The minimum energy that can be obtained through molecular collision, so that the reaction can start, is called activation energy. At a low value of activation energy, the value of the rate of reaction is high and at a high value of activation energy, the value of the rate of reaction is low.
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Form Arrhenius Law
K = Ko e^(-E/{RT}) ............(1)
Where
K = Rate Content
R = Universal gas Constant
Ko = Frequency factor or pure
E = Activation energy of the reaction taking the natural log
ln K = ln Ko + ln . e^(-E/{RT}
ln K = ln Ko - (E/{RT}) .…....(2)
According to equations 1 and 2, if 1/T is represented on the x-axis and ln K is represented on the y-axis then.
Let the rate constant at temperature T1 be K1 and the rate constant at temperature T2 be K2.
ln K1 = ln Ko = E/(RT1) ........(3)
ln K2 = ln Ko = E/(RT2) .......(4)
Equ 3 & 4
ln K2 - ln K1 = -E/{RT_1} + E/{RT_2}
ln (K_1/K_2) = - [1/T2 + 1/T2]
In this way, E can be easily calculated if all the data is known.
According to the thumb rule, the rate of reaction doubles when the temperature increases by 10°C. This is true only for specific combinations of some.
The rate of reaction is given by
r = KC^αA. C^βB
r = Ko .e-E/{RT}
When concentration is constant KC^αA. C^βB will also be constant. Let us assume that K'o = new factor in place of Ko.
r = K_o .e-E/{RT}
ln.r = ln K'_o + ln . e -E/{RT}
ln.r = -E/{RT} + lnK'_o
ln.r = -E/{RT}[1/T] + ln K'_o
It is clear from the above equation that the graph between ln r and 1/T will be a line whose slope will be - E/R. If the rate of reaction is r1&r2 at differential temperatures T1 and T2.
ln (r_1/r_2) = -E/R [1/T2 +1/T1]
Unit of activation energy = cal/mole or Jule/mole.
Activation Energy & Temperature Dependency
When molecules come physically closer to each other, the energy of the system changes. This energy reaches a maximum value which is obtained from the difference between the energies of the activated complex.
i). The graph of ln k vs 1/T from the Arrhenius equation gives a straight line whose slope gives a large slope for large E and a small slope for small E.
ii). Reactions are more sensitive at low temperatures than at high temperatures.
iii). By doubling the rate of reaction at low temperatures, the temperature difference is 87°K. Whereas at high temperatures, if the rate of reaction is doubled, the temperature difference is 1000°C.
iv). The reactions of high activation energy are more temperature sensitive, whereas the reactions of low activation energy are relatively less temperature sensitive.