6. Thermodynamics and Kinetics

a. Draw an approximate reaction-energy diagram for the acid–base reaction of phenol (see below) with 1-molar aqueous sodium hydroxide solution.

b. On the same diagram, draw an approximate reaction-energy diagram for the acid–base reaction of tert-butyl alcohol (see below) with 1-molar aqueous sodium hydroxide solution.

Phenol, <IMAGE> pKa= 10.0

Tert-butyl alcohol <IMAGE> pKa=18.0

 (••) For each of the reaction coordinate diagrams shown, 

(i) indicate the number of steps in the reaction, 

(ii) label the intermediates, 

(iii) identify the rate-determining step, and 

(iv) tell whether K_eq is greater than, less than, or equal to zero.

(a) <IMAGE>

(••) Draw a reaction coordinate diagram, making sure to label reactants (R), products (P), intermediates (I), transition states (‡), activation energies ( Eₐ) , and , ∆G° for each of the following.

(d) a slightly exothermic, three-step reaction where the third step is rate-determining.

The alkyl carbocation is estimated to be 15 kcal/mol more stable than the alkenyl carbocation. If this is also the difference in the energies of the transition state leading to each, what is the expected rate difference? 

<IMAGE>

Using Equation 5.8, calculate the difference in transition state energies that lead to the rate differences shown in Figure 24.35.

<IMAGE>

(••) Draw a reaction coordinate diagram, making sure to label reactants (R), products (P), intermediates (I), transition states (‡), activation energies ( Eₐ) , and , ∆G° for each of the following.

(b) an exothermic, two-step reaction where the second step is rate-determining

(••) Draw a reaction coordinate diagram, making sure to label reactants (R), products (P), intermediates (I), transition states (‡), activation energies ( Eₐ) , and , ∆G° for each of the following.

(c) a slightly endothermic, three-step reaction where the first step is rate-determining

Draw a reaction-energy diagram for the propagation steps of the free-radical addition of HBr to isobutylene. Draw curves representing the reactions leading to both the Markovnikov and the anti-Markovnikov products. Compare the values of ∆Gº and Ea and for the rate-limiting steps, and explain why only one of these products is observed.

Draw a reaction coordinate diagram for a reaction in which

a. the product is thermodynamically unstable and kinetically unstable.

b. the product is thermodynamically unstable and kinetically stable.

Draw a reaction coordinate diagram for a two-step reaction in which the first step is endergonic, the second

step is exergonic, and the overall reaction is endergonic. Label the reactants, products, intermediates, and

transition states.

The acid dissociation constant (Ka) for loss of a proton from cyclohexanol is 1*10-16.

a. Draw a reaction coordinate diagram for loss of a proton from cyclohexanol.

<IMAGE>

The reaction of tert-butyl chloride with methanol

(CH3)3C—Cl Tert-butylchloride + CH3—OH methanol —> (CH3)C—OCH3 methyltert-butylether + HCl

is found to follow the rate equation

rate= Kt[(CH3)3C—Cl]

b. What is the kinetic order with respect to methanol?

Under certain conditions, the bromination of cyclohexene follows an unusual rate law:

<IMAGE> + Br2 —> <IMAGE>

rate= Kr[cyclohexene][Br2]^2

c. What is the overall kinetic order?

The following reaction is a common synthesis used in the organic chemistry laboratory course.

CH3CH2CH2CH2Br 1-bromobutane + CH3O- methoxide ion —> CH3OH(methanol solvent—> CH3CH2Ch2Ch2OCH3 methoxybutane + Br- bromide ion

When we double the concentration of methoxide ion (CH3O–), we find that the reaction rate doubles. When we triple the concentration of 1-bromobutane, we find that the reaction rate triples.

a. What is the order of this reaction with respect to 1-bromobutane? What is the order with respect to methoxide ion?

Write the rate equation for this reaction.

What is the overall order?

Deuterium (D) is the hydrogen isotope of mass number 2, with a proton and a neutron in its nucleus. The chemistry of deuterium is nearly identical to the chemistry of hydrogen, except that the

C―D bond is slightly stronger than the

C―H bond by 5.0 kJ/mol (1.2 kcal/

mol). Reaction rates tend to be slower when a C―D bond (as opposed to a C―H bond) is broken in a rate-limiting step.

This effect, called a kinetic isotope effect, is clearly seen in the chlorination of methane. Methane undergoes free-radical chlorination 12 times as fast as tetradeuteriomethane (CD4)

Faster: CH4 + Cl⋅ —> CH3Cl + HCl relative rate= 12

Slower: CD4 + Cl⋅ —> CD3Cl + DCl

relative rate= 1

b. Monochlorination of deuterioethane

(C2H5D) leads to a mixture containing 93% C2H4DCland 7% C2H5Cl. Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterioethane.

Treatment of tert-butyl alcohol with concentrated HCl gives tert-butyl chloride.

Tert-butyl alcohol <IMAGE> + H⁺ + Cl^- → tert-butyl chloride <IMAGE> + H₂O

When the concentration of H⁺ is doubled, the reaction rate doubles.

When the concentration of tert-butyl alcohol is tripled, the reaction rate triples.

When the chloride ion concentration is quadrupled, however, the reaction rate is unchanged.

Write the rate equation for this reaction.

Under certain conditions, the reaction of 0.5 M 1-bromobutane with 1.0 M sodium methoxide forms 1-methoxybutane at a rate of 0.05 mol/L per second.

a. What would be the rate if 0.1 M 1-bromobutane and 2.0M NaOCH₃ were used?

When a small piece of platinum is added to a mixture of ethene and hydrogen, the ­following reaction occurs:

Ethene <IMAGE> + H2 hydrogen Pt catalyst —> ethane <IMAGE>

Doubling the concentration of hydrogen has no effect on the reaction rate. Doubling the concentration of ethene also has no effect.

b. Write the unusual rate equation for this reaction.

c. Explain this strange rate equation, and suggest what one might do to accelerate the reaction.

How will the rate of the reaction between bromomethane and hydroxide ion be affected if the following changes in concentration are made?

c. The concentration of the alkyl halide is cut in half and the concentration of the nucleophile is doubled.

Within the following pairs, pick which reaction you would expect to be faster based on having a higher value of the frequency factor (A).

(b) <IMAGE>

(••) For the following acid–base pairs,

(vi) draw a reaction coordinate diagram.

(e) <IMAGE>

All things being equal, would you expect a first-order reaction to be faster or slower than a second-order reaction?

Chapter 5 taught us that chemical reactions are random collisions. Experimentally, how can we make molecules collide more often?

(•••) For rotation around a bond, the rate constant is equal to the reaction rate. Why?

The rate constant for the uncatalyzed reaction of two molecules of glycine ethyl ester to form glycylglycine ethyl ester is 0.6 M - 1s - 1. In the presence of Co2+, the rate constant is 1.5 * 106 M - 1s - 1. What rate enhancement does the catalyst provide?

The rate constant for a reaction can be increased by ______ the stability of the reactant or by ______ the stability of the transition state.

From the Arrhenius equation, predict how

a. increasing the experimental activation energy affects the rate constant for a reaction.

From the Arrhenius equation, predict how

b. increasing the temperature affects the rate constant for a reaction.