reaction rate law formulas

Zero Order Rate Law

Rate = k[A]^o = k

Zero Order Integrated Rate Law

[A] = -kt + [A]_o

Zero Order Half Life

t_½ = [A]_o / 2k

First Order Rate Law

Rate = k[A]

First Order Integrated Rate Law

ln[A] = -kt + ln[A]_o

First Order Half Life

t_½ = ln2 / k  =  0.693 / k

Second Order Rate Law

Rate = k[A]²

Second Order Integrated Rate Law

  1     = kt +     1

  [A]               [A]_o

Second Order Half Life

t_½ = 1 / k[A]_o

Zero Order Graph

A(t) x t and slope = -k

First Order Graph

ln(A) x t and slope = -k

Second Order Graph

1/[A] x t and slope = k