First-order rate law (integral form)

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

• Zero Order Rate Law (Integral form)
• Zero Order  Half Life
• Zero Order Rate Law
• First Order Rate Law (Integral form)
• First Order Half Life
• First Order Rate Law
• Second Order Rate Law (Integral form)
• Second Order Half Life
• Second Order Rate Law

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

Related Topics

• First-order rate law (differential form)
• Rate law reaction (calculator)

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