Is the nomenclature "primary", "secondary", "tertiary", and "quaternary" carbon atoms limited to sp3 carbon atoms?

Question

In organic chemistry we can classify carbon atoms as primary, secondary, tertiary, or quaternary based on the number of additional carbon atoms bonded to the carbon atom of interest. The definitions in the textbook I teach from (Klein, 1st Ed. Wiley, 2011), as well as in several others I have, and from from several locations around the web, are:

• Primary $(1^\circ)$ carbon atom - bonded to one other carbon atom, e.g. $\ce{HO} {\bf \color{red}{\ce{C}}}\ce{H2CH3}$
• Secondary $(2^\circ)$ carbon atom - bonded to two other carbon atoms, e.g. $\ce{HO} {\bf \color{red}{\ce{C}}}\ce{H(CH3)2}$
• Tertiary $(3^\circ)$ carbon atom - bonded to three other carbon atoms, e.g. $\ce{HO} {\bf \color{red}{\ce{C}}}\ce{(CH3)3}$
• Quaternary $(4^\circ)$ carbon atom - bonded to four other carbon atoms, e.g. ${\bf \color{red}{\ce{C}}}\ce{(CH3)4}$

Is this labeling system limited to $sp^3$-hybridized carbon atoms? I do not see anything in the definitions that exclude $sp^2$- or $sp$-hybridized carbon atoms. Nor have I seen or read anything that explicitly excludes these atoms. However, the images in textbooks and around the web all show and discuss only $sp^3$-hybridized carbon atoms in this context. Are the following valid?

The central atom in propene $\ce{CH3 -}{\bf\color{red}{\ce{C}}}\ce{H=CH2}$ is a $2^\circ$ carbon atom because it is bonded to two other carbon atoms.

The carbon atoms in acetylene $\ce{HC#CH}$ are $1^\circ$ carbon atoms because they each are bonded to one other carbon atom.

The ipso carbon in toluene $\ce{C6H5CH3}$ (the carbon atom where the $\ce{CH3}$ is attached) is a $3^\circ$ carbon atom because it is bonded to three other carbon atoms.

Answer 1

To best of my knowledge, the classification primary to quaternary is used for discussing reactivity of hydrocarbons, i.e. alkanes. There the number of substituents matters, as it governs carbocation stability, steric hindrance, etc...

In all other cases, the electronic structure of the molecule rules the reactivity. As you mentioned alkenes, alkynes or aromates, there it makes no sense to discuss such subtle effect as number of neighbouring carbons, when you have $\pi$-system at hand.

The IUPAC Gold Book entry for alkyl groups supports this distinction:

The groups $\ce{RCH2}$, $\ce{R2CH}\ (\ce{R} ≠ \ce{H})$, and $\ce{R3C}\ (\ce{R} ≠ \ce{H})$ are primary, secondary and tertiary alkyl groups, respectively.

Answer 2

the correct definition is "a tertiary carbon atom has 3 bonds to ANY number of carbon atoms"

the carbon atoms in acetylene are tertiary, not primary (this came as a shock to me too the first time i heard it).

the reason for this is, you can further improve the classification by adding the hybridisation of the C atom, so in acetylene, the carbon atoms are both SP tertiary, while in isobutane, the central carbon atom is sp3 Tertiary.

if we would follow the flawed definition "a tertiary carbon is bound to 3 other carbon atoms" , then adding the hibridisation would be useless, as it would not alter the classification, which is why this definition is flawed.