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# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate is the speed at which reactants are converted into products in a chemical reaction. It's typically expressed as the change in concentration of a reactant or product per unit time. ### Rate Law A rate law is an equation that r...

# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate is the speed at which reactants are converted into products in a chemical reaction. It's typically expressed as the change in concentration of a reactant or product per unit time. ### Rate Law A rate law is an equation that relates the reaction rate to the concentrations of reactants. For a general reaction: $aA + bB \rightarrow cC + dD$ The rate law can be expressed as: $rate = k[A]^m[B]^n$ Where: * $k$ is the rate constant * $[A]$ and $[B]$ are the concentrations of reactants A and B * $m$ and $n$ are the reaction orders with respect to A and B, respectively. These are determined experimentally and are not necessarily related to the stoichiometric coefficients $a$ and $b$. ### Reaction Order The reaction order describes how the rate is affected by the concentration of each reactant. * **Zero order:** The rate is independent of the concentration of the reactant ($m$ or $n = 0$). * **First order:** The rate is directly proportional to the concentration of the reactant ($m$ or $n = 1$). * **Second order:** The rate is proportional to the square of the concentration of the reactant ($m$ or $n = 2$). The rate is sensitive to changes in concentration. ### Rate Constant The rate constant, $k$, is a proportionality constant that reflects the intrinsic speed of the reaction. It depends on temperature and the presence of catalysts. ## Factors Affecting Reaction Rate * **Concentration of Reactants:** Higher reactant concentrations generally lead to faster reaction rates, as there are more molecules available to react. * **Temperature:** Increasing the temperature typically increases the reaction rate because molecules have more kinetic energy, leading to more frequent and energetic collisions. * **Surface Area:** For heterogeneous reactions (reactions involving reactants in different phases), increasing the surface area of a solid reactant can increase the reaction rate. More surface area provides more contact points for the reaction to occur. * **Presence of a Catalyst:** A catalyst speeds up a reaction without being consumed in the process by providing an alternative reaction pathway with a lower activation energy. * **Pressure:** For reactions involving gases, increasing the pressure can increase the reaction rate by increasing the concentration of the gaseous reactants. The effect is similar to increasing the concentration of reactants in solution. ## Activation Energy The minimum energy that reacting molecules must possess in order to undergo a successful reaction is called activation energy, $E_a$. Higher activation energy means that the reaction requires more energy to start, and the reaction occurs more slowly. ### Arrhenius Equation This equation relates the rate constant ($k$) to the activation energy ($E_a$) and temperature ($T$): $k = Ae^{-\frac{E_a}{RT}}$ Where: * $A$ is the pre-exponential factor (frequency factor) * $R$ is the ideal gas constant ($8.314 J/(mol \cdot K)$) * $T$ is the absolute temperature (in Kelvin) Taking the natural logarithm of the Arrhenius equation gives: $lnk = lnA - \frac{E_a}{RT}$ This form is useful for determining $E_a$ graphically by plotting $lnk$ versus $\frac{1}{T}$. The slope of the line is equal to $-\frac{E_a}{R}$. ## Reaction Mechanisms A reaction mechanism is a step-by-step sequence of elementary reactions that describes the overall chemical change. ### Elementary Step An elementary step is a single molecular event in a reaction mechanism. The rate law for an elementary step can be directly determined from its stoichiometry. ### Rate-Determining Step The rate-determining step is the slowest elementary step in a reaction mechanism. It controls the overall rate of the reaction. The rate law for the overall reaction is often the same as the rate law for the rate-determining step. ### Intermediate An intermediate is a species that is produced in one elementary step and consumed in a subsequent step. Intermediates do not appear in the overall balanced equation for the reaction. ## Catalysis ### Homogeneous Catalyst A homogeneous catalyst is in the same phase as the reactants. ### Heterogeneous Catalyst A heterogeneous catalyst is in a different phase from the reactants. These catalysts typically provide a surface on which the reaction can occur. ### Enzymes Enzymes are biological catalysts, which are typically proteins, that speed up biochemical reactions in living organisms. # Summary Table | Term | Definition | Formula/Expression | Factors Affecting | | :-------------------- | :-------------------------------------------------------------------------- | :--------------------------------------------------------- | :------------------------------------------------------------ | | Reaction Rate | Speed at which reactants are converted to products | Change in concentration per unit time | Concentration, Temperature, Surface Area, Catalyst, Pressure | | Rate Law | Equation relating reaction rate to reactant concentrations | $rate = k[A]^m[B]^n$ | Reaction order, Rate constant | | Reaction Order | Influence of reactant concentrations on reaction rate | $m, n$ in the rate law | Stoichiometry of elementary steps | | Rate Constant ($k$) | Proportionality constant reflecting reaction speed | $k = Ae^{-\frac{E_a}{RT}}$ | Temperature, Activation energy | | Activation Energy ($E_a$) | Minimum energy needed for a reaction to occur | | Presence of a catalyst | | Arrhenius Equation | Relates rate constant to activation energy and temperature | $k = Ae^{-\frac{E_a}{RT}}, lnk = lnA -\frac{E_a}{RT}$ | Activation energy, Temperature | | Reaction Mechanism | Step-by-step sequence of elementary reactions | | | | Elementary Step | Single molecular event in a reaction mechanism | | | | Rate-Determining Step | Slowest elementary step in a reaction mechanism | | Activation energy | | Intermediate | Species produced in one step and consumed in a subsequent step | | Reaction mechanism | | Catalyst | Substance that speeds up a reaction without being consumed | | Reaction mechanism | | Homogeneous Catalyst | Catalyst in the same phase as reactants | | | | Heterogeneous Catalyst | Catalyst in a different phase from reactants | | Surface area | | Enzymes | Biological catalysts that speed up biochemical reactions | | pH, Temperature |