Organic Chemistry

Section 3.7 Thermodynamics and Kinetics 133

The smaller the rate constant,

the slower is the reaction.

reaction will double; if the concentrations of both A and B are doubled, the rate of the

reaction will quadruple; and so on. In this case, the rate constant kis a second-order

rate constant.

A reaction in which two molecules of A combine to form a molecule of B is also a

second-order reaction: If the concentration of A is doubled, the rate of the reaction will

quadruple.

Do not confuse the rate constantof a reaction with the rateof a reaction. The

rate constanttells us how easy it is to reach the transition state (how easy it is to get

over the energy barrier). Low energy barriers are associated with large rate constants

(Figures 3.4a and 3.4c), whereas high energy barriers have small rate constants

(Figures 3.4b and 3.4d). The reaction rateis a measure of the amount of product that

is formed per unit of time. The preceding equations show that the rateis the product of

the rate constant and the concentration(s)of the reactants. Thus, reaction rates de-

pend on concentration, whereas rate constants are independent of concentration.

Therefore, when we compare two reactions to see which one occurs more readily, we

must compare their rate constants and not their concentration-dependent rates of reac-

tion. (Appendix III explains how rate constants are determined.)

Although rate constants are independent of concentration, they depend on tempera-

ture. The Arrhenius equationrelates the rate constant of a reaction to the experimen-

tal energy of activation and to the temperature at which the reaction is carried out. A

good rule of thumb is that an increase of 10°C in temperature will double the rate con-

stant for a reaction and, therefore, double the rate of the reaction.

The Arrhenius equation:

where kis the rate constant, is the experimental energy of activation,Ris the gas

constant or Tis the ab-

solute temperature (K), and Ais the frequency factor. The frequency factor accounts

for the fraction of collisions that occur with the proper orientation for reaction. The

term corresponds to the fraction of the collisions that have the minimum ener-

gy needed to react. Taking the logarithm of both sides of the Arrhenius equation,

we obtain

Problem 43 on page 140 shows how this equation is used to calculate kinetic

parameters.

ln k=ln A-

Ea

RT

1 Ea 2

e-Ea>RT

(1.986* 10 -^3 kcalmol-^1 K-^1 , 8.314* 10 -^3 kJmol-^1 K-^1 ),

Ea

k=Ae-Ea>RT

(k)

A + AB

rate = k[A]^2

A + BC + D

rate = k[A][B]

Swedish chemist Svante August

Arrhenius (1859–1927)received a

Ph.D. from the University of Upp-

sala. Threatened with a low passing

grade on his dissertation because his

examiners did not understand his the-

sis on ionic dissociation, he sent the

work to several scientists, who subse-

quently defended it. His dissertation

earned Arrhenius the 1903 Nobel

Prize in chemistry. He was the first to

describe the “greenhouse”effect,

predicting that as concentrations of

atmospheric carbon dioxide

increase, so will Earth’s surface tem-

perature (Section 9.0).

(CO 2 )

THE DIFFERENCE BETWEEN

AND

Do not confuse the free energy of activation,

with the experimental energy of activation,in

the Arrhenius equation. The free energy of activation

has both an enthalpy component and

an entropy component, whereas the experimental energy of

1 ¢G‡=¢H‡-T¢S‡ 2

¢G‡, Ea,

Ea

≤G‡ activation has only an enthalpy component

since the entropy component is implicit in the A term in the Ar-

rhenius equation. Therefore, the experimental energy of activa-

tion is an approximate energy barrier to a reaction. The true

energy barrier to a reaction is given by because some re-

actions are driven by a change in enthalpy and some by a

change in entropy, but most by a change in both enthalpy and

entropy.

¢G‡

1 Ea=¢H‡+RT 2

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