Integrated Rate Equation Formula
To overcome the difficulty face by using differential rate equation,we integrate the differential equations. Thus, we get an equation relating to experimental data. Such type of equation is known as integrated rate equation.
General reaction:
aA + bB. —-> cC + dD
Integrated rate equation are following type
Zero order reaction, first order reaction and second order reaction.
Zero order reaction:
A reaction is said to be of zero order if it’s rate independent of the concentration of reactant that is the rate of proportional to zeroth power of the concentration of the reactant.
A —> B
Lets The reaction of zero order,
According to rate law;
rate= K [A]°
rate= K………(1)
According to instantaneous rate ;
At, t = 0. [A] = [A]°
[A]°= – K × 0 + C
C=[A]°
Put the value of C in the equation (4)
[A]= – Kt+[A]°
[A]-[A]°= Kt
Or
[A]°- [A] = Kt
So, this equation is said to be zero order equation
First order reaction
A reaction is said to be first order if it’s rate is determined by the change of one concentration term only.
At , t= 0. [A] = [A]°
ln [A]° = – K × 0 + C
C = ln [A]°
Put the value of C.
ln [A] = – Kt + ln [A]°
ln [A] – ln [A]°= Kt
Or
ln [A]°- ln [A] = Kt
So, this equation is said to be first order equation
Second order reaction
A reaction is said to be first order if it’s rate is determined by the variation of two concentration term only.
According to rate law;
rate= K (concentration)2
rate= K (a – x)2 ..,…….(1)
At t= 0, x = 0