Problem 178 - A Complete Resource Book in Chemistry for JEE Main

Question

$$ \text { The ratio of s-character in sp and } \mathrm{sp}^{3} \text { hybridization is } $$

Step-by-Step Solution

Answer

The ratio is 2.

Step 1: Understanding Hybridization

In hybridization, atomic orbitals mix to form new hybrid orbitals. In sp hybridization, one s orbital and one p orbital combine to form two equivalent sp hybrid orbitals. In sp³ hybridization, one s orbital and three p orbitals combine to form four equivalent sp³ hybrid orbitals.

Step 2: Determine the s-character of sp Hybridization

In sp hybridization, the s-character is determined by the proportion of s orbitals. Since 1 s orbital combines with 1 p orbital, the ratio of s orbitals is 1 out of 2 orbitals total, giving an s-character of \( \frac{1}{2} \) or 50%.

Step 3: Determine the s-character of sp³ Hybridization

In sp³ hybridization, the s-character is determined by the proportion of s orbitals. Since 1 s orbital combines with 3 p orbitals, the ratio of s orbitals is 1 out of 4 orbitals total, giving an s-character of \( \frac{1}{4} \) or 25%.

Step 4: Calculate the Ratio of s-character

The task is to find the ratio of the s-character in sp hybridization to that in sp³ hybridization. Using steps 2 and 3, the calculated s-characters are 50% and 25%, respectively. The ratio is \( \frac{50\%}{25\%} = \frac{1}{2} \div \frac{1}{4} = 2 \).

Key Concepts

s-character

When discussing hybridization, it's essential to understand the concept of s-character, which refers to the proportion of the s orbital in a hybridized orbital.In other words, it reflects how much of an orbital's identity is derived from the s orbital during the process of forming hybrid orbitals. This concept is key in determining the physical and chemical properties of molecules, such as bond angles and reactivity.
To calculate the s-character, consider the number of s orbitals compared to the total number of orbitals involved in hybridization. For example:

• In an \( sp \) hybridization, there is 1 s orbital and 1 p orbital, making a total of 2 orbitals. Hence, the s-character is \( \frac{1}{2} \) or 50%.
• In an \( sp^3 \) hybridization, 1 s orbital joins 3 p orbitals, making a total of 4 orbitals, giving an s-character of \( \frac{1}{4} \) or 25%.

Understanding the s-character is fundamental when examining the geometry and bonding characteristics in molecules.

sp hybridization

The process of sp hybridization involves the mixing of one s orbital and one p orbital from the same atom to produce two new equivalent orbitals known as sp hybrid orbitals. These orbitals are linearly combined and oriented 180 degrees apart, which gives them a linear shape.
This type of hybridization is found typically in molecules like acetylene, where the carbon atoms form linear structures.

• The two sp hybrid orbitals are significant as they allow the atom to form strong sigma bonds along the internuclear axis.
• Additionally, the remaining p orbitals, which do not take part in sp hybridization, are often involved in forming pi bonds, as seen in triple-bonded compounds.

The importance of sp hybridization lies in its ability to explain the linear geometry and bond properties of molecules.

sp³ hybridization

In sp³ hybridization, one s orbital mixes with three p orbitals to create four equivalent sp³ hybrid orbitals. These orbitals are arranged in a tetrahedral geometry, leading to bond angles of approximately 109.5 degrees.
This type of hybridization is common in organic molecules like methane, where carbon forms four single bonds.

• The sp³ hybrid orbitals have symmetrical distribution, which results in balanced forces across the molecule, making it geometrically stable.
• These hybrid orbitals are also highly effective at forming strong sigma bonds, which are essential for the structure and function of various organic compounds.

Understanding sp³ hybridization is crucial for grasping how simple hydrocarbons and some functional groups behave chemically and physically.