Units of Rate Constant

Different ordered reactions have different units for k.
For an nth order reaction
For the reaction nA → Products
rate =  k[A]n          
Therefore, k =     rate                  ………………….(1)
                           [Concentration]n          
  From relation (1) we can find order for various reactions


               











Integrated Rate Equations: These are equations relating the rate of a reaction and concentration of reactants. Different ordered reactions have different integrated rate law equations.
ü   For Zero Order Reaction: Zero order reactions are reactions in which the rate of reaction is proportional to zero power of the concentration of reactants.
Consider a zero order reaction     R → P
The rate expression for the above reaction is
r = – d[R] ………………. (1)
         dt
Rate law for the above reaction is
r= k[R]0 = k ………………… (2)
From equations (1) & (2), we can write 
k    =   – d[R]
                dt
The above equation is known as differential rate equation for zero order reaction.
d[R] = – kdt
On integrating the above equation, we get
[R] = – kt + C      …………………. (3)
Where C is the constant of integration. To calculate the value of C, consider the initial conditions. i.e., when t=0, [R] = [R]0
Substitute these values in equation (3)
[R]0 = – k × 0 + C
C = – [R]0
Substituting C in equation (3), we get
[R] = – kt  –  [R]0  …………. (4)
[R]0 – [R] = kt

k = [R]0 – [R]
             t

………………. (5)
 

This equation is of the form of a straight line y = mx + c. So if we plot [R] against t, we get a

 straight line with slope = – k and intercept equal to [R]0. 


        

The decomposition of gaseous ammonia on a hot platinum surface at high pressure.
N2 + H2 → 2 NH3
At high pressure, molecules. So, a further change in reaction conditions does not change the rate of the reaction. So, it becomes a zero order reaction.
Another e.g. is the thermal decomposition of HI on gold surface