Chemical Kinetics: Rate Laws | General Chemistry 2
Reactions Rates
Rate of reaction for the reagents:
-
α = stochiometric coefficient
[reagent] = concentration of the reagent (in mol.L-1)
Rate of reaction for the products:
α = stochiometric coefficient
[product] = concentration of the product (in mol.L-1)
Ex: a A + b B → c C
rate reaction = - = - =
Reaction rate can also be expressed as a product of the concentration of reagents:
aA + bB → products
rate of reaction:
k [A]α [B]β
k = rate constant
α = order of reaction with respect to A
β = order of reaction with respect to B
α + β = overall order of reaction
First-Order Reactions
Rate of reaction of first-order reaction: k[A]
Units of k: s-1
Dependence of [A] on time: - = k[A]
After integrating:
ln[A] = ln[A]0 – kt
⇒ ln = -kt
⇒ = e-kt
Test plot of first-order reaction: ln[A] versus t
Half-time t1/2: time it takes for one-half of the reactant to react
At t = t1/2:
ln = - kt1/2
⇒ t1/2 =
⇒ independent of [A]0: half-time of a first-order reaction is independent of the initial concentration of the reactant
Second-Order Reactions
Rate of reaction of second-order reaction: k[A]2
Units of k: M-1.s-1 (mol.L-1.s-1)
Dependence of [A] on time: - = k[A]2
After integrating:
= + kt
Test plot of second-order reaction: versus t
At t = t1/2: [A] =
= + kt1/2
⇒ t1/2 =
⇒ dependent of [A]0
Radioactive Decay
Radioactive decay: process by which an unstable atomic nucleus loses energy by emitting small particles (α-particles, β-particles, γ-rays)
Radioactive decay: first-order process
⇒ ln = -kt and t1/2 =
⇒ k =
⇒ ln = - x t
Relationship between half-life and number of particles in first-order nuclear decay:
The number of radioactive nuclei N is proportional to the concentration of the radioactive species
⇒ =
⇒ ln = - x t