve listed here to better understand ionization energy.

Energy itself, viewed from a physics perspective, is defined as the capacity to do work. Work, in the physics sense, is the result of a force acting over a distance. And a force is a pushing or pulling motion which causes an object to accelerate.

So if we imagine pushing (applying a force) an object, any object, a certain distance over say a table’s surface, then we would say we have performed work on that object. In essence what we did was transfer some of our own energy into the object to facilitate the object’s motion. So something is said to possess energy if it can do work. There are many different types of energies; electrical, mechanical, thermal, gravitational, chemical, etc., but we can generalize and categorize energies as either potential or kinetic energy. Potential energy is related to an object's position (where it is); or in other words it has the potential to do work but it’s currently not doing so. Kinetic energy is energy related to an object’s motion; if an object is moving in some manner then it has kinetic energy. Most objects do not have either entirely potential or kinetic energy, and instead possess a combination of the two (which combined are that object’s total energy).

Now looking at the units of force, work, and energy. In SI units, the unit of force is the newton (N), and the American customary unit is the pound-force (not to be confused with the pound-mass). Mathematically work is defined as the product of force and distance, F x d = w, where the SI unit of distance is the meter (m) and newton for force (and ‘w’ is the usual variable for work). So the SI unit for energy is the newton-meter (Nm), more commonly referred to as the joule (J). Since energy is related to work, energy’s unit is also the joule. In America the units of energy are foot-pounds or British thermal units (BTU). So this means 1 joule of energy is the amount of energy required to apply a 1 newton force on an object for a distance of 1 meter.

Watts (W) aren’t actually a unit of energy, rather a unit of power. Power is the amount of energy expended per unit of time, Power = energy/time. So 1 watt would be if we applied 1 joule of energy per 1 second to something. Using that power equation, we can get another commonly used energy unit called the kilowatt-hour (kWh), which is defined as the amount of energy needed to provided 1000 watts of power for 1 hour.

Amperes (A), or amps for short, aren’t a unit of energy either, rather a unit of electric current. If we imagine electrons moving in a wire (essentially what electricity is) like water in a stream, then we have a current in that wire. Current is defined as the amount of electrical charge (usually electrons) flowing per unit of time, current = charge/time. So 1 amp of current is defined as the flow of 1 coulomb (the unit for electrical charge) of charge per 1 second.

Volts (V) too aren’t a unit of energy, but they are closely related. Voltage can be thought of as the driving force which propels electrons and creates a current in a wire. Since electrons are negatively charged they are naturally attracted to positively charged objects (and repelled from negatively charged objects). So any kind of electrical device has a positively charged component which electrons travel towards, and a negatively charged component which they travel away from (collectively called electrodes). Electrical current is driven by a difference in potential energy caused by an electric field resulting from the charge difference on the two electrodes. This is why voltage is also referred to as potential difference or electrical potential. As an equation we can think of voltage as the amount of energy possessed by charge carriers (again almost always being electrons), Voltage = energy/charge. So using SI units, 1 volt is a difference of 1 joule of potential energy (J) per 1 unit of charge (C). So while voltage isn’t energy, it is closely related to energy and like watts we can create yet another common unit of energy called the electron-volt (eV). 1 electron-volt is the amount of kinetic energy gained by an electron as it passes through a voltage of 1 volt.

Now looking at ionization energy. Ionization energy is the amount of energy we need to input into an atom to remove an electron from that atom. If we think of it as work, it’s the amount of force we need to apply to the electron to move it a certain distance from the nucleus of the atom so that they no longer feel a force of attraction (because they have opposite charges). This means we could think of it as us pulling on the electron with a certain amount of pounds (force-pounds) so that it is sufficiently far from the nucleus the overcome the electrical attraction the two feel. The magnet analogy would also work (Ha) because we would be exerting a force on the steel in order to move it a certain distance so that it no longer felt a force of attraction. The work being done is attempting to overcome the magnetic force in the same way that ionization energy is work done to overcome the electric force.

