Integrated Rate Law Calculations 1st Order – Cost Calculator

First Order Integrated Rate Law Calculator

Calculate chemical concentration, rate constants, or time elapsed.

Initial Concentration ([A]₀)

Rate Constant (k) (in s⁻¹, min⁻¹, etc.)

Time Elapsed (t)

Calculation Results:

Understanding First-Order Kinetics

In chemical kinetics, a first-order reaction is a reaction whose rate depends linearly on only one reactant concentration. This calculator utilizes the integrated form of the rate law to predict how the concentration of a reactant changes over time.

The Integrated Rate Law Formula

For a first-order reaction (A → Products), the relationship between concentration and time is expressed by the following equation:

ln([A]_t) = -kt + ln([A]_₀)

Alternatively, in exponential form:

[A]_t = [A]_₀e^-kt

Variables Explained:

[A]_t: Concentration of the reactant at time t.
[A]_₀: Initial concentration of the reactant at time t = 0.
k: The rate constant (units are reciprocal time, such as s⁻¹ or min⁻¹).
t: The time interval that has elapsed.

Example Calculation

Imagine a reactant has an initial concentration of 0.800 M and a rate constant k = 0.05 min⁻¹. To find the concentration after 20 minutes:

Identify inputs: [A]₀ = 0.800, k = 0.05, t = 20.
Apply formula: [A]_t = 0.800 * e^{-(0.05 * 20)}
Calculate exponent: -(1.0)
Solve: 0.800 * 0.3678 = 0.294 M

Half-Life (t_1/2)

One unique property of first-order reactions is that the half-life is independent of the starting concentration. It is calculated solely based on the rate constant:

t_1/2 = 0.693 / k