Rate of Reaction: Definition & Dynamics

The Rate of Reaction is the speed at which reactants are converted into products. It is expressed as the change in molar concentration per unit time ($M \cdot s^{-1}$ or $mol \cdot L^{-1}s^{-1}$).

The Rate Equation
Rate ($r$) $= \pm \frac{1}{\nu} \frac{d[C]}{dt}$

Where $\nu$ is the stoichiometric coefficient and $[C]$ is the concentration.

Real-World Examples
  • Fast: Precipitation of $AgCl$ (Instantaneous).
  • Moderate: Hydrolysis of cane sugar.
  • Slow: Rusting of iron or radioactive decay.
Master Kinetics Engine
Arrhenius Activation Solver
Half-Life (t₁/₂)

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Result

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Eₐ (kJ/mol)

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Area beyond dashed line = Effective Collisions ($E > E_a$)

Detailed Chemical Kinetics for Advanced Exams

1. Integrated Rate Laws (JEE/GATE Focus)

For a reaction $n A \to \text{Products}$, the integrated laws used in this calculator are:

Zero Order: $[A]_t = [A]_0 - kt$
First Order: $\ln[A]_t = \ln[A]_0 - kt$
Second Order: $\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt$
Third Order: $\frac{1}{2[A]_t^2} - \frac{1}{2[A]_0^2} = kt$

2. General Half-Life ($t_{1/2}$) Formula

For any order $n$ (where $n \neq 1$), the half-life is proportional to initial concentration:

$t_{1/2} \propto \frac{1}{[A]_0^{n-1}}$

3. Arrhenius Equation & Activation Energy

The temperature dependence is expressed by $k = Ae^{-E_a/RT}$. Advanced problems often require solving for the frequency factor $A$ or the energy barrier $E_a$. This tool uses the two-point form:

$\log\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303R} \left[\frac{T_2 - T_1}{T_1 T_2}\right]$

4. Collision Theory Parameters

According to collision theory, the Rate $= Z \cdot \rho \cdot e^{-E_a/RT}$, where $Z$ is collision frequency and $\rho$ is the steric factor. In our simulation, green particles represent effective collisions (energy $> E_a$) and red particles represent ineffective ones.