When ionization energies are calculated experimentally we usually expose them to light of sufficient energy. The light transfers energy to the electron and grants it enough kinetic energy to escape from the pull of the protons on the nucleus. We measure the ionization energy based on the energy of the light required to ionize the atom.

Hope that helps.
(14 votes)
• So can we also remove the last electron of Lithium ?
(4 votes)
• To remove the last electron, people say it would take a lot to do it, but more specifically it takes 11,815 KJ/mol.
(6 votes)
• is it possible that lithium can lose its 1s1 electron as well and turn into Li3+?
(4 votes)
• It is possible but that would require a really high amount of energy to be supplied to the Li2+ ion.
(4 votes)
• Why is the first ionisation energy of Helium is more than that of Hydrogen ?
Please explain.
Thank you.
(3 votes)
• First I.E of He is more than that of H because He has two valence electrons and its charge is also greater than that of H . Also it is a noble gas and very stable , so we have to provide larger energy to remove an electron from its outer most shell.
(5 votes)
• How to calculate Ionization energy using Slater's Rules?
(3 votes)
• So slater's rules help calculate the effective nuclear charge which quantifies the attraction an electron feels for an atom's nucleus. Ionization energy is the amount of energy needed to remove an electron from a neutral gaseous atom and form an ion. The stronger an electron is bound to an atom the more ionization energy it requires, therefore these two are directly proportional.

As for calculating the actual values we can use a modified form of the Rydberg formula to do so: E = RH (Zeff^(2)/n^(2)), where E is the ionization energy, Zeff is the effective nuclear charge calculated from Slater's rules, n is the energy level of the electron being removed, and RH is the Rydberg constant. Depending on what units you want your ionization energy to be in will determine what value for the Rydberg constant you use. Most commonly electron volts (eV) is the energy unit used in which case the RH to be used is 13.6 eV. Kilojoules is also common in which case RH becomes 2.18 x 10^(-15) kJ.

Hope that helps.
(5 votes)
• why is he unit of I.E in kilojoules/mole?
I.E is just a type of energy so shouldn't it be just joules or kilojoules?
why to find it for a mole?
(3 votes)
• because it is the amount of energy to remove electrons from a certain number of atoms.
Obviously it takes more energy to remove an electron from each of 6.02*10^23 atoms than it does to remove an electron from one atom, right?
(4 votes)
• Why is the second ionisation enthalpy is smaller than the third ionisation enthalpy ?
Please explain.
(3 votes)
• As we continue to remove electrons from the atom, the effective nuclear charge increases , so it is pulled more strongly by the nucleus and hence 2nd I.E is smaller than 3rd I.E .
(4 votes)

