The Rate Constant and Its Temperature Dependence
What is Rate Constant?
Definition
Rate constant
The rate constant, $ k $, serves as a measure of how fast a reaction proceeds, and it varies with temperature.
This relationship is captured by the Arrhenius equation:
$$
k = A e^{-\frac{E_a}{RT}}
$$
where:
- $ k $: Rate constant.
- $ A $: Arrhenius (frequency) factor, representing the likelihood of correctly oriented collisions.
- $ E_a $: Activation energy ($ \text{J mol}^{-1} $), the minimum energy needed for a reaction to occur.
- $ R $: Gas constant ($ 8.31 \, \text{J K}^{-1} \text{mol}^{-1} $).
- $ T $: Absolute temperature (kelvin).
- As temperature increases, the term $ e^{-\frac{E_a}{RT}} $ becomes larger, leading to an increase in $ k $.
- This explains why reactions generally occur more quickly at higher temperatures.
- Reactions with higher activation energies ($ E_a $) are more sensitive to temperature changes.
- Even a small increase in temperature can significantly increase the rate constant.
Units of the Rate Constant
The units of the rate constant, $ k $, depend on the overall order of the reaction. To determine these units, consider the rate equation:
$$
\text{rate} = k [A]^n [B]^m
$$
where:
- $ [A] $ and $ [B] $: Reactant concentrations, measured in $ \text{mol dm}^{-3} $.
- $ n $ and $ m $: Orders of reaction with respect to $ A $ and $ B $, respectively.
- The overall order of the reaction is $ n + m $.
- The rate of reaction is typically measured in $ \text{mol dm}^{-3} \text{s}^{-1} $, so the units of $ k $ must balance the equation.
