half life of reaction refers to as the time

Question

 

Half life of reaction refers to as the time during which the concentration of the reactants is reduced to half of the initial concentration or it is the time essential for the completion of half of the reaction. It is denoted by 11/2.

Half life of zero order reaction: as already discussed, the integrated equation for zero order reaction is;
                                               
[R] = [R]₀ – kt
                                    
Now at t_1/2, [R] = ([R]₀)/2
                                                             
∴  ([R]₀)/2 = [R]₀ – kt
                          
Or, kt_1/2 = [R]₀ – ([R]₀)/2 = ([R]₀)/2
                                          
Or, t_1/2 = ([R]₀)/2k

From the above expression it is clear that the half life of a zero order reaction is directly proportional to initial concentration.
                                                   
i.e. t_1/2 [A]₀
                                  
At t_3/4, the concentration [R] = ¼ [R]₀
                                    
t3/4 = 1/k R₀-  1/4[R]₀) = 3/4 [R₀)/k 
                                         
Hence, t_3/4 = 3/2 t_1/2 = 1.5t1/2

Half life of first order reaction: for first order reaction, we know that
                                    
k = 2.303/t log ([A]_0)/([A]) or t = (2.303)/k log ([A]_0)/([A])
                                        
When t = t1/2 then [A] = ½ [A]0,
                                     
Therefore, t1/2 = (2.303)/k ½ ([A]_0)/([A]) = (2.303)/k  log 2
                                        
t1/2 = 0.693/k           [? log 2 = 0.3010]

It is quite clear from the above expression that the half life or half change time for first order reaction does not depend upon initial concentration of the reactants. Likewise, the time required to decrease the concentration of the reactant to any fraction of the initial concentration for the first order reaction is also independent of the initial concentration.