# What are some examples of linear sp hybrids?

Feb 24, 2016

An interesting example is $\text{H"-"C"-="C"-"H}$, acetylene.

We utilize the convention that the $z$ axis points along the internuclear axis. Since the $p$ orbital that overlaps head-on with the $s$ orbital is along the internuclear axis, the $2 {p}_{z}$ orbital of carbon will the one that is compatible with the $1 s$ of hydrogen AND the $2 s$ of carbon.

The two carbons each have $\setminus m a t h b f \left(s p\right)$ hybridization, where they mix their $2 s$ and $2 {p}_{z}$ orbitals together, achieving an $\setminus m a t h b f \left(s p\right)$ hybrid orbital of 50% $s$ character and 50% $p$ character, with a new, lower energy, between those of the two original atomic orbitals. This can overlap with hydrogen's $1 s$ orbital.

That accounts for each $\setminus m a t h b f \left(\sigma\right)$ bond that each carbon makes with the other carbon and one of the hydrogens; see (a).

Then, the remaining $2 {p}_{x}$ and $2 {p}_{y}$ orbitals of each carbon can respectively overlap with the $2 {p}_{x}$ and $2 {p}_{y}$ orbitals of the other carbon (i.e. $2 {p}_{y}$ with $2 {p}_{y}$). These CANNOT overlap with hydrogen's $1 s$ orbital.

These account for the two $\setminus m a t h b f \left(\pi\right)$ bonds; see (b).

Overall, we get that each carbon uses two $s p$ hybrid orbitals by mixing the $2 s + 2 {p}_{z}$ orbitals in order to overlap with hydrogen's $1 s$ orbital and form a $\setminus m a t h b f \left(\sigma\right)$ bond with one of the hydrogens and the other carbon, and each carbon uses its $2 {p}_{x}$ and $2 {p}_{y}$ orbitals to generate two $\setminus m a t h b f \left(\pi\right)$ bonds with the other carbon.

The two $\setminus m a t h b f \left(\pi\right)$ bonds and one $\setminus m a t h b f \left(\sigma\right)$ bond made by each carbon with the other carbon accounts for the triple bond.