Second Order Integrated Rate Law Calculator

The second order integrated rate law calculator helps determine reaction rates for chemical reactions where the rate depends on the square of the concentration of a reactant. This tool provides a quick way to calculate reaction progress over time using the integrated form of the second order rate law.

What is the Second Order Rate Law?

The second order rate law describes chemical reactions where the rate of reaction is proportional to the square of the concentration of one reactant. This occurs when two molecules collide to form products, and the reaction rate depends on the concentration of that reactant squared.

For a reaction A → Products, the differential rate law is:

d[A]/dt = -k[A]²

Where:

d[A]/dt = rate of disappearance of A
k = rate constant
[A] = concentration of A

Integrated Formula

The integrated form of the second order rate law allows calculation of concentration as a function of time:

1/[A] = kt + 1/[A]₀

Where:

[A] = concentration at time t
k = rate constant
t = time
[A]₀ = initial concentration

This formula shows how the concentration decreases over time following a hyperbolic curve.

How to Use This Calculator

Enter the initial concentration of the reactant in molarity (M)
Input the rate constant (k) in units of M⁻¹s⁻¹
Specify the time in seconds
Click "Calculate" to see the remaining concentration
View the result and chart showing concentration over time

Note: The calculator assumes the reaction follows the second order rate law exactly. For real reactions, other factors may affect the rate.

Example Calculation

Suppose we have a reaction with:

Initial concentration [A]₀ = 0.1 M
Rate constant k = 2 M⁻¹s⁻¹
Time t = 5 seconds

Using the integrated formula:

1/[A] = (2 M⁻¹s⁻¹)(5 s) + 1/0.1 M 1/[A] = 10 + 10 = 20 M⁻¹ [A] = 0.05 M

The remaining concentration after 5 seconds is 0.05 M.

Interpreting Results

The calculator provides:

The remaining concentration at the specified time
A chart showing how concentration changes over time
Visual representation of the hyperbolic decay pattern

The chart helps visualize how quickly the reaction progresses. The steep initial drop shows the characteristic behavior of second order reactions.

Frequently Asked Questions

What units should I use for the rate constant?

The rate constant should be in units of M⁻¹s⁻¹ for this calculator, assuming concentration is in molarity (M) and time in seconds (s).

Can this calculator handle different time units?

Yes, you can convert your time to seconds before entering it into the calculator. The formula will work with any consistent time unit.

What if my reaction is not exactly second order?

This calculator provides an approximation. For reactions that don't strictly follow second order kinetics, experimental data should be used for more accurate predictions.

How accurate are the results?

The results are mathematically precise based on the second order integrated rate law. Real-world reactions may have additional factors affecting the rate.