Lecture 10: Integrated Rate Laws and Half Lives

What does the integrated rate law tell you?

The concentration as a function of time (the curve)

Zero order rate law

Rate = k

Zero Order Integrated Rate Law

[A] = -kt + [A]₀

Zero order linear graph axis

[A] versus t

Zero order relationship of rate constant to slope of line

Slope = -k

Zero order half-life

t_1/2 = [A]₀/2k

First order rate law

rate = k[A]

First order units of rate constant

s^-1

zero order units of rate constant

M s^-1

First order integrated rate law

ln[A] = -kt + ln[A]₀

First order linear graph axis

ln[A] versus t

first order linear relationship

k = -slope

First order half-life

t_1/2 = 0.693/k

Second order rate law

rate = k[A]²

Second Order units of rate constant

M^-1s^-1

Second order integrated rate law

1/[A] = kt + (1/[A]₀)

Second order linear graph axis

1/[A] versus t

Second order relationship linear relationship

k = slope

Second order half-life

t_1/2 = 1/[A]₀k

Half-Life

The time required for one-half of a reactant to react