# Explain the hybridization of "AgC"_2"H"?

Nov 25, 2016

Carbon uses $s p$ orbitals in this compound for its $\sigma$ bonds, and $2 {p}_{x}$ and $2 {p}_{y}$ atomic orbitals in its $\pi$ bonds. Only the $2 s$ and $2 {p}_{z}$ are hybridized to form the two $s p$-hybridized atomic orbitals on $\text{C}$.

Silver acetylide can be thought of as analogous to acetylene, ${\text{C"_2"H}}_{2}$, since the valence orbitals on carbon do not change whether it is ${\text{Ag}}^{+}$ or ${\text{H}}^{+}$ bonding to $\text{C}$.

stackrel((+))("Ag") :stackrel((-))("C"):::"C":"H"

or

stackrel((+))("Ag")-stackrel((-))("C")-="C"-"H"

Choosing the right $\text{C"-"H}$ bond for simplicity, hydrogen can only contribute a $1 s$ atomic orbital in a linear combination to overlap with carbon's atomic orbital in a $\sigma$/sigma fashion (head-on overlap).

Here are examples of $\boldsymbol{\sigma}$ (head-on) and $\boldsymbol{\pi}$ (sidelong) overlap:

Note that the same-signed lobes overlap to create a bonding molecular orbital.

Although carbon could offer its $2 {p}_{z}$ atomic orbital, it also needs to bond to the other carbon atom. It's more favorable if both orbital lobes are the same sign, but originally, a $2 {p}_{z}$ atomic orbital has oppositely-signed lobes.

So, a regular $2 {p}_{z}$ is not sufficient.

As a result, each carbon hybridizes its $\underline{2 {p}_{z}}$ atomic orbital with its $\underline{2 s}$ atomic orbital to form two $\boldsymbol{s p}$-hybridized atomic orbitals (and we should expect from conservation of orbitals that we get two hybridized orbitals out from two pure orbitals in).

Orbital depiction:

Electron configuration depiction:

This allows both carbons to bond with both each other and hydrogen and silver in silver acetylide. Here is an MO depiction for acetylene for reference:

By analogy, silver can bond with carbon's $s p$-hybridized atomic orbital by overlapping its $\setminus m a t h b f \left(5 s\right)$ atomic orbital (just like how hydrogen uses its $1 s$ atomic orbital), since it is singly-occupied in the configuration $\left[K r\right] 5 {s}^{1} 4 {d}^{10}$ as an "exception" to the Aufbau Principle.

The only difference between acetylene and silver acetylide is that silver contributes a different orbital in the linear combination. Carbon contributes the same orbital as with hydrogen.