You can accurately predict trends in bond strengths if you comprehend the idea of hybrid orbitals (see previous post). We'll provide several examples of how to do this in this post.
1. A brief test
Let's begin with a brief test.
Which of the C-H bonds below is the strongest?
Which C-H bond has the highest bond-dissociation energy, in other words?
The response is C.
In example (a), the bond dissociation energy is 105 kcal/mol, and the carbon is sp3 hybridised.
In case (b), the bond dissociation energy is 110 kcal/mol, and the carbon atom is sp2 hybridised.
In case (c), the bond dissociation energy is 126 kcal/mol, and the carbon is sp hybridised.
2. Key Concept Regarding Bond Strengths And Orbital Hybridization: the bigger The Stronger The Bond, an S-character
Note that the trend for bond strengths is sp > sp2 > sp3 in the table above.
In other words, the bond is stronger the more carbon has the s-character.
Let's give it another go. These three C-C bonds, what about them?
I hope you gave them an A, B, and C ranking
An sp-sp3 bond is stronger than a sp2-sp3 bond, which is stronger than an sp3-sp3 bond, all things being equal.
Why?
3. Compared to their corresponding p-orbital counterparts, electrons in s-orbitals are closer to the nucleus.
On average, electrons in s orbitals experience a greater effective positive charge than electrons in the corresponding p orbitals because they are closer to the nucleus.
The nucleus will therefore be more attracted to electrons in a sp orbital (50% s-character) than in a sp2 (33% s-character) or sp3 (25% s-character) orbital.
The term "bond dissociation energy" (BDE) refers to the quantity of energy needed to homolytically cleave a bond (homo = same; lysis = breaking). Bond Dissociation Energies = Homolytic Cleavage [See Post]
In other words, it counts the amount of energy needed to break a bond so that every atom has the same number of electrons at the end, as in the following reactions:
In the aforementioned homolytic cleavage reactions, one electron is taken out of the C-H molecular orbital and put on hydrogen, causing it to dissociate. On carbon, the other electron is still there.
The sp-H bond has a higher bond dissociation energy than the sp3-H bond because it takes more force (energy) to remove an electron from the closer-bound sp-H molecular orbital and place it solely on the hydrogen atom.
Since they are nearer the nucleus, electrons in orbitals with more s character will experience a stronger electrostatic force.
This explains why the bond energy is higher.
Understanding the different kinds of bonds that exist in molecules is an important skill. (Additionally, C-C sigma bonds come in six different subtypes, while C-C pi bonds only exist in one).
This concludes the post's main lesson for the majority of purposes.
4. In the absence of other factors, the stronger the bond, the higher the s-character.
But… Read on if you're having trouble explaining an apparent contradiction that stems from a different section of the course.
5. Bonus Section: A Response to a Concern That A Few Readers May Have
Stronger acids than typical alkanes (pKa > 50) are alkynes (pKa 25).
Alkynes, for instance, are easily deprotonated by powerful bases like NaNH2, whereas alkanes are not.
Why? The conjugate base is more stable because the C-H bond in an alkyne has more s-character and the resulting lone pair on carbon is held to the nucleus more tightly.
I'm sorry. An angry mob appears to be moving in their direction.
WAIT! Alkyne C-H bonds are stronger than alkane C-H bonds because they have more s-character, but now you're saying that they are also more easily broken because they have more s-character.
Given that the C-H bonds have a higher s-character, shouldn't that make alkynes less acidic?
Put the pitchforks away! This can be explained in a perfectly logical way!
6. Bond Cleavage: Homolytic versus Heterolytic
What's causing this confusion, exactly?
Follow the electrons, shall we?
Understanding the distinction between homolytic cleavage, which is what bond dissociation energy measures, and heterolytic cleavage, which is what happens in an acid-base reaction and results in the loss of H+, is the key to solving this conundrum.
Now let's examine these two procedures.
An electron is completely transferred from the vicinity of the carbon to the hydrogen during the homolytic cleavage of a C-H bond. An electron can be removed from a sp-hybridized carbon more easily than from an sp3 hybridised carbon due to the bond's stronger s-character. Alkyne C-H bonds have higher bond-dissociation energies than alkane C-H bonds because of what we stated above.
The C-H bond also breaks in an acid-base reaction, but this time the pair of electrons remain attached to the carbon atom. It is known as a heterolytic bond cleavage (hetero = different, lysis = breaking) because the bond breaks in a way that results in an unequal distribution of electrons.
Repeat after me: during an acid-base reaction, a pair of electrons remain on carbon, resulting in a negatively charged carbon atom (a "carbanion").
Acidity is a measure of the equilibrium between an acid and its conjugate base, as determined by the pKa scale. The lower the pKa and the stronger the acid, the more the equilibrium favours the conjugate base. With those words:
Acidity is increased by any element that increases the stability of the conjugate base.
The lone pair is held in a sp- orbital with 50% s-character in the conjugate base of an alkyne.
The lone pair is held in an sp3 orbital with 25% s-character in the conjugate base of an alkane.
Which one will be a more stable lone pair?
The sole pair adhered closer to the nucleus, or the sp-orbital.
Because the conjugate base is more stable, alkynes are more acidic than alkanes.
This should make it more apparent that increased C-H acidity and stronger C-H bonds are two aspects of the same phenomenon.
The idea that sp orbitals have a higher effective electronegativity than sp2 orbitals, which in turn have a higher electronegativity than sp3 orbitals, may be useful. The reason why alkynes are more acidic than alkenes is thus not all that dissimilar from the reason why H-F is more acidic than water.]
7. An Exam For You
There is a third aspect of this phenomenon to take into consideration, at the risk of rambling on.
There is only one way that homolysis can take place. You may have noticed that I only demonstrated one of the two possible ways to depict the heterolytic cleavage of a C-H bond.
There is a second (although remote) possibility for heterolytic cleavage. Instead of migrating to carbon, the C-H bond's two electrons could move to hydrogen, creating a hydride anion and a carbocation. Again, extremely unlikely, but stick with me.
I have a test for you right here. Which of the two products below (A or B), given everything we've gone through so far, would be more stable?
Give it some thought.
We must take two electrons out of a sp-hybridized carbon in order to create A.
We must take two electrons away from an sp3-hybridized carbon in order to create B.
What is more advantageous?
An sp-hybridized carbon would need to have two electrons removed in order for reaction to give A to occur.
An sp3 hybridised carbon would need to have two electrons removed in order for reaction to give B to occur.
The electrons are held less tightly, so the reaction to produce B should be much simpler. Carbocations that are sp3-hybridized have been seen and even isolated.
Sp-hybridized carbocations, such as A, on the other hand, are incredibly unstable and have never been seen in the wild. [Note 1]
This observation agrees with all the previous ones as well.
8. Finally, this idea also clarifies why CH3+ is more stable than NH3+.
It may be helpful to think of sp-hybridized carbons as having a higher effective electronegativity than sp2-hybridized carbons, which in turn have a higher electronegativity than sp3 hybridised carbons, as I mentioned above. In the same way that H-F is a stronger acid than H2O, we used this to explain why alkynes are stronger acids than alkanes.
The same as in our previous carbocation example, this too can be turned around.
The amount of unstable electron-deficient species increases with the atom's electronegativity.
Increasing electronegativity has the same effect on the stability of electron-deficient species as increasing s-character, which helps to explain why, for instance, H3C+ (with six valence electrons) is much more stable than H3N+ (also with six valence electrons), which in turn is much more stable than oxygen or fluorine with six valence electrons.
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