## Video transcript

In the previous videos we've talked about only the first ionization energy. In this video, we're going to compare the first and the second ionization energies, and we're going to use lithium as our example. So in the previous video, we already know that lithium has an atomic number of 3, so there are three protons in the nucleus. In a neutral atom of lithium, the number of electrons equals the number of protons, and so we know there are three electrons in lithium here. The electron configuration is 1s2 2s1. So we have two electrons in the 1s orbital so we can go ahead and put those two electrons in the 1s orbital like that. And then we have one more electron, and that electron's going to go into the 2s orbital like this. And so that would be a very simple picture of the neutral lithium atom. If we apply enough energy, we can actually pull away this outer electron here. So we can pull away that electron, and we call this the first ionization energy. And to pull away that electron takes approximately 520 kilojoules per mole. And so once we've pulled that electron away, we no longer have a neutral lithium atom, right? We would have a lithium ion because we would still have three positive charges in the nucleus, but we have only two negative charges now. We only have two electrons because we pulled one away. So 3 minus 2 gives us plus 1. So this is the lithium plus 1 cation. And the electron configuration would just be 1s2 because we lost the electron in the 2s orbital. And so we could keep going. We could apply some more energy and pull away another electron. So let's say that we pull away this electron this time. OK, so we're taking a second electron away, and so we wouldn't call this ionization energy 1. We would therefore call this ionization energy 2 because this is to take away the second electron. And this value turns out to be approximately 7,298 kilojoules per mole. And so if we take away that second electron, once again we still have three positive charges in the nucleus, but we have only one negative charge now. There's only one electron so this is no longer the lithium plus 1 cation. This is the lithium plus 2 cation because 3 minus 1 is plus 2. So this is lithium plus 2 here, and the electron configuration would be only one electron in a 1s orbital, so 1s1. So we can see that there is a big difference between the first ionization energy and the second ionization energy, so 520 versus 7,298. So let's see if we can explain the reasoning for this extremely large difference in ionization energies. And we're going to use the three factors that we've talked about in the previous videos. So the first factor we discussed was nuclear charge, which refers to the number of protons in the nucleus. So if we look at the neutral lithium atom, three positive charges in the nucleus. That positive charge is what's going to attract this electron in magenta here. And if we look at the lithium plus 1 cation, similar situation. We still have three protons in the nucleus, and so that positive charge is what's going to be attracting this electron as well. And so because of the same number of protons, we have to think more about effective nuclear charge, as opposed to how many protons there are in the nucleus. And before we do that, we have to consider the effect of electron shielding. So let's talk about electron shielding next. So electron shielding, also called electron screening, so electron shielding slash screening. So when we think about electron shielding, we're thinking about the inner orbital electrons here. So going back to the neutral lithium atom, these two inner shell electrons right here are going to repel this outer shell electron. So this one is going to repel this one as well. And so we can think about it as they screen the electron in magenta from feeling the full force of the positive 3 charge in the nucleus because electrons repel other electrons. And so the way to calculate the effect of nuclear charge-- so we've done this in the previous videos as well-- the simple way of calculating effective nuclear charge is take the number of protons, so plus 3, and from that you subtract the number of shielding electrons. So in this case, it would be these two electrons in the 1s orbital. So 3 minus 2 gives us an effective nuclear charge of plus 1. And so the electron in magenta isn't feeling a nuclear charge of plus 3. It's really only feeling an effective nuclear charge close to positive 1 because the actual value is approximately 1.3 when you do the more complicated calculations. And so the effect of electron shielding is to decrease the overall nuclear charge that this electron magenta feels. And so when we move over here to this electron, so I'm talking about this electron in magenta for the lithium plus 1 cation, it's not the same situation, right? There's not much electron shielding. This electron over here might repel it a little bit, but there are no inner shell electrons repelling this electron in magenta. And because of that, the electron in magenta is going to feel this positive 3 charge, much more of the full positive 3 charge of the nucleus. And so therefore, there's going to be a much greater attractive force holding this electron in magenta to this nucleus. And therefore, you have to apply more energy to pull that electron away. So the effect of electron shielding tells you the second electron is much harder to remove than the first, and so we see a large increase in ionization energy from the first ionization energy to the second ionization energy. The last factor that we discussed was distance, so the distance of those electrons in magenta from the nucleus. So on the left, once again going back to the neutral lithium atom, this electron is in the second energy level. So it's further away than this electron. This electron is in the first energy level, in the 1s2, so this distance here is smaller than the distance on the left. And so since the distance is smaller, this electron in magenta feels more of an attractive force from the nucleus. Once again, that's Coulomb's law. And so therefore, there's an increased attractive force. Therefore, you take more energy to pull that electron away. So it takes much more energy to pull the second electron away than the first, and so that's why we see an increase in ionization energy. So distance says the fact that this electron is closer means it takes more energy to pull it away, and that's another reason why this number for the second ionization energy is so much larger than the first. So it takes a heck of lot more energy to pull away your second electron. And that explains why we see lithium forming a plus 1 cation, because it doesn't take anywhere near as much energy to pull away one electron as it does to take away two to form a lithium 2 plus. And so this is one way to tell what kind of an ion will form. Look at the ionization energies, and when you see a huge jump, that clues you in as to which ions are easier to form.