Chemical Kinetics

Introduced to this in AP Chemistry

Rate Laws §

• Study the reaction directly after the reaction starts - so you only study reactants
• 2 types of rate laws:
  • Differential - rate depends on [concentration]
    • [] references to the molarity of
  • Integrated - concentration depends on time
  • Use whichever is easier to experimentally determine

The Differential Rate Law §

If the question asks “Rate Law” then it’s referring to Differential Rate Law. Do NOT use Integrated

The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers

Rate law (DIFFERENTIAL REMEMBER!) can ONLY be determined experimentally

aA + bB -> cC + dD

Rate = k[A]${}^x$[B]${}^y$

k = rate constant x and y = calculated values

reaction is x${}^{th}$ order in A

reaction is y${}^{th}$ order in B

reaction is (x+y)${}^{th}$ order overall

Example §

F${}_2$ (g) + 2 ClO${}_2$ (g) -> 2FClO${}_2$ (g)

Rate = k[F${}_2$]${}^x$[ClO${}_2$]${}^y$

Calculate value of x and y

Comparing trial 1 and 3

Double [F${}_2$] with [ClO${}_2$] constant -> Rate doubles -> x = 1

Comparing trial 1 and 2

Quadruple [ClO${}_2$] with [F${}_2$] constant -> Rate quadruple -> y = 1

Summary §

• Reaction order is always defined in terms of reactant (not product) concentrations
• Rate laws are always determined experimentally
• The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation

Integrated Rate Law §

Concentration and time data

Must graph data to determine the order of the rxn

Order	Linear Graph:
Zero	[concentration] vs. time
First	ln [concentration] vs. time
Second	1/[concentration] vs. time

First-Order Reactions §

rate = k[A]

After integration you get [A] = [A]${}_0$e${}^{-kt}$

ln[A] = -kt + ln[A]${}_0$

[A] is the concentration of A at any time t [A]${}_0$ is the concentration of A at time t = 0

The half-life, t${}_{\frac{1}{2}}$ is the time required for the concentration of a reactant to decrease to half of its initial concentration

t${}_{\frac{1}{2}}$ = $\frac{ln2}{k}$ = $\frac{0.693}{k}$ (3 significant digits)

Half life does NOT depend on the concentration ([A])

Second-Order Reactions §

rate = k[A]${}^2$

$\frac{1}{[A]}$ = kt + $\frac{1}{[A{]}_0}$

Zero-Order Reactions §

rate = k[A]${}^0$ = k

[A] = -kt + [A]${}_0$

Units for the rate constant §

Chemical concept of a reaction §

• 0 order = the change in concentration of that reactant does not change the rate of reaction
• 1st order = doubling the concentration causes the rate to double
• n${}^{th}$ order = doubling the concentration causes a 2${}^n$ increase in rate
• The rate constant does not depend on concentration