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Effect of Temperature on Rate
aA + bB → products
1
Rate = k[A]
n
[B]
m
This equation shows how rate depends on concentration.
Temperature is not included in this
equation.
However, rates are definitely temperature dependent.
In general, a higher temperature
means a faster reaction.
Although temperature is not explicitly in the rate equation, the rate constant k
is temperature dependent.
So, as temperature increases, k increases, and thus the rate will also
increase.
Collision Theory
Reactants A and B cannot react if they are in different parts of the world.
If reactants A and B
react, they must have an encounter—a
collision
.
A collision is a necessary but not a sufficient
condition for a reaction of two different species.
If there is a reaction, there must have been a
collision.
But the converse is not necessarily true.
Every collision does not produce a reaction.
A higher temperature means molecules are moving faster.
This will increase collision
frequency, but this increased collision frequency is not the main explanation for the temperature
dependence of rate.
Let’s analyze what happens if the temperature is increased slightly, from room temperature,
298 K, to 10K above that, 308 K.
The average velocity of molecule is given by:
v =
M
RT
3
where T is the temperature and M is the molar mass
Compare two identical gases (same molar mass) at temperatures T
2
and T
1
.
v
2
=
M
RT
3
2
v
1
=
M
RT
3
1
Comparing by ratio:
1
2
v
v
=
1
2
T
T
If T
2
= 308 K and T
1
= 298 K, then
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2
T
T
=
298
308
= 1.017
This means that at 308 K, the molecules move about 1.7% faster than the molecules move at
298 K, meaning a relatively small increase in collision frequency
Generally, we find rates are much more temperature dependent than can be predicted by just
an increase in collision frequency.
A rough guideline states:
a 10 K increase in temperature doubles
the rate of a slow reaction.
This is not an exact rule, but just a “ballpark” figure.
Some reaction rates
may increase by less than double, some more than double, for a 10 K temperature increase.
But the
velocity increase of 1.7% is
much
less than a doubling.
The increase in rate must be explained by
something more than just an increased collision frequency.
The equation v =
M
RT
3
represents the
average
velocity.
But most collisions do not result in
a reaction.
Only collisions with enough energy (called the activation energy) result in a chemical
reaction.
In most cases, this means only a small percentage of
the collisions actually result in a
reaction.
Thus, an analysis of changes in the average velocity is irrelevant, since these “average”
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 Spring '08
 siegal

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