Rate Equations

Rate of Reaction: This is defined as the change in concentration of a reactant or product per unit of time, typically measured in $mol \, dm^{-3} \, s^{-1}$.

The Rate Equation: A mathematical expression, $\text{Rate} = k[A]^m[B]^n$, where $[A]$ and $[B]$ are reactant concentrations and $k$ is the rate constant.

Reaction Order: The powers $m$ and $n$ are the 'orders' with respect to each reactant, indicating how sensitive the rate is to changes in that specific concentration.

Overall Order: This is the sum of all individual orders ($m + n + ...$) in the rate equation, representing the total concentration dependence of the reaction.

Temperature Dependence: The rate constant $k$ increases exponentially with temperature because a higher fraction of molecules possess energy greater than the activation energy ($E_a$).

Mathematical Form: Expressed as $k = Ae^{-\frac{E_a}{RT}}$, where $A$ is the pre-exponential factor, $R$ is the gas constant ($8.31 \, J \, K^{-1} \, mol^{-1}$), and $T$ is temperature in Kelvin.

Logarithmic Form: Rearranging to $\ln k = -\frac{E_a}{R}(\frac{1}{T}) + \ln A$ allows for linear plotting to determine $E_a$ and $A$ experimentally.

Arrhenius Plots: A graph of $\ln k$ against $1/T$ yields a straight line with a gradient equal to $-E_a/R$ and a y-intercept of $\ln A$.

Units of k: Always derive the units for the rate constant based on the overall order; they are never fixed (e.g., for 2nd order: $dm^3 \, mol^{-1} \, s^{-1}$).

Temperature Conversion: Ensure all temperatures are converted to Kelvin ($K = ^\circ C + 273$) before using the Arrhenius equation.

Gradient Calculation: When using Arrhenius plots, remember the gradient is negative; $E_a$ must always be a positive value in $J \, mol^{-1}$ before converting to $kJ \, mol^{-1}$.

Initial Rates Method: When analyzing tables, look for experiments where only one reactant concentration changes to isolate its specific order.