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# Chemical Kinetics ## Reaction Rates ### Definition * The rate of a reaction is the speed at which reactants are converted to products. ### Factors Affecting Reaction Rate * **Concentration of Reactants:** Higher concentration usually increases the reaction rate. * **Temperature:** Higher...

# Chemical Kinetics ## Reaction Rates ### Definition * The rate of a reaction is the speed at which reactants are converted to products. ### Factors Affecting Reaction Rate * **Concentration of Reactants:** Higher concentration usually increases the reaction rate. * **Temperature:** Higher temperature usually increases the reaction rate. * **Surface Area:** Increased surface area of solid reactants increases the reaction rate. * **Catalysts:** Catalysts speed up reactions without being consumed. * **Pressure:** Increased pressure in gaseous reactions increases the reaction rate. * **Light:** Light can initiate or accelerate certain reactions (photochemical reactions). * **Solvent:** The solvent can affect the reaction rate. ### Rate Law * Expresses the relationship between the rate of a reaction and the concentration of reactants. $rate = k[A]^m[B]^n$ * 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 reactants A and B ### Reaction Order * Determined experimentally and indicates how the rate is affected by the concentration of each reactant. * **Zero order:** Rate is independent of reactant concentration. * **First Order:** Rate is directly proportional to the reactant concentration. * **Second Order:** Rate is proportional to the square of the reactant concentration. ## Rate constant ### Definition * The proportionality constant in the rate law. ### Factors Affecting Rate Constant * **Temperature:** The rate constant increases with increasing temperature (Arrhenius equation). * **Activation Energy:** Lower activation energy leads to a larger rate constant. * **Catalyst:** Catalysts increase the rate constant by lowering the activation energy. ### Arrhenius Equation * Describes the temperature dependence of the rate constant. $k = Ae^{-\frac{E_a}{RT}}$ * k is the rate constant * A is the pre-exponential factor * $E_a$ is the activation energy * R is the gas constant ($8.314 J mol^{-1} K^{-1}$) * T is the absolute temperature in Kelvin ## Reaction Mechanisms ### Definition * The step-by-step sequence of elementary reactions by which the overall chemical change occurs ### Elementary Steps * Each step in a reaction mechanism * Describes the actual molecular events that occur in a single step. ### Rate-Determining Step * The slowest step in a reaction mechanism * Determines the overall rate of the reaction. ### Intermediates * Species that are produced in one step and consumed in a subsequent step. * Not present in the overall balanced equation. ## Activation Energy ### Definition * The minimum energy required for a reaction to occur ### Transition State * The highest energy state in a reaction * Also known as the activated complex ### Catalysts * Substances that increase the reaction rate without being consumed in the reaction. * Provide an alternative reaction pathway with a lower activation energy ### Types of Catalysis * **Homogeneous catalysis:** Catalyst is in the same phase as the reactants. * **Heterogeneous catalysis:** Catalyst is in a different phase from the reactants. * **Enzyme catalysis:** Biological catalysts (enzymes) that are highly specific. ## Integrated Rate Laws ### Definition * Relate the concentration of reactants to time * Used to determine the order of the reaction and calculate the rate constant. ### Zero-Order Reactions $[A]_t = -kt + [A]_0$ $t_{1/2}=\frac{[A]_0}{2k}$ ### First-Order Reactions $ln[A]_t = -kt + ln[A]_0$ $t_{1/2}=\frac{0.693}{k}$ ### Second-Order Reactions $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ $t_{1/2}=\frac{1}{k[A]_0}$ ### Equations definition * $[A]_t$ is the concentration of reactant A at time t * $[A]_0$ is the initial concentration of reactant A * $t_{1/2}$ is the half-life ## Collision Theory ### Basic Principles * Reactant particles must collide in order to react * Collisions must occur with sufficient energy(activation energy) * Collisions must have the proper orientation ### Factors Affecting Collisions * **Concentration**: Higher concentration leads to more frequent collisions * **Temperature:** Higher temperature leads to more energetic and frequent collisions * **Surface Area:** Larger surface area provides more sites for collisions to occur. * **Catalysts:** Catalysts increase the probability of successful collisions. ## Transition State Theory ### Basic Principles * Reactions proceed through a high-energy intermediate state called the transition state * The transition state is a short-lived species * The rate of reaction depends on the concentration of the transition state and the frequency with which it decomposes to form products ### Eyring Equation $k = \frac{k_BT}{h}e^{\frac{-\Delta G^{\ddagger}}{RT}}$ * $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23} J/K$) * h is the Planck's constant ($6.626 \times 10^{-34} Js$) * $\Delta G^{\ddagger}$ is the Gibbs free energy of activation * R is the gas constant ($8.314 J mol^{-1} K^{-1}$) * T is the absolute temperature in Kelvin