ChemistryKineticsA-Level
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Integrated Rate Law (2nd Order) Calculator

Concentration over time for 2nd order.

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1 / Concentration

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Overview

The integrated rate law for a second-order reaction describes the concentration of a reactant over time when the reaction rate is proportional to the square of its concentration. It is characterized by a linear relationship between the reciprocal of the reactant concentration and time, where the slope represents the rate constant.

Symbols

Variables

1/[A] = 1 / Concentration, k = Rate Constant, t = Time, 1/[A]_0 = Initial 1/[A]0

1/[A]
1 / Concentration
Rate Constant
Time
Initial 1/[A]0

Apply it well

When To Use

When to use: Use this equation when kinetic experiments show that a plot of 1/[A] versus time produces a straight line. It is applicable to elementary bimolecular reactions where two identical molecules collide, or situations where two different reactants have equal initial concentrations.

Why it matters: This law is essential for modeling industrial dimerization processes and environmental pollutant degradation. Understanding second-order kinetics allows chemical engineers to predict how effectively concentration changes can accelerate or slow down a reaction compared to first-order systems.

Avoid these traps

Common Mistakes

  • Using ln[A] instead of 1/[A] for 2nd order.
  • Convert units and scales before substituting, especially when the inputs mix M^-1, M^-1 s^-1, s.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

A decomposition reaction follows second-order kinetics with a rate constant of 0.250 M⁻¹s⁻¹. If the initial concentration of the reactant is 0.500 M, what will the concentration be after 10.0 seconds?

Rate Constant0.25 M^-1 s^-1
Initial 1/[A]02 M^-1
Time10 s

Solve for: invA

Hint: Calculate the reciprocal of the initial concentration first, then add the product of k and t.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Atkins Physical Chemistry
  2. McQuarrie & Simon, Physical Chemistry: A Molecular Approach
  3. Wikipedia: Rate equation
  4. Atkins' Physical Chemistry
  5. McQuarrie, Donald A. 'Physical Chemistry: A Molecular Approach'
  6. Atkins, P. W., & de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press.
  7. Chang, R. (2010). Chemistry (10th ed.). McGraw-Hill.
  8. Standard curriculum — A-Level Chemistry (Kinetics extension)