Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 50

The specific rotation of a pure optically active compound is \(+12^{\circ} .\) The specific rotation of the sample in a reaction with \(20 \%\) racemization and \(80 \%\) retension of configuration will be (a) \(+12^{\circ}\) (b) \(-12^{\circ}\) (c) \(+9.6^{\circ}\) (d) \(-2.4^{\circ}\)

Short Answer

Expert verified
Answer: +9.6°

Step by step solution

01

Understand terms in the problem

The terms used in the problem are essential for understanding and solving the problem. Here's what they mean: - Specific rotation: The angle by which the plane of polarized light is rotated when it passes through a solution of an optically active compound. - Racemization: The process of converting an optically active compound into a racemic mixture, which consists of equal amounts of the enantiomers. - Retention of configuration: The property of a reaction where the stereochemistry of the product is the same as that of the reactant.
02

Calculate the optical rotation for the racemic and retained portions

In a reaction with \(20\%\) racemization, it means that \(20\%\) of the sample is converted into a racemic mixture, while \(80\%\) of the sample retains its original configuration. Since the racemic mixture's effect on the plane of polarized light is zero, the optical rotation of the \(20\%\) racemic portion is \(0^{\circ}\). The optical rotation of the \(80\%\) retained portion remains the same as the initial specific rotation i.e., \(+12^{\circ}\).
03

Calculate the combined optical rotation after the reaction

Now, we need to calculate the combined optical rotation of the sample after the reaction. We can do this by taking a weighted average of the optical rotations of both portions. The weighted average specific rotation is given by: \(\text{Specific rotation}_{\text{combined}} = \frac{\text{% portion}_{\text{racemized}} \times \text{specific rotation}_{\text{racemized}} + \text{% portion}_{\text{retained}} \times \text{specific rotation}_{\text{retained}}}{100}\) Substitute the values: \(\text{Specific rotation}_{\text{combined}} = \frac{(20\% \times 0^{\circ}) + (80\% \times +12^{\circ})}{100}\)
04

Solve for the combined specific rotation

Now, we solve for the combined specific rotation: \(\text{Specific rotation}_{\text{combined}} = \frac{(0) + (80\% \times +12^{\circ})}{100}\) \(\text{Specific rotation}_{\text{combined}} = \frac{(0) + (9.6^{\circ})}{100}\) \(\text{Specific rotation}_{\text{combined}} = +9.6^{\circ}\) So, the specific rotation of the sample after the reaction with \(20\%\) racemization and \(80\%\) retention of configuration is \(+9.6^{\circ}\). The correct answer is (c) \(+9.6^{\circ}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which of the following is not true about a homolytic fission? (a) The products are free radicals. (b) The reaction occurs under the influence of heat or light. (c) It occurs when the bond breakage is between two atoms of the same electronegativity. (d) Intermediates may undergo rearrangement.

Which of the following species is/are stabilized by isovalent hyperconjugation? (a) Free radicals (b) Carbanion (c) Alkenes (d) Carbocations

The number of optically active stereoisomers possible for the compound 2,3 -dihydroxy butane are (a) 4 (b) 2 (c) 6 (d) 8

Arrange the acids (I-V) listed below in the decreasing order of their acid strength and justify. (i) Butanoic acid (ii) Trichloro acetic acid (iii) Chloroacetic acid (iv) Trimethyl acetic acid (v) Bromo acetic acid

The hyperconjugative effect of the group \(\mathrm{R}\) in the compound \(\mathrm{R}-\mathrm{CH}=\mathrm{CH}_{2}\) follows the order. (a) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}>\mathrm{CH}_{3}>\mathrm{CH}_{3} \mathrm{CH}_{2}-\) (b) \(\mathrm{CH}_{3}->\mathrm{CH}_{3} \mathrm{CH}_{2}->\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}->\mathrm{CH}_{3}-\mathrm{CH}_{2}->\mathrm{CH}_{3}-\) (d) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}->\mathrm{CH}_{3}-\mathrm{CH}_{2}->\mathrm{CH}_{3}-\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free