Chapter 8, Problem 8.18P

(a)

Interpretation Introduction

Interpretation:

The standard enthalpy of reaction has to be calculated using the values of bond dissociation enthalpies.

Concept Introduction:

The value of standard enthalpy change ${\text{ΔH}}^{\text{ο}}$ of the given reaction is calculated by the formula,

  ${\text{ΔH}}^{\text{ο}}\text{=}{{\displaystyle \sum {\text{n}}_{\text{p}}{\text{ΔH}}_{\text{f}}^{\text{ο}}}}_{\left(\text{products}\right)}-{{\displaystyle \sum {\text{n}}_{\text{r}}{\text{ΔH}}_{\text{f}}^{\text{ο}}}}_{\left(\text{reactants}\right)}$

Where,

  $\begin{array}{c}{\text{ΔH}}_{\text{f}}^{\text{ο}}{}_{\left(\text{reactants}\right)}\text{=}\text{the standard enthalpy of formation for the reactants}\\ {\text{ΔH}}_{\text{f}}^{\text{ο}}{}_{\left(\text{products}\right)}\text{=}\text{the standard enthalpy of formation for the products}\\ {\text{n}}_{\text{p}}\text{=}\text{number of products molecule}\\ {\text{n}}_{\text{r}}\text{=}\text{number of reactants molecule}\end{array}$

Explanation of Solution

Given reaction (1): $\text{C}{H}_{3}C{H}_{2}C{H}_3+F_2\to \text{C}{H}_{3}C{H}_{2}C{H}_{2}F+HF$

The reaction is given below:

  $\begin{array}{l}{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{3}}\text{+}{\text{F}}_{\text{2}}\to {\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{2}}\text{F}\text{+}\text{HF}\\ {\text{ΔH}}^{\text{o}}\left(\text{+422}\right)\left(\text{+159}\right)\left(\text{-472}\right)\left(\text{-568}\right)\end{array}$

  $\begin{array}{l}{\text{ΔH}}^{\text{ο}}\text{=}{\text{ΔH}}^{\text{ο}}{}_{\left(\text{bond breaking}\right)}{\text{+ ΔH}}_{\text{f}}{{}^{\text{ο}}}_{\left(\text{bond formation}\right)}\\ \\ \text{=}\left[\left(\text{-472}\right)\text{+}\left(\text{-568}\right)\right]+\left[\left(\text{+422}\right)\text{+}\left(\text{+159}\right)\right]\text{kJ/mol}\\ \\ \text{=}-459kJ/mol.\end{array}$

Therefore, standard enthalpy of given reaction is $-459kJ/mol.$

Given reaction (2): $\text{C}{H}_{3}C{H}_{2}C{H}_3+F_2\to \text{C}{H}_{3}CH\left(-F\right)C{H}_3+HF$

The reaction is given below:

  $\begin{array}{l}{\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{3}}\text{+}{\text{F}}_{\text{2}}\to {\text{CH}}_{\text{3}}\text{CH}\left(\text{-F}\right){\text{CH}}_{\text{3}}\text{+}\text{HF}\\ {\text{ΔH}}^{\text{o}}\left(\text{+414}\right)\left(\text{+159}\right)\left(\text{-464}\right)\left(\text{-568}\right)\end{array}$

  $\begin{array}{l}{\text{ΔH}}^{\text{ο}}\text{=}{\text{ΔH}}^{\text{ο}}{}_{\left(\text{bond breaking}\right)}{\text{+ ΔH}}_{\text{f}}{{}^{\text{ο}}}_{\left(\text{bond formation}\right)}\\ \\ \text{=}\left[\left(\text{-464}\right)\text{+}\left(\text{-568}\right)\right]+\left[\left(\text{+414}\right)\text{+}\left(\text{+159}\right)\right]\text{kJ/mol}\\ \\ \text{=}-459kJ/mol.\end{array}$

Therefore, standard enthalpy of given reaction is $-459kJ/mol.$

(b)

Interpretation Introduction

Interpretation:

A pair of chain propagation steps for each reaction has to be proposed; the value of ${\text{ΔH}}^{\text{ο}}$ has to be calculated for each step.

Concept Introduction:

Radical Bromination: A type of halogenation reaction in which the bromine atom gets bonded with the alkane or alkyl substituents resulting to the product with added bromine atom via radical mechanism.

