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# Chemical Kinetics ## Rates of Chemical Reactions ### Introduction Chemical kinetics is the branch of chemistry that deals with the **rates of chemical reactions**. **Reaction rate** is the speed at which reactants are converted into products in a chemical reaction. ### Factors Affecting React...

# Chemical Kinetics ## Rates of Chemical Reactions ### Introduction Chemical kinetics is the branch of chemistry that deals with the **rates of chemical reactions**. **Reaction rate** is the speed at which reactants are converted into products in a chemical reaction. ### Factors Affecting Reaction Rates 1. **Concentration of Reactants**: * Higher concentration leads to more frequent collisions between reactant molecules, increasing the reaction rate. 2. **Temperature**: * Higher temperature provides more energy to the reactant molecules, increasing the frequency and effectiveness of collisions. 3. **Surface Area**: * For reactions involving solids, increasing the surface area (e.g., by grinding a solid into a powder) increases the area of contact between reactants, increasing the reaction rate. 4. **Catalysts**: * Catalysts speed up a reaction by providing an alternative reaction pathway with a lower activation energy. They are not consumed in the reaction. 5. **Pressure**: * For reactions involving gases, increasing the pressure increases the concentration of the gases, leading to a higher reaction rate. 6. **Light**: * Some reactions are initiated or accelerated by light (photochemical reactions). ### Rate Laws A **rate law** is an equation that relates the rate of a reaction to the concentrations of reactants. For a general reaction: $aA + bB \rightarrow cC + dD$ The rate law is typically of the form: $rate = k[A]^m[B]^n$ Where: * $k$ is the **rate constant**. * $[A]$ and $[B]$ are the concentrations of reactants A and B, respectively. * $m$ and $n$ are the **reaction orders** with respect to A and B, respectively. The **overall reaction order** is the sum of the individual reaction orders ($m + n$). ### Reaction Order 1. **Zero-Order Reaction**: * The rate is independent of the concentration of the reactant. * Rate Law: $rate = k$ 2. **First-Order Reaction**: * The rate is directly proportional to the concentration of one reactant. * Rate Law: $rate = k[A]$ 3. **Second-Order Reaction**: * The rate is proportional to the square of the concentration of one reactant, or to the product of the concentrations of two reactants. * Rate Laws: $rate = k[A]^2$ or $rate = k[A][B]$ ### Integrated Rate Laws Integrated rate laws relate the concentration of reactants to time. 1. **Zero-Order**: * $[A]_t = -kt + [A]_0$ 2. **First-Order**: * $ln[A]_t = -kt + ln[A]_0$ 3. **Second-Order**: * $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ Where: * $[A]_t$ is the concentration of A at time t. * $[A]_0$ is the initial concentration of A. * $k$ is the rate constant. ### Half-Life **Half-life** ($t_{1/2}$) is the time required for the concentration of a reactant to decrease to one-half of its initial value. * **First-Order**: $t_{1/2} = \frac{0.693}{k}$ ### Collision Theory * The **collision theory** states that for a reaction to occur, reactant molecules must collide with sufficient energy (activation energy) and proper orientation. ### Activation Energy * **Activation energy** ($E_a$) is the minimum energy required for a reaction to occur. ### Arrhenius Equation * The **Arrhenius 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 frequency factor. * $R$ is the gas constant (8.314 J/mol·K). * $T$ is the temperature in Kelvin. ### Catalysis * A **catalyst** is a substance that speeds up a reaction without being consumed in the process. * **Homogeneous catalysts** are in the same phase as the reactants. * **Heterogeneous catalysts** are in a different phase from the reactants, usually solids. * **Enzymes** are biological catalysts. ### Reaction Mechanisms * A **reaction mechanism** is a series of elementary steps that describe the pathway of a reaction. * The **rate-determining step** is the slowest step in the mechanism and determines the overall rate of the reaction.