First-order rate law (integral form)

`[A] = [A]_0*e^-(k*t)`

Enter a value for all fields

The First-order Rate Law (Integral Form) calculator computes the concentration of a substance (A) based on a Rate Law equation, the initial concentration (A₀), the rate constant (k) and the duration of the reaction (s).

INSTRUCTIONS: Choose units and enter the following:

[A₀] Initial Concentration of the Substance.
(k) Rate Constant.
(s) Duration of the Reaction.

Concentration of Substance [A]: The calculator returns the concentration of the substance after the reaction in moles per liter (mol/L). However, this can be automatically converted to other concentration units via the pull-down menu.

Chemistry Rate Law Calculators

The Science

The first order rate integral^[1] equation calculates the rate at which the reactants turn in to products. Unlike the differential form of the first-order equation, the integral form looks at the amount of reactants have been converted to products at a specific point in the reaction. A full integration of the equation can be found here.

The Math

The equation for the first-order rate reaction is

[A]=[A]_oe^−kt [2]

Where:

[A] is the concentration of substance after reaction.
[A]_o is the initial concentration in units of (mol/L)
k is the rate constant in units of (1/sec)
t is time of the concentration (sec

Supplement Material

Khan Academy: Rate law and reaction order

References

[1] https://en.wikipedia.org/wiki/Rate_equation

[2]Whitten, et al. 10th Edition. Pp. 626,629,631

[Picture]http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Kinetics/Reaction_Rates/First-Order_Reactions