Radical reaction of $B{r}_2$ is radical substitution of alkane and generates the alkyl halide and hydrogen iodide.

Stability of Radicals: Radicals are highly unstable due to its unpaired valence electron of an atom.

The increasing order of radical stability is given below,

Benzylic > allylic > tertiary > secondary > primary > methyl

Radical chain reaction:

Initiation reaction:

Chain propagation:

Chain termination:

Explanation of Solution

Given reaction (1): $\text{C}{H}_{3}C{H}_{2}C{H}_3+F_2\to \text{C}{H}_{3}C{H}_{2}C{H}_{2}F+HF$

The propagation step involves extremely reactive fluorine radicals react towards the propane by abstracting the terminal hydrogen forming primary radical and $\text{HF}$; later the radical reacts with another mole of Fluorine molecule forming the major product propyl fluoride.

Hence, the pair of propagation steps is shown above.

  $\begin{array}{l}{\text{ΔH}}^{\text{ο}}\text{=}{\text{ΔH}}^{\text{ο}}{}_{\left(\text{bond breaking}\right)}{\text{+ ΔH}}_{\text{f}}{{}^{\text{ο}}}_{\left(\text{bond formation}\right)}\\ \\ \text{For}\text{First}\text{Step:}\left[\left(\text{+422}\right)\text{+}\left(\text{-568}\right)\right]\text{kJ/mol}\text{=}\text{-146}\text{kJ/mol}\text{.}\\ \\ \text{For}\text{Second}\text{Step:}\left[\left(\text{+159}\right)\text{+}\left(\text{-472}\right)\right]\text{kJ/mol}\text{=}\text{-313kJ/mol}\text{.}\end{array}$

Given reaction (2): $\text{C}{H}_{3}C{H}_{2}C{H}_3+F_2\to \text{C}{H}_{3}CH\left(-F\right)C{H}_3+HF$

Initiation step involves the homolytic bond cleavage of fluorine molecule by irradiation of light or heat leads to the formation of two Fluorine radicals.

The propagation step involves extremely reactive fluorine radicals react towards the propane by abstracting the secondary hydrogen forming secondary radical and $\text{HF}$; later the radical reacts with another mole of Fluorine molecule forming the major product 2-Fluoropropane.

Hence, the pair of propagation steps is shown above.

  $\begin{array}{l}{\text{ΔH}}^{\text{ο}}\text{=}{\text{ΔH}}^{\text{ο}}{}_{\left(\text{bond breaking}\right)}{\text{+ ΔH}}_{\text{f}}{{}^{\text{ο}}}_{\left(\text{bond formation}\right)}\\ \\ \text{For}\text{First}\text{Step:}\left[\left(\text{+414}\right)\text{+}\left(\text{-568}\right)\right]\text{kJ/mol}\text{=}\text{-154}\text{kJ/mol}\text{.}\\ \\ \text{For}\text{Second}\text{Step:}\left[\left(\text{+159}\right)\text{+}\left(\text{-464}\right)\right]\text{kJ/mol}\text{=}\text{-305 kJ/mol}\text{.}\end{array}$

Therefore, for each reaction step the value of ${\text{ΔH}}^{\text{ο}}$ has calculated as shown above.

(c)

Interpretation Introduction

Interpretation:

The regioselectivity of radical fluorination relative to that of radical chlorination and Bromination has to be predicted using Hammond’s postulate.

Concept Introduction:

Radical Bromination: A type of halogenation reaction in which the fluorine atom gets bonded with the alkane or alkyl substituents resulting to the product with added fluorine atom via radical mechanism.

Radical reaction of $B{r}_2$ is radical substitution of alkane and generates the alkyl halide and hydrogen iodide.

Stability of Radicals: Radicals are highly unstable due to its unpaired valence electron of an atom.

The increasing order of radical stability is given below,

Benzylic > allylic > tertiary > secondary > primary > methyl

Radical chain reaction:

Initiation reaction:

Chain propagation:

Chain termination:

Explanation of Solution

In each radical fluorination sequence, the hydrogen abstraction step is highly exothermic, thus the transition state is reached too early and the transition state more closely resembles the reactant; so the intermediate has very little radical character of product.  Therefore, the relative stabilities of primary versus secondary radical is of little of importance in determination of product.