Ch. 10 Kinetics

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Reaction Rates

• rate of change in concentration per unit time ($M\pu{/s}=\pu{mol/Ls}$)
• rate of appearance of products equals negative the rate of disappearance of reactants
• rates of appearance/disappearance in a reaction follow the mole ratio calculations

Factors that Affect Reaction Rates

• Concentration: if concentration is a part of the rate law, it will affect reaction rate
  • rate law written in the form $\text{Rate}=k[A]^x[B]^y[C]^z$, where $k$ is the rate constant
  • exponents must be found experimentally (with data)
    1. Start with the general form
    2. Plug in known values from experiments
    3. Use the equations to solve for unknown values
• Temperature: increasing always increases rate; decreasing always decreases rate
  • Arrhenius equation: $k=Ae^{-E_a/RT}$, where $k$ is the rate constant, $A$ is a proportionality constant, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the Kelvin temperature
  • the natural log of the above results in $\ln{k}=\frac{-E_a}{RT}+\ln{A}\rightarrow$ straight-line graph of $\ln{k}$ vs $1/T$
  • activation energy is always positive
• Ability to Meet: gas/solution/fine solids react mre easily
• Catalyst Presence: increases reaction rate

Reaction Order

Zero-Order Reactions

$\text{Rate}=k$
$[A]=-kt+[A]_0$

• does not depend on concentration
• concentration vs time graph is a straight line
• half-life: $t_{1/2}=[A]_0/2k$

First-Order Reactions

$\text{Rate}=k[A]$
$\ln{[A]}=-kt+\ln{[A]_0}$

• $\ln$ concentration vs time graph is a straight line
• half-life: $t_{1/2}=\ln2/k$
• radioactive decay is a first-order process

Second-Order Reactions

$\text{Rate}=k[A]^2\text{ or }\text{Rate}=k[A][B]$
$\frac{1}{[A]}=kt+\frac{1}{[A]_0}\textit{, when }[A]=[B]$

• reciprocal concentration vs time graph is straight
• half=life: $t_{1/2}=1/k[A]_0$

Kinetic Theories

• Collision Theory: reaction rate equals frequency of effective collisions between reactants
  • when molecules collide, kinetic energy is converted into potential energy
  • if $\Delta\text{(Potential Energy)}>E_a$ and collide in the right direction, reaction occurs
  • by kinetic molecular theory, fraction of collisions reaching $E_a$ increases as temperature increases
  • $\text{Rate}=Nf_ef_o$, where $N$ is collisions per second, $f_e$ is fraction of collisions with minimum energy, and $f_o$ is fraction of collisions in the right direction
• Transition-State Theory: colliding molecules distort orbitals that weaken bonds, breaking and forming new ones
  • otherwise similar to collision theory
  • potential energy diagram's height difference is $E_a$
    • $k$ is inversely proportional to $E_a$
  • heat of reaction, $\Delta H=\text{PE}_\text{products}-\text{PE}_\text{reactants}\rightarrow$ endothermic/exothermic
  • catalyst reduces $E_a$

Reaction Mechanisms

• set of elementary steps that make up a reaction
• elementary reactions: one molecule breaks apart or two molecules collide
• coefficients are exponents in the rate law
• rate-determining/rate-limiting step: slowest step that determines overall reaction rate
• intermediate: substance that is part of a mechanism but not the overall reaction
• the correct reaction mechanism:
  1. adds up to the overall reaction
  2. has a slow step that matches the observed reaction rate
• to determine the rate law of an elementary step
  1. use the same general formula, converting coefficients to exponents
  2. if an intermediate appears, assume the forward and reverse reactions are equal and substitute