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# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate is the change in concentration of a reactant or product with respect to time. ### Rate Law The rate law is an equation that relates the reaction rate to the concentrations of reactants. For a reaction: $aA + bB \rightarrow c...

# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate is the change in concentration of a reactant or product with respect to time. ### Rate Law The rate law is an equation that relates the reaction rate to the concentrations of reactants. For a reaction: $aA + bB \rightarrow cC + dD$ The rate law is: Rate = $k[A]^m[B]^n$ Where: * $k$ is the rate constant * $[A]$ and $[B]$ are the concentrations of reactants * $m$ and $n$ are the orders of the reaction with respect to $A$ and $B$, respectively. ### Order of Reaction The order of a reaction is the sum of the exponents in the rate law. Overall order = $m + n$ * $m$: order with respect to reactant A * $n$: order with respect to reactant B ## Elementary Reactions ### Definition Elementary reactions are reactions that occur in a single step. ### Molecularity The molecularity of an elementary reaction is the number of molecules that participate in the reaction. * Unimolecular: one molecule participates * Bimolecular: two molecules participate * Termolecular: three molecules participate ### Rate Law The rate law for an elementary reaction can be determined from the stoichiometry of the reaction. ## Complex Reactions ### Definition Complex reactions are reactions that occur in multiple steps. ### Rate-Determining Step The rate-determining step is the slowest step in a complex reaction. The rate law for a complex reaction is determined by the rate-determining step. ## Reaction Mechanisms ### Definition A reaction mechanism is a series of elementary reactions that describe the overall reaction. ### Intermediates Intermediates are species that are formed in one step of a reaction mechanism and consumed in a subsequent step. ### Catalysts Catalysts are substances that increase the rate of a reaction without being consumed in the reaction. Catalysts provide an alternative reaction pathway with a lower activation energy. ## Temperature Dependence of Reaction Rates ### Arrhenius Equation The Arrhenius equation relates the rate constant to the temperature and activation energy: $k = Ae^{-E_a/RT}$ Where: * $k$ is the rate constant * $A$ is the pre-exponential factor * $E_a$ is the activation energy * $R$ is the gas constant ($8.314 J/(mol*K)$) * $T$ is the temperature in Kelvin ### Activation Energy The activation energy is the minimum energy required for a reaction to occur. ### Graphical Determination of Activation Energy The activation energy can be determined graphically by plotting $\ln(k)$ versus $1/T$. The slope of the line is equal to $-E_a/R$. ## Catalysis ### Homogeneous Catalysis Homogeneous catalysis is catalysis in which the catalyst is in the same phase as the reactants. ### Heterogeneous Catalysis Heterogeneous catalysis is catalysis in which the catalyst is in a different phase from the reactants. ### Enzymes Enzymes are biological catalysts. Enzymes are highly specific and can catalyze reactions at very high rates. ## Summary Table | Topic | Description | | :------------------------- | :--------------------------------------------------------------------------------- | | **Reaction Rate** | Change in concentration of reactant or product with time. | | **Rate Law** | Equation relating reaction rate to concentrations of reactants. | | **Order of Reaction** | Sum of exponents in the rate law. | | **Elementary Reactions** | Reactions that occur in a single step. | | **Molecularity** | Number of molecules participating in an elementary reaction. | | **Complex Reactions** | Reactions that occur in multiple steps. | | **Rate-Determining Step** | Slowest step in a complex reaction. | | **Reaction Mechanisms** | Series of elementary reactions describing overall reaction. | | **Intermediates** | Species formed in one step and consumed in a subsequent step. | | **Catalysts** | Substances that increase reaction rate without being consumed. | | **Arrhenius Equation** | Relates rate constant to temperature and activation energy: $k = Ae^{-E_a/RT}$. | | **Activation Energy** | Minimum energy required for a reaction to occur. | | **Homogeneous Catalysis** | Catalyst is in the same phase as reactants. | | **Heterogeneous Catalysis**| Catalyst is in a different phase from reactants. | | **Enzymes** | Biological catalysts. |