Draw an MO energy diagram and predict the bond order of Li 2 + and Li 2 - . Do you expect these molecules to exist in the gas phase?

Welcome back everyone to another video, draw an mo energy diagram and predict the bond order or helium two with a positive charge and helium two with a negative charge to expect these molecules to exist in the gas phase. So first of all, let's consider our molecular orbital energy diagrams, we can essentially draw our energy levels. We know that we are considering helium. Let's understand that helium based on its position in the periodic table has two valence electrons, right. That's what we, that's what we know. And not only two valence electrons, the total number of electrons would be two electrons total. So if we are considering the total number of electrons, because that's exactly what we need to do for the orbital diagram, it would be more appropriate to use the number of electrons. Now, what we're going to do is just understand that we construct our molecular orbital diagrams based on the atomic orbitals. So helium is in the first period, meaning we're going to consider that the energy level N equals one to begin with. Let's start with helium two with a positive charge. And now what we can tell from here is that helium two with a positive charge would have two multiplied by two electrons. So we have four electrons total, right. But due to that positive charge, we end up with three electrons. So we're going to say that helium two with a positive charge has three electrons. And now similarly, helium two with a negative charge would have two multiplied by two plus one due to the negative charge. That's five electrons. Now let's start drawing our diagram. First of all, for helium two plus, let's draw the atomic orbitals from one S. So we're going to draw one square. OK. And we're going to label it as a one S orbital. And similarly, we're going to do the same on the other side because we have two helium atoms. OK. So 11 s once again and we're going to label them as a O which stands for the atomic orbital. Now, if we have two atomic orbitals, when they interact, they will form two molecular orbitals, one will be our bonding orbital, which we call sigma. OK. So we're going to say sigma one S and the other one will be higher in energy which is called sigma star one S this is our anti bonding orbital. And similarly, what we want to do from here, we just want to draw the two S level in case we have it. So we're going to say that OK. What if we have two S we're going to draw another orbital, those are the atomic orbitals, two S on each side. And now once again, we're forming two molecular orbitals out of them. One of them is sigma two S and the other one is sigma star two s higher in energy. And now for helium two with a negative charge, we're just going to repeat the process, we will have our atomic orbitals starting with one S. So we're drawing two boxes for each helium atom, then we are drawing our two molecular orbitals. So Sigma one S and Sigma star one s let's fix the handwriting a bit. So one S and now we are going to perform the same steps for the two orbitals just in case we have any electrons there. So to us, and now we are forming our molecular orbitals which are Sigma to S and Sigma star to S OK. So let's start adding our electrons for helium to the positive charge. We need to add we electrons. OK. So we can essentially add two electrons for one helium atom and one unpaired electrons or the other helium atom. And now based on the FB principle, as well as the hunts rule, we can essentially start filling our electrons starting with the lowest energy level because we only have one box, we can only add two electrons immediately. And we are left with one electron which goes into the sigma star, one S orbital for helium two with a negative charge. We know that we have five electrons total. So this might be a bit confusing but it should not be too difficult. First of all, we will just fill our one S orbitals for each helium. And now we are going to use those electrons to fill our sigma one S orbital. So two electrons go there. Our next energy, our next higher energy molecular orbital is sigma star one S and that one ace electron simply goes into the next orbital that we have, which is sigma two S we're just going along our energy levels, right? So we're adding that electron and we realize that this additional fifth electron can essentially come from the two s orbital of helium two with a negative charge. So we can essentially add it. And then we have our molecular orbitals from here. Our next step is to predict the bond order. So how do we see that? Well, essentially we have to recall that the bond order is equal to. Now we are taking one half and we need to subtract bonding electrons. How many do we have? Well, we have two and anti bonding electrons, we have one. So we get one half as a bond order for helium two with a positive charge. What about the bond order for helium two with a negative charge? Well, we take one half and we apply the same formula. How many burning electrons do we have? Well, 123 and we subtract the anti boning electrons from the sigma star one s orbital. And once again, we have the same bond order of one half. Now, our final question is, do you expect these molecules to exist in the gas phase? And the answer is yes, simply because the bond order that we got is positive, each value is positive. So they can definitely exist in a gas phase. If we get a zero bond order or a negative value. It basically tells us that such a bond cannot exist. And the higher the value is the stronger the bond. So in this case, that's it for today, we have got our mo energy diagrams, two bond orders. And finally, we said yes, these species can exist in the gas phase. That would be it for today. And thank you for watching.

Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory

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Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory

Problem 72

Chapter 10, Problem 72

Draw an MO energy diagram and predict the bond order of Li₂⁺ and Li₂^-. Do you expect these molecules to exist in the gas phase?

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Start by identifying the atomic orbitals involved in the formation of molecular orbitals for lithium (Li). Each Li atom has electrons in the 1s and 2s orbitals.

Construct the molecular orbital (MO) diagram for Li2. The 1s orbitals form the sigma (σ) 1s bonding and sigma star (σ*) 1s antibonding orbitals, while the 2s orbitals form the sigma (σ) 2s bonding and sigma star (σ*) 2s antibonding orbitals.

For Li2+, remove one electron from the highest occupied molecular orbital (HOMO) of Li2. For Li2-, add one electron to the lowest unoccupied molecular orbital (LUMO) of Li2.

Calculate the bond order for each species using the formula: Bond Order = (Number of electrons in bonding MOs - Number of electrons in antibonding MOs) / 2.

Discuss the stability of Li2+ and Li2- in the gas phase based on their bond orders. Generally, a positive bond order suggests that the molecule can exist, while a bond order of zero or negative suggests instability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Orbital Theory

Molecular Orbital (MO) Theory describes the behavior of electrons in molecules by combining atomic orbitals to form molecular orbitals. These orbitals can be bonding, antibonding, or non-bonding, and their energy levels determine the stability and reactivity of the molecule. Understanding MO theory is essential for predicting bond order and the existence of molecules in the gas phase.

Bond Order

Bond order is a measure of the number of chemical bonds between a pair of atoms, calculated as the difference between the number of bonding and antibonding electrons divided by two. A higher bond order indicates a stronger bond and greater stability of the molecule. For Li2+ and Li2-, calculating the bond order helps predict their stability and likelihood of existing in the gas phase.

Stability of Molecules in the Gas Phase

The stability of molecules in the gas phase is influenced by their bond order and the energy of their molecular orbitals. Molecules with a positive bond order are generally stable and can exist in the gas phase, while those with a bond order of zero or negative are less likely to be stable. Evaluating the bond order of Li2+ and Li2- will provide insight into their potential existence as gaseous species.