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Chapter 13: Problem 178

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

Short Answer

Expert verified
The ratio is 2.

Step by step solution

01

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 sp鲁 hybridization, one s orbital and three p orbitals combine to form four equivalent sp鲁 hybrid orbitals.
02

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%.
03

Determine the s-character of sp鲁 Hybridization

In sp鲁 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%.
04

Calculate the Ratio of s-character

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.
sp鲁 hybridization
In sp鲁 hybridization, one s orbital mixes with three p orbitals to create four equivalent sp鲁 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 sp鲁 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 sp鲁 hybridization is crucial for grasping how simple hydrocarbons and some functional groups behave chemically and physically.

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