Rate Laws and Half Life Reactions

Zeroth Order Differential Rate Law

Rate=k\left\lbrack A\right\rbrack^0

First Order Differential Rate Law

Rate=k\left\lbrack A\right\rbrack^1

Second Order Differential Rate Law

Rate=k\left\lbrack A\right\rbrack^2

Zeroth Order Integrated Rate Law

\left\lbrack A\right\rbrack_{t}=-kt+\left\lbrack A\right\rbrack_0

First Order Integrated Rate Law

\ln\left\lbrack A\right\rbrack_{t}=-kt+\ln\left\lbrack A\right\rbrack_0

First Order Integrated Rate Law (Alternate)

\ln\frac{\left\lbrack A\right\rbrack_{t}}{\left\lbrack A\right\rbrack_0}=-kt

Second Order Integrated Rate Law

\frac{1}{\left\lbrack A\right\rbrack_{t}}=kt+\frac{1}{\left\lbrack A\right\rbrack_0}

Zeroth Order Half Life Expression

t_{\frac12}=\frac{\left\lbrack A\right\rbrack_0}{2k}

First Order Half Life Expression

t_{\frac12}=\frac{\ln\left(2\right)}{k}

Second Order Half Life Expression

t_{\frac12}=\frac{1}{k\left\lbrack A\right\rbrack_0}