This document contains tables summarizing rate laws, integrated rate laws, and derivations for several common reaction orders and conditions: Table 7a describes zero-order, first-order, second-order, and general nth-order reactions for a single reactant A. It shows the rate law, integrated rate law, derivations, and graphs for each order. Table 7b describes reactions with two reactants A and B, where the rate is given by the rate law rate = k[A]x[B]y. It lists the specific rate laws and integrated rate laws for different values of x and y.

1. TABLE 7a: For reaction aA→ Products
Order n=0 n =1 n =2 n any integer, ≠1
d [ A] d [ A] d [ A] d [ A] ak[A]n=k [A]n
Rate Law − = ak [A]0= kA − = ak[A]=kA[A] − = ak[A]2=kA[A]2 −
dt
= A
dt dt dt
[ A ]t t [ A]t t
d [ A]
Derivation − ∫ d [ A] = ∫ k A dt − ∫
[ A] o [ A]n ∫
= k Adt
0
[ A ]o 0
of the [ A]t
∫ [ A]
−n
integrated − [ A]t − (−[ A]o ) = k A t − 0 − d [ A] = k At
[ A] o
rate law [ A]o − [ A]t = k A t
[ A]t− n +1  [ A]o n +1 
−
− −−
 − n + 1  = k At

− n +1  
− [ A]t− n +1 + [ A]o n +1 = (− n + 1)k At
−
1 1
− = (n − 1)k At
[ A]tn −1 [ A]0 −1
n
Unit of k Mol L-1s-1 s-1
Graph [A]t vs. t with m = -kA ln[A]t vs. t with m = -kA 1/[A]t vs. t with m = kA log t1/2 vs. [A]0 with m= -(1-n)
0.5[ A]o t1 / 2
Derivation − ∫ d [ A] = ∫k A dt
of the half- [ A ]o 0
life − 0.5[ A] o + [ A] o = k A t1 / 2
0.5[ A] o = k A t1 / 2
0.5[ A] o
t1 / 2 =
kA
[ A] o ln 2 1 2 n−1 − 1
t1 / 2 = t1 / 2 = t1 / 2 = t1 / 2 =
2k A kA k A [ A]o (n − 1)k A [ A]0 −1
n
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2. TABLE 7b: For reaction aA+ bB→ Products with rate law, rate = k[A]x[B]y
Condition Rate Law Integrated rate law
a = b =1, x = 0, y = 0 d [ A] [ A]o − [ A]t = kt
− = ak [A]0 = kA
dt
a = b =1, x =1, y = 0 d [ A] ln[ A]o − ln[ A]t = kt
− = k[A]
dt
a = b =1,x = 0, y = 1 d [ B] ln[ B]o − ln[ B ]t = kt
− = k[B]
dt
a = b =1, x =2, y = 0 d [ A] 1 1
− = k[A]2 −
[ A]t [ A]0
=kt
dt
a = b =1,x =0, y = 2 d [ B] 1 1
− = k[B]2 −
[ B ]t [ B ]0
=kt
dt
a = b =1,x =1, y = 1 d [ A] 1 1
− = k[A][B]= k([A]o-x)([B]o-x) − =kt
[A]o=B]o [ A]t [ A]0
dt
= k([A]o-x)2 = k[A]2
a = b=1 or ≠1,x =1, y = 1 d [ A] ([ A]o − ax) [ A]o
[A]o≠B]o − = k[A][B] ln = (b[ A]o − a[ B]o )kt + ln
dt ([ B]o − bx) [ B]o
d ([ A] o − ax) 1 dx
− = = k([A]o-ax)([B]o-bx)
dt a dt
d ([ B ] o − bx) 1 dx
− = = k([A]o-ax)([B]o-bx)
dt b dt
a = b ≠1, dx
x =1or 2, y = 1or 2 = k[A]o ([B]o-bx) =k‘[B]y
dt
[A]o≥B]o dx
= k([A]o-ax)[B]o =k‘[A]x
dt
[A]o≤ B]o
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