Reaction Order  Differential Rate Law  Integrated Rate Law  Linear Form 
Characteristic Kinetic Plot 
Halflife Expression 
Units of Rate Constant 


Zero 

[A] = [A]_{0}  k t  [A] = k t + [A]_{0}  [A] vs t 

mole L^{1} sec^{1}  
First 

[A] = [A]_{0} e^{ k t}  ln[A] = kt + ln[A]_{0}  ln [A] vs t 

sec^{1}  
Second 



1/[A] vs t 

L mole^{1} sec^{1} 
The series of three graphs shown below illustrate the use of the characteristic kinetic plots. The graph on the left shows [A] vs t plots for a zeroorder (red line), firstorder (green line), and secondorder (blue line) reaction. The graph in the middle shows ln [A] vs t plots and the graph on the right shows 1/[A] vs t plots for each reaction order.
–d[A] (1) rate = ————— = k dtDifferential Rate Law
(2) d[A] = –kdt
(3) 
[A]  t  
∫  d[A]  = –k  ∫  dt  
[A]_{0}  0 
(4) [A] – [A]_{0} = –kt
(5) [A] = –kt + [A]_{0}Integrated rate law (linear form)
Remember: 

∫  dx  = x  
–d[A] (1) rate = ————— = k[A] dtDifferential Rate Law
d[A] (2)  = –kdt [A]
(3) 
[A]  t  
∫  d[A]  = –k  ∫  dt  
———— 

[A]  
[A]_{0}  0 
(4) ln[A] – ln[A]_{0} = –kt
(5) ln[A] = –kt + ln[A]_{0}Integrated rate law (linear form)
Remember: 

∫  dx  = ln(x)  
————  
x 
–d[A] (1) rate = ————— = k[A]^{2} dtDifferential Rate Law
– d[A] (2)  = kdt [A]^{2}
(3) 
[A]  t  
– ∫  d[A]  = k  ∫  dt  
———— 

[A]^{2}  
[A]_{0}  0 
(4) –((–1/[A]) – (–1/[A]_{0})) = kt
(5) (1/[A]) – (1/[A]_{0}) = kt
(6) (1/[A]) = kt + (1/[A]_{0})Integrated rate law (linear form)
Remember: 

∫  dx  1  
————  = – ———  
x^{2}  x 
Order  Sample Rate Law  Units 
0  rate = k  M/s or M s^{–1} 
1  rate = k[A]^{1}  1/s or s^{–1} 
2  rate = k[A]^{2}  1/(M s) or M^{–1} s^{–1} 