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2.
First order reaction
A certain level of response
A=B
The reaction rate is expressed by the change in the concentration of reactant A, and the differential expression of the reaction rate equation is
Organize, get
The initial concentration of reactant A is [A] 0 , the concentration at time t is [A] t , and both sides of the above formula are integrated simultaneously
Get
In[A] t -In[A] 0 =-k t
Convert to common logarithm
From the integral expression of the first-order reaction rate equation, the instantaneous concentration of the reactants of the first-order reaction can be obtained
.
Substituting [A] t =1/2[A] 0 into the integral expression of the rate equation of the first-order reaction, the half-life of the first-order reaction is
It can be seen that the half-life of the first-order reaction is only related to the rate constant, and has nothing to do with the initial concentration of the reactants
.
This is an outstanding feature of the first-order reaction
[Example 3-3] The changes in the concentration of reactant A over time are as follows:
Find (1) the rate constant of the reaction; (2) the instantaneous rate of the reaction at 3 min
.
Solution From the data in the table, it can be seen that the time required for the concentration of the reactant to decrease from 1mol·dm -3 to 0.
50mol·dm -3 is 2 minutes, which is reduced from 0.
5mol·dm -3 to 0.
25mol·dm -3 .
The time required is also 2min
(1) For the first order reaction
Get
k=0.
347(min -1 )
(2) The rate equation of the reaction is
r=k[A]
When the reaction reaches 3min, the instantaneous rate of the reaction
r 3min =k[A] 3min =0.
347×0.
36=0.
3.
Using the differential expressions of the second-order and third-order reaction rate equations, the integral expressions and half-life expressions of the second-order and third-order reactions with only one reactant can be obtained through integration processing
1) Secondary reaction
Differential expression of rate equation
Integral expression of rate equation
half life
2) Tertiary reaction
Differential expression of rate equation
Integral expression of rate equation
half life
