# First-order reaction

First-order reaction may refer to:

• Order of reaction, in chemical kinetics, the power to which the concentration term of a certain reactant in the rate equation is raised
• Rate equation#First-order reaction, a reaction that depends on the concentration of only one reactant. Mathematically,

$\frac{dC}{dt} =-kC$

Solving the above differential equation, we get

$C=C_ie^{-kt}$

From Arrhenius equation,

$k=k_0e^{\frac{-E_a}{RT}}$

     $t$   = time in seconds (s)
$C$  = the concentration of the reactant (mol/m^3, other units are also used, e.g. kg/m^3)
$C_i$  = the initial concentration of the reactant ($mol m^{-3}$)
$k_0$ = pre-exponential factor (1/s)
$E_a$ = the activation energy (J/mol)
$k$  = reaction rate constant (1/s) which is usually described by the Arrhenius equation: .
$R$  = the universal gas constant (J/mol.K, K is temperature in kelvin not to be confused with little k, the reaction constant)