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Atkins' Physical Chemistry | 11th Edition | ISBN: 9780198769866 | Authors: Atkins, Peter; De Paula, Julio; Keeler, James ISBN: 9780198769866 2042

Solution for problem P10B.3 Chapter 10B

Atkins' Physical Chemistry | 11th Edition

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Atkins' Physical Chemistry | 11th Edition | ISBN: 9780198769866 | Authors: Atkins, Peter; De Paula, Julio; Keeler, James

Atkins' Physical Chemistry | 11th Edition

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Problem P10B.3

Consider the \(\mathrm{H}_{2} \mathrm{O}\) molecule, which belongs to the group \(C_{2 v}\). Take the molecule to lie in the yz-plane, with z directed along the \(C_{2}\) axis; the mirror plane \(\boldsymbol{\sigma}_{\mathrm{v}}^{\prime}\) is the yz-plane, and \(\sigma_{\mathrm{v}}\) is the xz-plane. Take as a basis the two H1s orbitals and the four valence orbitals of the O atom and set up the 6 × 6 matrices that represent the group in this basis. (a) Confirm, by explicit matrix multiplication, that \(C_{2} \sigma_{\mathrm{v}}=\sigma_{\mathrm{v}}^{\prime}\) and \(\sigma_{v} \sigma_{v}^{\prime}=C_{2}\). (b) Show that the representation is reducible and spans \(3 A_{1}+B_{1}+2 B_{2}\).

Text Transcription:

H_2O

C_2v

C_2

sigma_v^prime

Sigma_v

C_2sigma_v=sigma_v^prime

sigma_vsigma_v^prime=C_2

3A_1+B_1+2B_2

Step-by-Step Solution:
Step 1 of 3

Chemistry Notes­ Unit 3 Week of 3/14 and 3/16 1. Gas Laws Continued a. Dalton’s Law of Partial Pressures i. The partial pressure of a gas in a mixture ii. Dalton’s Law states that the sum on the partial pressure of the component gases is equal to the total pressure of the mixture iii. P = P +P +P … Total 1 2 3 b. Avogadro’s Law i. This only applies if the gas pressure and temperature are constant ii. Calculates the number of particles and their relation to volume 1. Volume is directly proportional to number of particles a. If number of particles increases, the volume increases b. If number of particles decreases, the volume decreases 2. Always represented in moles iii. An equal volume of any gas contains the same amount of molecules V 1 = V 2 iv. N 1 N 2 c. Ideal Gas Law i. Mathematical representation of the relationship between volume, pressure, temperature, and number of moles in a gas ii. PV=nRT 1. P = pressure 2. V = volume 3. n = moles 0.0821atmx L 4. R = given constant ( molxK )

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Chapter 10B, Problem P10B.3 is Solved
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Textbook: Atkins' Physical Chemistry
Edition: 11
Author: Atkins, Peter; De Paula, Julio; Keeler, James
ISBN: 9780198769866

This textbook survival guide was created for the textbook: Atkins' Physical Chemistry, edition: 11. This full solution covers the following key subjects: . This expansive textbook survival guide covers 327 chapters, and 1120 solutions. The answer to “?Consider the \(\mathrm{H}_{2} \mathrm{O}\) molecule, which belongs to the group \(C_{2 v}\). Take the molecule to lie in the yz-plane, with z directed along the \(C_{2}\) axis; the mirror plane \(\boldsymbol{\sigma}_{\mathrm{v}}^{\prime}\) is the yz-plane, and \(\sigma_{\mathrm{v}}\) is the xz-plane. Take as a basis the two H1s orbitals and the four valence orbitals of the O atom and set up the 6 × 6 matrices that represent the group in this basis. (a) Confirm, by explicit matrix multiplication, that \(C_{2} \sigma_{\mathrm{v}}=\sigma_{\mathrm{v}}^{\prime}\) and \(\sigma_{v} \sigma_{v}^{\prime}=C_{2}\). (b) Show that the representation is reducible and spans \(3 A_{1}+B_{1}+2 B_{2}\).Text Transcription:H_2OC_2vC_2sigma_v^primeSigma_vC_2sigma_v=sigma_v^primesigma_vsigma_v^prime=C_23A_1+B_1+2B_2” is broken down into a number of easy to follow steps, and 96 words. Since the solution to P10B.3 from 10B chapter was answered, more than 202 students have viewed the full step-by-step answer. The full step-by-step solution to problem: P10B.3 from chapter: 10B was answered by Aimee Notetaker, our top Chemistry solution expert on 04/25/22, 03:45PM. Atkins' Physical Chemistry was written by Aimee Notetaker and is associated to the ISBN: 9780198769866.

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