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Types of Rate of Reactions

Average Rate, Instantaneous Rate, and Initial Rate explained.

By chemca Team • Updated Jan 2026

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. Depending on the time interval chosen, the rate can be classified as Average or Instantaneous.

1. Average Rate ($r_{av}$)

Over a Finite Time Interval

The average rate is the change in concentration of reactants or products divided by the time interval ($\Delta t$) over which the change occurs.

For a reaction $R \rightarrow P$:

$$ r_{av} = -\frac{\Delta [R]}{\Delta t} = +\frac{\Delta [P]}{\Delta t} $$

• Negative Sign: Indicates that the concentration of Reactant [R] is decreasing.
• Positive Sign: Indicates that the concentration of Product [P] is increasing.
• Graphical: It represents the slope of the Secant line connecting concentrations at time $t_1$ and $t_2$.

2. Instantaneous Rate ($r_{inst}$)

At a Specific Moment

The instantaneous rate is the rate of reaction at a particular instant of time. It is obtained when the time interval approaches zero ($\Delta t \to 0$).

$$ r_{inst} = \lim_{\Delta t \to 0} \left( -\frac{\Delta [R]}{\Delta t} \right) = -\frac{d[R]}{dt} $$ $$ r_{inst} = +\frac{d[P]}{dt} $$

Graphical Determination: It is equal to the slope of the Tangent drawn to the concentration vs. time curve at that specific time point $t$.
Slope = tan $\theta$ = dC/dt

Initial Rate: The instantaneous rate at $t=0$ (the very beginning of the reaction) is called the Initial Rate.

3. Rate Expressions & Stoichiometry

General Reaction

For a reaction where stoichiometric coefficients are not 1, the rate of change of individual species must be divided by their respective coefficients to get a unique Rate of Reaction.

Consider: $aA + bB \rightarrow cC + dD$

$$ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt} $$

Example: $N_2 + 3H_2 \rightarrow 2NH_3$

$$ \text{Rate} = -\frac{d[N_2]}{dt} = -\frac{1}{3}\frac{d[H_2]}{dt} = +\frac{1}{2}\frac{d[NH_3]}{dt} $$

Important Distinction:

• $-\frac{d[H_2]}{dt}$: Rate of disappearance of Hydrogen.
• $-\frac{1}{3}\frac{d[H_2]}{dt}$: Rate of Reaction.

4. Units of Rate

The rate is concentration change per unit time.

$$ \text{Unit} = \frac{\text{Concentration}}{\text{Time}} = \frac{mol \cdot L^{-1}}{s} = mol \cdot L^{-1} \cdot s^{-1} $$

For Gaseous Reactions: Concentration is replaced by Partial Pressure.
Unit = $atm \cdot s^{-1}$ or $bar \cdot min^{-1}$.

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