Chapter 25, Problem 25.42P

Interpretation Introduction

(a)

Interpretation:

The structure of the two isomeric propyl radicals that are formed on hydrogen abstraction from propane by $\text{H}·$ are to be drawn.

Concept introduction:

Radicals are species containing an unpaired electron, i.e., they are electron-poor species. Being electron-poor, they are highly unstable, and therefore, highly reactive species. They react with any other species present.

In the case of alkanes, a radical like $\text{H}·$ will abstract a hydrogen atom from the alkane. If the alkane contains structurally different types of hydrogens, a mixture of different types of radicals is produced.

Answer to Problem 25.42P

The two alkyl radicals produced when $\text{H}·$ abstracts a hydrogen atom from propane are

Explanation of Solution

Propane has two types of hydrogens, one attached to a primary carbon and one to a secondary carbon. The abstraction of the two types of hydrogens will produce two radicals – a primary propyl radical and a secondary propyl radical.

Conclusion

The type of radical produced when $\text{H}·$ abstracts a hydrogen atom from propane is determined on the basis of the structurally different hydrogens present in the molecule.

Interpretation Introduction

(b)

Interpretation:

The curved arrow notation for the formation of the two isomeric propyl radicals that are formed on hydrogen abstraction from propane by $\text{H}·$ is to be drawn.

Concept introduction:

In the case of alkanes, a radical like $\text{H}·$ will abstract a hydrogen atom from the alkane. If the alkane contains structurally different types of hydrogens, a mixture of different types of radicals is produced.

Curved arrow notation represents the movement of electron(s) in a reaction or resonance. Movement of a single electron is represented by a curved arrow with a half arrowhead. The arrow starts at the electron and ends on the atom or the region where it moves.

Answer to Problem 25.42P

The curved arrow notation for the formation of the two alkyl radicals produced when $\text{H}·$ abstracts a hydrogen atom from propane is

Explanation of Solution

Propane has two types of hydrogens, one attached to a primary carbon and one to a secondary carbon. The abstraction of the two types of hydrogens will produce two radicals – a primary propyl radical and a secondary propyl radical.

The $\text{H}·$ that abstracts hydrogen uses its electron to form a bond with primary hydrogen, along with one of the electrons from that hydrogen’s bond with the carbon atom. This results in the homolysis of the $\text{C}-\text{H}$ bond, with the second electron moving to the carbon. This results in the formation of the primary propyl radical and a hydrogen molecule. This is represented by two half arrows, one from the $\text{H}·$ electron and the other from the electron of the $\text{C}-\text{H}$ bond. Similarly, when one of the secondary hydrogens is abstracted, the bond with $\text{H}·$ is formed by the electron from $\text{H}·$ and one of the electrons from the secondary $\text{C}-\text{H}$ bond. The other electron from the bond moves to the carbon, producing the secondary propyl radical and a hydrogen molecule.

Thus, the curved arrow representation of the formation of the two radicals can be shown as

Conclusion

The curved arrow representation of the formation of the two radicals is drawn using half arrows on the basis of the type of hydrogen abstracted.

Interpretation Introduction

(c)

Interpretation:

The percentage of each propyl radical formed is to be calculated taking into account the different numbers of each type of hydrogen in propane.

Concept introduction:

The ease with which a hydrogen is abstracted from an alkane in its reaction with a radical depends on the relative stability of the type of alkyl radical that is produced. The relative stability of alkyl radicals changes as ${\text{3}}^{\text{o}}{\text{ > 2}}^{\text{o}}{\text{ > 1}}^{\text{o}}$. The ease with which the different types of alkyl radicals are produced changes in the same order. The reactivities of ${\text{1}}^{\text{o}}{\text{ and 2}}^{\text{o}}$ hydrogens towards radical abstractions are in the ratio 1:5.

The likelihood of abstraction of a particular type of hydrogen from an alkane also increases with the number of hydrogens of that type present in the molecule.

The percentage of formation of a particular type of alkyl radical is calculated from the product of the number of that type of hydrogens present in the molecule and its reactivity.

Answer to Problem 25.42P

The percentages of the ${\text{1}}^{\text{o}}{\text{ and 2}}^{\text{o}}$ radicals reduced are 37.5% and 62.5% respectively.

Explanation of Solution

The percentage of formation of each type of alkyl radical is calculated from the product of the number of that type of hydrogens present in the molecule and its reactivity.

$\begin{array}{l}\text{Probability of abstraction = number of H atoms × reactivity}\\ \text{Percent of abstraction = }\frac{\text{relativeprobability}}{\text{totalprobability}}\text{×100}\end{array}$

There are six primary hydrogens and two secondary hydrogens in propane, and the reactivities of the two types are 1 and 5 respectively.

$\begin{array}{rll}{\text{Probability of abstraction of 1}}^{\text{o}}\text{ H }& =& {\text{ number of 1}}^{\text{o}}\text{ H atoms × reactivity of 1}\\ & =& \text{ 6 atoms × 1}\\ & =& \text{ 6}\\ {\text{Probability of abstraction of 2}}^{\text{o}}\text{ H }& =& {\text{ number of 2}}^{\text{o}}\text{ H atoms × reactivity of 6}\\ & =& \text{ 2 atoms × 5}\\ & =& \text{ 10}\\ {\text{Percent of abstraction of 1}}^{\text{o}}\text{ H }& =& \frac{6}{\text{6 + 10}}\text{×100}\\ & =& \text{ 37}\text{.5\%}\\ {\text{Percent of abstraction of 2}}^{\text{o}}\text{ H }& =& \frac{10}{\text{6 + 10}}\text{×100}\\ & =& \text{ 62}\text{.5\%}\end{array}$

Thus, the percentages of the ${\text{1}}^{\text{o}}{\text{ and 2}}^{\text{o}}$ radicals produced are 37.5% and 62.5% respectively.

Conclusion

The percentage of each type of radical produced is calculated from the number of hydrogens of each type and their relative reactivities.