The Foundations of Chemistry

Antimony powder reacts with bromine more rapidly at 75°C (left) than at 25°C (right).

16-8 Temperature: The Arrhenius Equation 685

This is because fewer collisions take place with sufficient energy to get over a high-energy
barrier (see Figure 16-13b).
The Arrhenius equation predicts that increasing Tresults in a faster reaction for the
same Eaand concentrations.

inc

I

r

f

e

T

ases

:F 

de

E

c

a

r

/

e

R

a

T

ses

:F 

i



nc

E

r

a

e

/

a

R

se

T

s

:F 

in

e

cr

E

e

a/

a

R

s

T

es

:F 

incr

k

eases

:F 

s

R

p

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Let’s look at how the rate constant varies with temperature for a given single reaction.
Assume that the activation energy and the factor Ado not vary with temperature. We can
write the Arrhenius equation for two different temperatures. Then we subtract one equa-
tion from the other and rearrange the result to obtain

ln 
 

Let’s substitute some typical values into this equation. The activation energy for many
reactions that occur near room temperature is about 50 kJ/mol. For such a reaction, a
temperature increase from 300 K to 310 K would result in

ln 
 0.647

1.91 2

Chemists sometimes use the rule of thumb that near room temperature the rate of a reac-
tion approximately doubles with a 10°C rise in temperature. Such a “rule” must be used
with care, however, because it obviously depends on the activation energy.

k 2



k 1

1



310 K

1



300 K

50,000 J/mol



(8.314 J/molK)

k 2



k 1

1



T 2

1



T 1

Ea



R

k 2



k 1

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 15.11, Control of Reaction Rates

(3): Temperature Dependence.

Which egg will cook faster—the

one in ice water (left) or the one in

boiling water (right)? Why—in

terms of what you have learned in

this chapter?