Rank C―H σ the following bonds in terms of their bond length. ...

Question

Rank C―H σ the following bonds in terms of their bond length. Explain your ranking ( 1= longest ; 3 = shortest).

Diagram comparing bond lengths of C-H bonds in different molecular structures, with arrows indicating hydrogen atoms.

Accepted Answer

All right. Hello everyone. So for this question, let's go ahead and arrange the indicated bonds in terms of increasing bond length. Explain the ranking here. We have three different compounds in which one of their carbon hydrogen bonds is highlighted for this question. So underneath the structures themselves are four different answer choices labeled A through D proposing different rankings as well as different explanations for the trend. It's worth mentioning here that the explanations proposed for each of the answer choices discusses a correlation between S character and bond length. So let's go ahead and talk about that. But before we do, I just want to point out here that increasing bond length means that we're going to arrange these compounds from smallest bond length or shortest, two, largest or longest. Actually, I should write that we're going from shortest to the longest. So with this in mind, let's go ahead and talk about what the concept of S character means and what it tells us about bond length. S character refers to the percentage of an S orbital or percentage of S orbital used in a given hybrid orbital. Now, in organic chemistry, the main hybrid orbitals we study are SP three SP two and SP So in this case, for example, an SP three hybrid orbital is composed of one S orbital and three P orbitals giving me a total of four. Because one quarter of the P three hybrid orbital is S that means that it has 25% S character. And so we can apply the same logic to the remaining orbitals that we have listed here. An SP two hybrid orbital, for example, is composed of one S orbital and two P orbitals giving me a total of three. Now, because one third of the hybrid orbital is s then an SP two orbital has 33.33% S character. And lastly, we have an SP orbital composed of one S and one P giving us a total of two. Now, because one half of the orbital is S that an P orbital has 50% S character. And so from this, we can gather the S characters of each of the primary orbitals that we study in organic chemistry, the hybrid orbitals. So recall that there is a correlation between the S character and the bond's length and strength, the greater the S character, the stronger and shorter the bond happens to be. So because were going from shortest to longest, in the case of this question, an sp hybrid orbital would be the shortest, followed by SP two and then followed by SP three, which would be the longest and therefore the weakest. So to understand the order in which we would rank these compounds, we have to understand the hybridization of both atoms and vault. Now, as discussed previously, all of the bonds indicated are examples of carbon hydrogen bonds because hydrogen can only use an S orbital. We're going to have to focus our attention on the hybridization of the carbon atom. So to find the hybridization of anything, recall that we're going to have to take into consideration the number of quote unquote groups surrounding the atom in question. Now, when I talk about the number of groups surrounding a central atom, I'm referring to two general categories. I'm referring to atoms bound to the central atom as well as any lone payers that that atom happens to have. So the sum total of all of the groups orbiting a particular atom tells us the hybridization of that particular atom. For example, if I have a total of four groups, then that corresponds to SP three hybridization. If I have three groups in total, that's SB two. And if I have a total of two groups, then that's sp hybridization. So let's go ahead and start with the indicated carbon atom of compound number one, the carbon atom of compound number one happens to have three groups surrounding it because I have three atoms bound to it and zero lone pairs. So three groups in total means that this carbon atom is SP two hybridized. So moving on to compound two here, let's go ahead and talk about the hybridization of the indicated carbon atom in compound two. In this case, it just so happens that this particular carbon atom only has two atoms connecting to it as well as zero lone pairs of electrons. So because that gives me a total of two groups, then this carbon atom is sp hybridized. And lastly, we have the indicated carbon atom or rather the carbon atom of the indicated bond or compound three. Now, at face value, it might be very easy to recognize that there are only three atoms surrounding the carbon atom in question, but recall these are line structures. So there's actually another hydrogen atom that's implied but not actually shown in the structure. So to illustrate this point, I'm going to go ahead and draw it and circle it because even though it's not shown it's implied and therefore counts right. So four groups in total means that this carbon atom is sp three hybridized. And so from this, we can go ahead and arrange these compounds according to the trend that we talked about previously correlating character to bond length because compound two involves an sp orbital or an sp hybrid orbital, it is going to be the shortest followed by compound one that features an sp two hybrid orbital followed by compound three, which would be the longest as it involves an SP three orbital. So our answer is going to be option a in the multiple choice. So from shortest to longest, we have compound two, followed by compound one and finally compound three. And so the lesser the s character, the longer the bond happens to be. So with all that being said, if you stuck around until the end, thank you so very much for watching. I appreciate it. And I hope you found this helpful.

Rank C―H σ the following bonds in terms of their bond length. Explain your ranking ( 1= longest ; 3 = shortest).

Key Concepts

Bond Length

σ Bonds

Factors Affecting Bond Length

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