# Equations¶

#### Rate law expressions. The sum ($x+y$) gives the overall order of the reaction.

$rate=k[A]^x[B]^y$

#### Relationship between concentration and time for a first-order reaction.¶

$\ln\frac{[A]_t}{[B]_0}=-kt$

#### Equation for the graphical determination of $k$ for a first-order reaction.

$\ln[A]_t=-kt+\ln[A]_0$

#### Half-life for a first order reaction.¶

$t_\frac{1}{2}=\frac{0.693}{k}$

#### Relationship between concentration and time for a second-order reaction.¶

$\frac{1}{[A]_t}=-kt+\frac{1}{[A]_0}$