Summary

For a second order reaction:

Differential rate equation:
rate = k[A]²

Integrated rate equation

1	=	kt	+	1
[A]				[A]₀

If a plot of 1/[A] vs. t is linear, the reaction is second order in A, and the slope of the line is k.

Half life:

t_1/2	=	1
		k[A]₀

For a first order reaction:

Differential rate equation:
rate = k[A]

Integrated rate equation:

ln[A] = -kt + ln[A]₀

If a plot of ln[A] vs. t is linear, the reaction is first order in A, and the slope of the line is -k.

Half life:

t_1/2	=	ln 2
		k

If the half-life doesn't depend on concentration, the reaction is first order.