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Rate Laws From Experimental Data

Rate law: Rate = k[A]m[B]nk[A]^m[B]^n

  • Must be determined experimentally
  • Cannot be determined from balanced equation
Rate laws from experimental data

Definition Of Reaction Rate

Rate of change of concentration of reactant or product over time: Rate=−1ad[A]dt=1bd[B]dt\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt}

Definition of Reaction Rate

Order Of Reaction (Reaction Orders)

Reaction order: Power to which concentration is raised in rate law

  • Zero order: Rate independent of concentration
  • First order: Rate directly proportional to concentration
  • Second order: Rate proportional to square of concentration
  • Overall order = sum of individual orders
Order of Reaction (Reaction Orders)

Rate Constant Units

OrderUnits of k
Zeromol/L - s
First1/s or s-1
SecondL/mol - s
ThirdL2/mol2 - s
Rate Constant Units

Integrated Rate Laws (Zero, First, Second Order)

OrderRate LawIntegrated FormHalf-life
ZeroRate = k[A]t=[A]0−kt[A]_t = [A]_0 - ktt1/2=[A]0/2kt_{1/2} = [A]_0 / 2k
FirstRate = k[A]ln⁡[A]t=ln⁡[A]0−kt\ln[A]_t = \ln[A]_0 - ktt1/2=ln⁡2/kt_{1/2} = \ln 2 / k
SecondRate = k[A]21/[A]t=1/[A]0+kt1/[A]_t = 1/[A]_0 + ktt1/2=1/k[A]0t_{1/2} = 1 / k[A]_0
Integrated Rate Laws (Zero, First, Second Order)

Half-life Calculations

First-order half-life: Independent of initial concentration t1/2=ln⁡2k=0.693kt_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k}

Half-Life Calculations

Molecularity

Elementary reaction: Single molecular event

  • Unimolecular: One molecule decomposes/rearranges (A -> products)
  • Bimolecular: Two molecules collide (A + B -> products)
  • Termolecular: Three molecules collide (rare)
Molecularity

Effective Collisions And Orientation

For reaction to occur:

  1. Molecules must collide (proper frequency)
  2. Sufficient energy (≥ activation energy)
  3. Proper orientation
Effective Collisions and Orientation

Activation Energy And Temperature (Arrhenius)

Activation energy (EaE_a): Minimum energy required for reaction Arrhenius equation: k=Ae−Ea/RTk = Ae^{-E_a/RT}

  • k = rate constant
  • A = frequency factor
  • R = 8.314 J/mol - K
  • T = absolute temperature (K)
Activation Energy and Temperature (Arrhenius)

Transition State And Activation Energy

Transition state: High-energy arrangement of atoms during reaction

  • Cannot be isolated
  • Maximum on reaction coordinate diagram

Activation energy: Energy difference between reactants and transition state

  • Catalyst lowers Ea (provides alternative pathway)
Transition State and Activation Energy

Rate-determining Step

(RDS):** Slowest elementary step in mechanism

  • Determines overall rate law
  • Other steps assumed much faster
Rate-Determining Step

Intermediates And Catalysts

Reaction intermediate: Species produced in one step, consumed in another

  • Not in overall reaction equation
  • Typically at low concentration

Catalyst: Substance that increases rate without being consumed

  • Lowers activation energy
  • Not consumed in overall reaction
  • Homogeneous: same phase as reactants
  • Heterogeneous: different phase
Intermediates and Catalysts

Effect Of Catalyst On Activation Energy

Catalyst provides alternative reaction pathway with lower Ea

  • Increases rate constant (k)
  • Does not affect equilibrium position
  • Lowers activation energy for both forward and reverse reactions
Effect of Catalyst on Activation Energy