Problem 62 - A Complete Resource Book in Chemistry for JEE Main

Question

How many \(\sigma\) and \(\pi\)-bonds are there in the molecule of tetracyanoethylene? (a) \(9 \sigma\) and \(9 \pi\) (b) \(5 \sigma\) and \(9 \pi\) (c) \(9 \sigma\) and \(7 \pi\) (d) \(5 \sigma\) and \(8 \pi\)

Step-by-Step Solution

Answer

The answer is (a) 9 sigma and 9 pi bonds.

Step 1: Understanding the structure of tetracyanoethylene

Tetracyanoethylene (TCNE) has the formula C2(CN)4. It consists of a carbon-carbon double bond (C=C) and four cyano groups (C≡N). Each cyano group contains a triple bond.

Step 2: Counting the sigma (σ) bonds

Sigma bonds are present in every single bond, the first bond in a double bond, and the first bond in a triple bond. The structure of TCNE has: - 1 σ-bond in the C=C bond - 1 σ-bond for each C-N in the C≡N groups (4 bonds in total are between C and N ) - In addition, each C in a CN group forms one σ-bond with the double-bonded C Total number of σ-bonds = 1 (C=C) + 4 (C-N) + 4 (additional C-N) = 9 σ-bonds.

Step 3: Counting the pi (π) bonds

Pi bonds are the second bond in double bonds and the second and third bonds in triple bonds. In TCNE: - The C=C double bond contains one π-bond. - Each of the four C≡N triple bonds contains two π-bonds. Total number of π-bonds = 1 (from C=C) + 4 (from C≡N) * 2 = 1 + 8 = 9 π-bonds.

Step 4: Comparing with the provided options

Having established there are 9 σ-bonds and 9 π-bonds in TCNE, compare these totals to the given options. The correct option that matches is (a) 9 σ and 9 π.

Key Concepts

Sigma Bonds

Sigma (\(\sigma\)) bonds are crucial in understanding the basic framework of molecular structures. They are the strongest type of covalent chemical bond and form by the head-on overlapping of orbitals.
This direct overlap allows sigma bonds to be quite strong and to have a symmetric distribution of electrons between the atoms.
In every single bond, such as C-H or C-C, you will find one sigma bond.
In double and triple bonds, the scenario remains consistent as the first bond is always a sigma bond.

• In a double bond, like in the carbon-carbon double bond (C=C) found in tetracyanoethylene, the first bond is a sigma bond.
• In triple bonds, such as the carbon-nitrogen bonds (C≡N) found in cyano groups, the first bond is also a sigma bond.

With this understanding in mind, the total number of sigma bonds in a molecule can be calculated by counting each single bond and the first bond in any multiple-bonded situations within the molecule.

Pi Bonds

Pi (\(\pi\)) bonds offer unique insights into the reactivity and properties of molecules. Unlike sigma bonds, pi bonds occur from the side-to-side overlap of adjacent p orbitals.
This overlapping results in a bond that is less strong due to the electron density being concentrated above and below the plane of the bonded atoms.
Pi bonds are key components in compounds containing delocalized electrons, like benzene. Their presence also influences the shape and geometry of the molecule.

• In double bonds, such as C=C in tetracyanoethylene, the second bond is a pi bond.
• In triple bonds, such as C≡N, both the second and third bonds are pi bonds, accounting for the extra pairs of shared electrons.

Understanding the role of pi bonds adds depth to your knowledge of molecular stability and influences predictions about how a molecule might behave in a chemical reaction.

Double Bond

Double bonds introduce complexity into a molecule's shape and stability.
They consist of one sigma bond and one pi bond, linking two atoms more tightly than a single bond would.
This arrangement affects various properties of the molecule including its reactivity.
For example, in tetracyanoethylene, the presence of a carbon-carbon double bond (C=C) signifies both sigma and pi bonding:

• The sigma bond provides a strong attachment between the two carbon atoms.
• The pi bond contributes additional shared electrons, leading to increased strength compared to a single bond, but not as strong as a triple bond.

Double bonds result in restricted rotation around the bond axis. This geometry restriction can affect the chemical reactivity and the three-dimensional shape of the molecule.

Triple Bond

Triple bonds are extremely strong and highly significant in molecular chemistry. They consist of one sigma bond and two pi bonds.
Both sigma and pi bonds provide additional layers of connection between atoms. This results in a bond that offers exceptional stability and strength.
Consider the cyano group in tetracyanoethylene, characterized by the carbon-nitrogen triple bond (C≡N).

• The initial bond is a sigma bond, followed by two pi bonds that extend above and below the bond axis.
• This creates a state of high electron density, making triple bonds significantly stronger than single or double bonds.

The linear arrangement in triple bonds leads to a smaller bond angle and shorter bond length, which affects the molecule's overall geometry and how it interacts with other substances in chemical reactions.