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Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics
Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition
Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471Not the one you use?Change textbook
All textbooksMullins 1st EditionCh. 5 - Chemical Reaction Analysis: Thermodynamics and KineticsProblem 45a
Chapter 4, Problem 45a

The radical fluorination of 2-methyl propane resulted in a 14:86 ratio of products.
Diagram showing the radical fluorination of 2-methyl propane, with product ratios of 14% and 86%.
(a) On the basis of this ratio, calculate the relative reactivity of 1° and 3° C―H bonds in the radical fluorination.

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1
Identify the types of C―H bonds in 2-methylpropane. The molecule has primary (1°) hydrogens attached to the methyl groups and tertiary (3°) hydrogens attached to the central carbon.
Determine the number of each type of C―H bond. In 2-methylpropane, there are 9 primary hydrogens (3 hydrogens on each of the three methyl groups) and 1 tertiary hydrogen (on the central carbon).
Use the given product ratio (14:86) to determine the relative likelihood of abstraction of each type of hydrogen. The ratio corresponds to the number of products formed from primary and tertiary hydrogens, respectively.
Set up the relative reactivity equation. The relative reactivity of 1° to 3° C―H bonds can be calculated using the formula: \( \text{Relative Reactivity} = \frac{\text{Product Ratio}}{\text{Number of Hydrogens}} \). For primary hydrogens: \( \text{Reactivity of 1°} = \frac{14}{9} \), and for tertiary hydrogens: \( \text{Reactivity of 3°} = \frac{86}{1} \).
Calculate the relative reactivity of 1° to 3° C―H bonds by dividing the reactivity of 3° hydrogens by the reactivity of 1° hydrogens. This will give the relative reactivity ratio.

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Key Concepts

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

Radical Reactivity

Radical reactivity refers to the tendency of different types of carbon-hydrogen (C-H) bonds to undergo homolytic cleavage and form radicals. In the context of fluorination, primary (1°) and tertiary (3°) C-H bonds exhibit different reactivities due to the stability of the resulting radicals. Tertiary radicals are generally more stable than primary radicals, leading to a higher likelihood of fluorination occurring at 3° C-H bonds compared to 1° C-H bonds.
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Product Ratio Interpretation

The product ratio obtained from the radical fluorination (14:86) indicates the relative amounts of products formed from 1° and 3° C-H bond reactions. This ratio can be used to infer the relative reactivity of the C-H bonds involved. By analyzing the ratio, one can deduce how many times more reactive one type of bond is compared to another, which is essential for calculating the relative reactivity of 1° and 3° C-H bonds in this reaction.
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Calculating Relative Reactivity

To calculate the relative reactivity of 1° and 3° C-H bonds, one can use the product ratio derived from the radical fluorination. The formula involves comparing the number of products formed from each type of bond. By setting up a ratio based on the product distribution, one can derive a numerical value that quantifies how much more reactive one type of C-H bond is compared to the other, providing insight into the mechanism of the reaction.
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Related Practice
Textbook Question

The following are all substitution reactions, two of which we study in later chapters. With no knowledge of mechanism, what would you expect the ratio of products to be for each reaction, based on a random statistical distribution?

(b) Replacing a hydrogen (H) with bromine (Br):

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Textbook Question

Through the course of this chapter, we have discussed only alkane chlorination and bromination, yet there are two other halogens we have not discussed.

(b) Is radical iodination a favorable reaction? Do you expect it to be selective? Show your calculations.

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Textbook Question

Predict the major monohalogenation product(s) of the following reactions. Indicate whether you think the reaction will be selective and justify your position.

(c)

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Textbook Question

Given the ratio of products obtained in the bromination of propane, calculate the relative reactivity of a 1° C–H bond to a 2° C–H bond under these conditions.

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Textbook Question

The radical fluorination of 2-methyl propane resulted in a 14:86 ratio of products.

(b) From the relative reactivity, calculate the difference in energy between the transition states of the first propagation steps leading to a 1° and 3° radical.

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Textbook Question

Predict the major monohalogenation product(s) of the following reactions. Indicate whether you think the reaction will be selective and justify your position.

(a)

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