Calculate the rate constant (k) based on initial concentration, final concentration, time elapsed, and reaction order.
Zero Order (0)
First Order (1)
Second Order (2)
Calculation Results
Rate Constant (k):
Half-Life (t½): time units
Note: The unit of time in the result corresponds to the unit you entered (e.g., seconds, minutes).
How to Calculate Rate Constant from Concentration and Time
In chemical kinetics, determining the rate constant ($k$) is fundamental to understanding the speed of a reaction. The method for calculating this constant depends entirely on the reaction order. The reaction order dictates the mathematical relationship between the concentration of reactants and time, known as the Integrated Rate Law.
Formulas by Reaction Order
Different reaction orders utilize distinct formulas derived from calculus. Here is how $k$ is calculated for the most common orders:
Zero Order Reactions
In a zero-order reaction, the rate is independent of the concentration of the reactant. The concentration decreases linearly with time.
Formula: k = ([A]₀ – [A]ₜ) / t
Unit of k: M/time (e.g., M·s⁻¹)
First Order Reactions
In a first-order reaction, the rate depends linearly on the concentration of one reactant. This is common in radioactive decay.
Formula: k = ln([A]₀ / [A]ₜ) / t
Unit of k: 1/time (e.g., s⁻¹)
Second Order Reactions
In a second-order reaction, the rate is proportional to the square of the concentration of a single reactant (or the product of two reactants).
Formula: k = ((1 / [A]ₜ) – (1 / [A]₀)) / t
Unit of k: 1/(M·time) (e.g., M⁻¹·s⁻¹)
Definitions of Variables
[A]₀ (Initial Concentration): The molarity of the reactant at the start of the measurement (time = 0).
[A]ₜ (Concentration at time t): The molarity of the reactant after specific time $t$ has passed.
t (Time): The duration over which the reaction has occurred.
k (Rate Constant): The proportionality constant relating the rate of the reaction to the concentrations of reactants.