Rate of Reaction and Temperature: Most of
the chemical reactions are accelerated by increase in temperature. It has been
found that for a chemical reaction, when the temperature is increased by 10°,
the rate of the reaction and the rate constant is nearly doubled. The ratio of the rate constants of a reaction
at two temperatures differing by 100 is called temperature coefficient.
i.e., Temperature coefficient = Rate
constant of the reaction at (T + 10)K
Rate
constant of the reaction at T K
The
temperature dependence of the rate of a chemical reaction can be accurately
explained by Arrhenius equation. The
equation is:
k = A e -
Ea /RT ……………………………….. (1)
Where A is a constant called the Arrhenius
parameter or the frequency factor or the pre-exponential factor. It is constant
for a particular reaction.
R is the universal gas constant and Ea
is activation energy measured in joules/mole (J mol –1).
Threshold Energy: The
minimum energy which the colliding molecules must have in order that the
collision between them may be effective is called threshold energy.
Activation Energy: The
minimum extra amount of energy absorbed by the reactant molecules so that their
energy becomes equal to threshold value is called activation energy.
Threshold
energy = Activation energy + Energy possessed by the reactants
Less is the activation energy, faster is the
reaction. In order that the reactants may change into products, they have to
cross an energy barrier (corresponding to threshold
energy). Reactant molecules absorb energy and
form an intermediate called activated complex which immediately dissociates to
form the products.
For Example:
Arrhenius equation:
Quantatively,
the temperature dependence of the rate of a chemical reaction can be explained
by Arrhenius equation
k = A e -
Ea /RT
where A is the
Arrhenius factor or the frequency factor or pre-exponential factor. R is gas
constant and E a is activation energy measured in joules/mole.
The factor e -
Ea /RT corresponds to the fraction of molecules that have kinetic energy
greater than Ea.
Thus, it has been
found from Arrhenius equation that increasing the temperature or decreasing the
activation energy will result in an increase in the rate of the reaction and an
exponential increase in the rate constant.
Taking natural
logarithm of both sides of equation
ln K = - Ea + ln A
RT
At temperature
T1, equation
ln K1 = - Ea + ln A
RT1
At temperature
T2, equation
ln K2 = - Ea + ln A
RT2
(since A is
constant for a given reaction)
K1
and K2 are the values of rate
constants at temperatures T1 and T2 respectively.
Subtracting
equation form, we obtain
ln K2 - ln K1 = Ea - Ea
RT1 RT2
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