91Ó°ÊÓ

Homolysis of the indicated C-H bond in propene forms a resonance-stabilized radical.

1. Draw the two possible resonance structures for this radical.
2. Use half-headed curved arrows to illustrate how one resonance structure can be converted to the other.
3. Draw a structure for the resonance hybrid.

As we learned in Chapter 4, propane $\left({\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{CH}}_3\right)$has both $\mathbf{1}\mathbf{°}$and $\mathbf{2}\mathbf{°}$hydrogens.

1. Draw the carbon radical formed by homolysis of each type of C-H bond.
2. Use the values in Table 6.2 to determine which C-H bond is stronger.
3. Explain how this information can be used to determine the relative stability of the two radicals formed. Which radical formed from propane is more stable?

Given each value, determine whether the starting material or the product is favored at equilibrium.

a.${\mathbf{K}}_{\mathbf{eq}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5}$

b.$\mathbf{∆}\mathbf{G}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{100}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

c.$\mathbf{∆}\mathbf{H}\mathbf{°}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

d. ${\mathbf{K}}_{\mathbf{eq}}\mathbf{=}\mathbf{16}$

e.$\mathbf{∆}\mathbf{G}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

f.$\mathbf{∆}\mathbf{H}\mathbf{°}\mathbf{=}\mathbf{200}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

g.$\mathbf{∆}\mathbf{S}\mathbf{°}\mathbf{=}\mathbf{8}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{(}\mathbf{K}\mathbf{.}\mathbf{mol}\mathbf{)}$

h.$\mathbf{∆}\mathbf{S}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{8}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{(}\mathbf{K}\mathbf{.}\mathbf{mol}\mathbf{)}$

Use curved arrows to show the movement of electrons in each equation.

a.

b.

As we learned in Chapter 4, monosubstituted cyclohexanes exist as an equilibrium mixture of two conformations having either an axial or equatorial substituent. When $\mathbf{R}\mathbf{=}{\mathbf{CH}}_{\mathbf{2}}{\mathbf{CH}}_{\mathbf{3}}$, ${\mathbf{K}}_{\mathbf{eq}}$for this process is 23. When $\mathbf{R}\mathbf{=}\mathbf{C}{\mathbf{\left(}{\mathbf{CH}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{3}}$,${\mathbf{K}}_{\mathbf{eq}}$for this process is 4000.

a. When , which conformation is present in higher concentration?

b. Which R shows the higher percentage of equatorial conformation at equilibrium?

c. Which R shows the higher percentage of axial conformation at equilibrium?

d. For which R is more negative?

e. How is the size of R related to the amount of axial and equatorial conformations at equilibrium?

For which of the following reactions is $\mathbf{∆}\mathbf{S}\mathbf{°}$a positive value?

a.

b.

Draw the transition state for each reaction.

a.

b.

Draw an energy diagram for each reaction. Label the axes, the starting material, product, transition state, ${\mathbf{Δ\pm á}}^{\mathbf{°}}$, and ${\mathbf{E}}_{\mathbf{a}}$.

a.a concertedwith ${\mathbf{Δ\pm á}}^{\mathbf{°}}\mathbf{=}\mathbf{-}\mathbf{80}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$and ${\mathbf{E}}_{\mathbf{a}}\mathbf{=}\mathbf{16}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$.

b. a two-step reaction, $\mathbf{A}\mathbf{→}\mathbf{B}\mathbf{→}\mathbf{C}$, in which the relative energy of the compounds is $\mathbf{A}\mathbf{<}\mathbf{C}\mathbf{<}\mathbf{B}$, and the step $\mathbf{A}\mathbf{→}\mathbf{B}$is rate-determining.

Consider the following reaction: ${\mathbf{CH}}_{\mathbf{4}}\mathbf{+}\mathbf{Cl}\mathbf{·}\underset{}{\mathbf{→}}\mathbf{·}{\mathbf{CH}}_{\mathbf{3}}\mathbf{+}\mathbf{HCl}\mathbf{.}$

a. Use curved arrows to show the movement of electrons.

b. Calculate $\mathbf{∆}\mathbf{H}\mathbf{°}$using the bond dissociation energies in Table 6.2.

c. Draw an energy diagram assuming that ${\mathbf{E}}_{\mathbf{a}}\mathbf{=}\mathbf{16}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{.}$

d. What is ${\mathbf{E}}_{\mathbf{a}}$for the reverse reaction $\left(·{\mathrm{CH}}_3+\mathrm{HCl}\stackrel{}{→}{\mathrm{CH}}_4+\mathrm{Cl}·\right)$?

Consider the following energy diagram for the conversion of $\mathit{A}\stackrel{}{\mathbf{→}\mathbf{G}}$.

a. Which points on the graph correspond to transition states?

b. Which points on the graph correspond to reactive intermediates?

c. How many steps are present in the reaction mechanism?

d. Label each step of the mechanism as endothermic or exothermic.

e. Label the overall reaction as endothermic or exothermic.