Integrated Rate Law Calculator 1st Order

The Integrated Rate Law Calculator helps you determine the concentration of a reactant over time for first-order reactions. This tool is essential for chemistry students and professionals working with reaction kinetics.

What is Integrated Rate Law?

The integrated rate law describes how the concentration of a reactant changes over time in a chemical reaction. It provides a mathematical relationship between the concentration of reactants and the time elapsed since the reaction began.

Integrated rate laws are derived from differential rate laws and are essential for predicting reaction progress and determining reaction half-lives.

First-Order Integrated Rate Law

The first-order integrated rate law is used when the reaction rate depends linearly on the concentration of one reactant. The formula is:

ln([A]₀/[A]ₜ) = kt

Where:

[A]₀ = Initial concentration of reactant A (M)
[A]ₜ = Concentration of reactant A at time t (M)
k = Rate constant (s⁻¹)
t = Time elapsed (s)

This equation allows you to calculate the remaining concentration of a reactant after a given time or determine how long it takes for the concentration to reach a certain level.

Note: The first-order integrated rate law assumes that the reaction follows first-order kinetics and that the initial concentration is not too low.

How to Use the Calculator

Enter the initial concentration of the reactant in moles per liter (M).
Enter the rate constant in per second (s⁻¹).
Select the time unit (seconds, minutes, or hours).
Enter the time elapsed since the reaction began.
Click "Calculate" to see the remaining concentration.
Use the "Reset" button to clear all inputs.

The calculator will display the remaining concentration of the reactant and show a graph of the concentration over time.

Example Calculation

Let's say we have a first-order reaction with an initial concentration of 0.5 M and a rate constant of 0.2 s⁻¹. We want to find the concentration after 10 seconds.

ln([A]₀/[A]ₜ) = kt

ln(0.5/[A]ₜ) = 0.2 × 10

ln(0.5/[A]ₜ) = 2

0.5/[A]ₜ = e² ≈ 7.389

[A]ₜ ≈ 0.5 / 7.389 ≈ 0.067 M

After 10 seconds, the concentration of the reactant is approximately 0.067 M.

Frequently Asked Questions

What is the difference between differential and integrated rate laws?: The differential rate law describes the rate of change of reactant concentrations at any instant, while the integrated rate law describes the concentration of reactants as a function of time.
When is the first-order integrated rate law used?: The first-order integrated rate law is used when the reaction rate depends linearly on the concentration of one reactant, and the reaction follows first-order kinetics.
What units should I use for the rate constant?: The rate constant should be in per second (s⁻¹) if time is in seconds. Adjust the units accordingly if you're using minutes or hours.
How accurate is this calculator?: The calculator provides precise calculations based on the first-order integrated rate law formula. However, real-world reactions may have additional factors that affect the accuracy.
Can I use this calculator for zero-order reactions?: No, this calculator is specifically designed for first-order reactions. For zero-order reactions, you would need a different calculator.