The Rate Constant, k and Its Units HL Only
Quick Notes
- The rate constant (k) links rate and concentration in the rate equation: rate = k[A]m[B]n.
- The value of k is specific to a reaction and increases with temperature.
- Units of k depend on the overall order of the reaction.
- Units can be determined by rearranging the rate equation using:
- Rate units = mol dm⁻³ s⁻¹
- Concentration units = mol dm⁻³
Full Notes
What Is the Rate Constant, k?
The rate constant (k) appears in the rate equation for a reaction and reflects how temperature, activation energy, and collision orientation influence the reaction rate.
Temperature dependence: as temperature increases, more particles overcome the activation barrier, so k increases.
Rate Equation and Units of k
A rate equation (also called a rate law) takes the general form:
rate = k[A]m[B]n
- Units of rate: mol dm⁻³ s⁻¹
- Units of concentration: mol dm⁻³
Units of k vary depending on the overall order of the reaction:
- Zero Order: rate = k → Units of k: mol dm⁻³ s⁻¹
- First Order: rate = k[A] → Units of k: s⁻¹
- Second Order: rate = k[A]² or k[A][B] → Units of k: mol⁻¹ dm³ s⁻¹
- Third Order: rate = k[A]²[B] → Units of k: mol⁻² dm⁶ s⁻¹
Determine the units of k if a reaction is first order in A and second order in B.
- Rate law: rate = k[A][B]²
- Units:
- rate = mol dm⁻³ s⁻¹
- [A] = mol dm⁻³
- [B]² = (mol dm⁻³)² = mol² dm⁻⁶
- Solve for k:
k = rate / ([A][B]²)
Units = (mol dm⁻³ s⁻¹) / (mol dm⁻³ × mol² dm⁻⁶) = mol⁻² dm⁶ s⁻¹
Summary
- k is temperature dependent and specific to each reaction.
- Units of k depend on the overall order of the reaction.
- Units must be derived carefully using the rate law.
Linked Course Question
What are the rate equations and units of k for the reactions of primary and tertiary halogenoalkanes with aqueous alkali?
Primary halogenoalkanes follow an SN2 mechanism (bimolecular): Rate = k[halogenoalkane][OH⁻]. Overall order = 2. Units of k: mol⁻¹ dm³ s⁻¹.
Tertiary halogenoalkanes follow an SN1 mechanism (unimolecular): Rate = k[halogenoalkane]. Overall order = 1. Units of k: s⁻¹.
The different rate laws reflect the different mechanisms and species involved in the rate-determining step.