Generally, the rate of a reaction increase with increasing temperature. However, there are very few exceptions. The magnitude of this increase in rate is different for different reactions.

**Arrhenius
equation - The effect of temperature on reaction rate**

Generally, the rate of a reaction increase with increasing temperature. However, there are very few exceptions. The magnitude of this increase in rate is different for different reactions. As a rough rule, for many reactions near room temperature, reaction rate tends to double when the temperature is increased by 10ºC .

A large number of
reactions are known which do not take place at room temperature but occur
readily at higher temperatures. Example: Reaction between H_{2} and O_{2}
to form H_{2}O takes place only when an electric spark is passed.

Arrhenius suggested that
the rates of most reactions vary with temperature in such a way that the rate
constant is directly proportional to e^{-(E}^{0}^{/RT)} and he proposed a
relation between the rate constant and temperature.

Where A the frequency
factor,

R the gas constant,

E_{a} the activation
energy of the reaction and,

T the absolute
temperature (in K)

The frequency factor (A)
is related to the frequency of collisions (number of collisions per second)
between the reactant molecules. The factor A does not vary significantly with
temperature and hence it may be taken as a constant.

E_{a} is the
activation energy of the reaction, which Arrhenius considered as the minimum
energy that a molecule must have to posses to react.

Taking logarithm on both
side of the equation (1)

The above equation is of
the form of a straight line y = mx + c.

A plot of ln k Vs 1/T gives
a straight line with a negative slope – E_{a}/R. If the rate constant
for a reaction at two different temperatures is known, we can calculate the
activation energy as follows.

At temperature T = T_{1}
; the rate constant k = k_{1}

At temperature T = T_{2}
; the rate constant k = k_{2}

This equation can be
used to calculate from rate constants k_{1} and k_{2} at
temperatures T_{1} and T_{2} _{.}

The rate constant of a reaction at
400 and 200K are 0.04 and 0.02 s-1 respectively. Calculate the value of
activation energy.

According to Arrhenius equation

Ea = 2305 J mol−1

Rate constant k of a reaction varies
with temperature T according to the following Arrhenius equation

Where Ea is the activation energy.
When a graph is plotted for log k Vs 1/T a straight line with a slope of - 4000K
is obtained. Calculate the activation energy

**Solution**

E_{a} = − 2.303 R m

E_{a} = − 2.303 x 8.314 J K^{−1}
mol^{−1} x (− 4000K )

E_{a} = 76,589J mol^{−1}

E_{a} = 76.589 kJ mol^{−1}

For a first order reaction the rate
constant at 500K is 8 X 10^{−4} s^{−1} . Calculate the
frequency factor, if the energy of activation for the reaction is 190 kJ mol^{-1}
.

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