ln A . So we can calculate E a and A using these values. At temperature T , equation ( . ) is ln k = – RT + ln A ( .
) At temperature T , equation ( . ) is ln k = – RT + ln A ( . ) (since A is constant for a given reaction) k and k are the values of rate constants at temperatures T and T respectively. Fig.
. : Distribution curve showing temperature dependence of rate of a reaction temperature is raised, the maximum of the curve moves to the higher energy value (Fig. . ) and the curve broadens out, i.e., spreads to the right such that there is a greater proportion of molecules with much higher energies.
The area under the curve must be constant since total probability must be one at all times. We can mark the position of E a on Maxwell Boltzmann distribution curve (Fig. . ).
Increasing the temperature of the substance increases the fraction of molecules, which collide with energies greater than E a . It is clear from the diagram that in the curve at ( t + ), the area showing the fraction of molecules having energy equal to or greater than activation energy gets doubled leading to doubling the rate of a reaction. In the Arrhenius equation ( . ) the factor e - E a / RT corresponds to the fraction of molecules that have kinetic energy greater than E a .
Taking natural logarithm of both sides of equation ( . ) ln k = – RT + ln A ( . ) The plot of ln k vs /T gives a straight line according to the equation ( . ) as shown in Fig.
. . 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.
The rate constants of a reaction at 500K and 700K are .02s – and .07s – respectively. Calculate the values of E a and