Chemical Kinetics: Rate Laws | General Chemistry 2

The rate laws in chemical kinetics are studied in this chapter: reactions rates, first-order and second-order reactions (specific rate of reaction, relation between concentration and time, half-time), radioactive decay.

Reactions Rates

Rate of reaction for the reagents:

1α [reagent]t

α = stochiometric coefficient
[reagent] = concentration of the reagent (in mol.L-1)

 

Rate of reaction for the products:

1α [product]t

α = stochiometric coefficient
[product] = concentration of the product (in mol.L-1)

 

Ex: A + B → C
rate reaction = - 1a [A]t = - 1b [B]t = 1c [C]t

 

 

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: - [A]t = k[A]

After integrating:

ln[A] = ln[A]0 – kt

⇒ ln [A][A]0 = -kt

⇒ [A][A]0 = 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[A] = [A]02 
 

ln [A]02 [A]0 = - kt1/2 

⇒ t1/2ln 2k

⇒ 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: - [A]t = k[A]2
After integrating:

1[A] = 1[A]0 + kt

 

Test plot of second-order reaction: 1[A] versus t

 

At t = t1/2: [A] = [A]02

2[A]0 = 1[A]0 + kt1/2

⇒ t1/2 = 1k [A]0

⇒ 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 [A][A]0 = -kt and t1/2ln 2k

⇒ k = ln 2t1/2 

⇒ ln [A][A]0 = -  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

⇒ [A][A]0 = NN0 

⇒ ln NN0 = - ln 2t1/2 x t