Problem 101 - General Chemistry: Principles and Modern Applications

Question

What is the total number of (a) \(\sigma\) bonds and (b) \(\pi\) bonds in the molecule \(\mathrm{CH}_{3} \mathrm{NCO}\) ?

Step-by-Step Solution

Answer

The molecule \(\mathrm{CH}_{3} \mathrm{NCO}\) has a total of 6 sigma bonds and 2 pi bonds.

Step 1: Break down molecule into structural formula

Firstly, it is necessary to know the molecular structure of \(\mathrm{CH}_{3} \mathrm{NCO}\). The structure is H3C-N=C=O, where the hyrdocarbon \(CH_{3}\) is bonded with Nitrogen, Nitrogen is double bonded with Carbon and Carbon is double bonded with Oxygen.

Step 2: Count sigma bonds

Each single bond and each part of a double or triple bond is a sigma bond. So, in the molecule structure, there are three sigma bonds in the \(\mathrm{CH}_{3}\) group (between Carbon and Hydrogen atoms) and three more within the rest of the molecule (between Carbon-Nitrogen and Carbon-Oxygen). So, in total there are 6 sigma bonds.

Step 3: Count pi bonds

Pi bonds are the 'extra' bonds in a double bond (N=C, C=O). For each double bond, there is one pi bond. Therefore, there are two pi bonds in the \(\mathrm{CH}_{3} \mathrm{NCO}\) molecule.

Key Concepts

Sigma Bonds

Sigma bonds are the first bonds formed between two atoms in a molecule. They are the strongest type of covalent bond due to the head-on overlapping of atomic orbitals. The sigma bond (denoted as \( \sigma \) bond) allows for free rotation of bonded atoms, which can influence the shape of the molecule.
In the molecule \( \text{CH}_3\text{NCO} \), sigma bonds are found in several places:

• Three sigma bonds are present between the carbon atom and the three hydrogen atoms in the \( \text{CH}_3 \) group.
• One sigma bond exists between the carbon atom and the nitrogen atom.
• Another sigma bond is found between the nitrogen atom and the carbon atom.
• Finally, there is a sigma bond between the carbon and oxygen atoms.

This brings us to a total of six sigma bonds in the molecule. Remember, every single bond is a sigma bond, and each double or triple bond includes one sigma bond.

Pi Bonds

Pi bonds (\( \pi \) bonds) are formed by the side-by-side overlap of p orbitals. They occur in addition to a sigma bond, which is why they are known as the 'extra' bonds in double or triple bonds. Unlike sigma bonds, pi bonds restrict the rotation of bonded atoms, playing a significant role in determining the molecule's geometry.
In a molecule like \( \text{CH}_3\text{NCO} \):

• There is one pi bond between the nitrogen (N) and the central carbon (C), as they are doubly bonded.
• Similarly, one pi bond exists between the carbon (C) and the oxygen (O), also connected by a double bond.

Thus, there are two pi bonds within the molecule. Always remember that pi bonds do not occur in single bonds and are essential for multi-bond structures.

Molecular Structure

Understanding the molecular structure of a compound is key to identifying the number and types of bonds it contains. The molecular structure of \( \text{CH}_3\text{NCO} \) can be visualized as a series of atoms bonded in a chain: H\( _3 \)C-N=C=O.
To interpret this structure:

• The \( \text{CH}_3 \) group forms a chain with three hydrogen atoms bonded to a central carbon atom.
• The carbon atom is then bonded to nitrogen, which is indicated in the formula.
• Following the nitrogen, the carbon atom forms a double bond, indicated by \( = \), with an oxygen atom.

These bonds define the molecule's shape, determine the bond angles, and influence physical and chemical properties. The arrangement of sigma and pi bonds in this structure leads to specific reactivity and stability, which are crucial in chemical reactions and behaviors.