Rate Laws, Half-Life Formulas, and Units of k for Reactions

Differential rate law for a zero-order reaction

Rate = k

Integrated rate law for a zero-order reaction

[A] = [A]0 − kt

Straight-line plot for a zero-order reaction

[A] vs. time (t), slope = −k

Half-life formula for a zero-order reaction

t1/2 = [A]0 / (2k)

Differential rate law for a first-order reaction

Rate = k[A]

Integrated rate law for a first-order reaction

ln[A] = ln[A]0 − kt

Straight-line plot for a first-order reaction

ln[A] vs. time (t), slope = −k

Half-life formula for a first-order reaction

t1/2 = 0.693 / k

Differential rate law for a second-order reaction (single reactant)

Rate = k[A]^2

Integrated rate law for a second-order reaction

1/[A] = 1/[A]0 + kt

Straight-line plot for a second-order reaction

1/[A] vs. time (t), slope = +k

Half-life formula for a second-order reaction

t1/2 = 1 / (k[A]0)

What are the units of k for a zero-order reaction?

mol·L⁻¹·s⁻¹

What are the units of k for a first-order reaction?

s⁻¹

What are the units of k for a second-order reaction?

L·mol⁻¹·s⁻¹

most probable velocity

square root (2RT/M)

average velocity

square root (8RT/piM)

root mean square velocity

square root (3RT/M)