Ch.9 - Molecular Geometry and Bonding Theories

Problem 94b

Chapter 9, Problem 94b

The O—H bond lengths in the water molecule (H2O) are 0.96 Å, and the H—O—H angle is 104.5°. The overall dipole moment of the water molecule is 1.85 D. b. Calculate the magnitude of the bond dipole of the O─H bonds. (Note: You will need to use vector addition to do this.)

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Identify the given values: bond length of O—H is 0.96 Å, H—O—H angle is 104.5°, and the overall dipole moment of water is 1.85 D.

Understand that the dipole moment is a vector quantity, and the overall dipole moment is the vector sum of the individual bond dipoles.

Use the formula for the dipole moment: \( \mu = q \times d \), where \( \mu \) is the dipole moment, \( q \) is the charge, and \( d \) is the distance (bond length).

Set up the vector addition for the dipole moments of the two O—H bonds, considering the angle between them (104.5°).

Use trigonometry to resolve the vector components of the bond dipoles and apply the law of cosines or vector addition to find the magnitude of the bond dipole.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Bond Dipole Moment

The bond dipole moment is a measure of the polarity of a bond, arising from the difference in electronegativity between the bonded atoms. In a polar bond, the more electronegative atom attracts the shared electrons more strongly, creating a dipole with a positive and a negative end. The bond dipole is represented as a vector, with its magnitude proportional to the charge difference and its direction pointing from the positive to the negative end.

Vector Addition

Vector addition is a mathematical process used to combine vectors, which have both magnitude and direction. In the context of molecular dipoles, the individual bond dipoles of a molecule can be represented as vectors that need to be added together to find the resultant dipole moment. This involves breaking down the vectors into their components, typically along the x and y axes, and then summing these components to determine the overall dipole moment.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule, which significantly influences its physical and chemical properties. In water (H2O), the bent shape due to the H—O—H angle of 104.5° leads to an uneven distribution of charge, contributing to its overall dipole moment. Understanding molecular geometry is essential for predicting how molecules interact with each other and their environment.

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