Definition

The rate of reaction is the change in concentration of a reactant or product per unit time.

$\text{Rate} = \pm\frac{\Delta[\text{species}]}{\Delta t}$

The sign is negative for reactants (concentration decreases) and positive for products (concentration increases).

General Expression

For reaction $aA + bB \rightarrow cC + dD$:

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

Division by stoichiometric coefficients ensures a unique rate value regardless of which species is monitored.

Average vs Instantaneous Rate

• Average rate: $\frac{\Delta[\text{species}]}{\Delta t}$ over a finite time interval
• Instantaneous rate: $\frac{d[\text{species}]}{dt}$ at a specific moment (slope of tangent to concentration-time curve)

Units of Rate

$\text{Rate units} = \frac{\text{mol}}{\text{L} \cdot \text{s}} = \text{mol}\,\text{L}^{-1}\,\text{s}^{-1}$

Example Calculation

For $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$:

$\text{rate} = -\frac{d[\text{N}_2]}{dt} = -\frac{1}{3}\frac{d[\text{H}_2]}{dt} = +\frac{1}{2}\frac{d[\text{NH}_3]}{dt}$

If d[$NH_{3}$]/dt = 0.6 mol/L/s, then rate of disappearance of $H_{2}$ = (3/2) × 0.6 = 0.9 mol/L/s.