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# Chemical Kinetics ## Reaction Rates ### Definition of Reaction Rate For a reaction: $aA + bB \rightarrow cC + dD$ Rate $= -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt}$ ### Factors Affecting Reaction Rates 1. **Conce...

# Chemical Kinetics ## Reaction Rates ### Definition of Reaction Rate For a reaction: $aA + bB \rightarrow cC + dD$ Rate $= -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = \frac{1}{c} \frac{d[C]}{dt} = \frac{1}{d} \frac{d[D]}{dt}$ ### Factors Affecting Reaction Rates 1. **Concentration of Reactants:** Higher concentration generally leads to faster reaction rates. 2. **Temperature:** Reaction rate increases with temperature, as described by the Arrhenius equation. 3. **Surface Area of a Solid Reactant:** Increased surface area leads to faster reaction rates. 4. **Presence of a Catalyst:** Catalysts speed up reactions without being consumed. 5. **Pressure of Gaseous Reactants:** For gases, increasing pressure increases concentration, leading to faster reaction rates. 6. **Light:** Some reactions are accelerated by light (photochemical reactions). 7. **Nature of Reactants:** The specific properties and reactivity of the reactants themselves. ### Rate Law Experimental determination of how rate depends on concentration. For a reaction: $aA + bB \rightarrow cC + dD$ Rate $= k[A]^x[B]^y$ * $k$ is the rate constant * $x$ is the order with respect to A * $y$ is the order with respect to B * $x + y$ is the overall order of the reaction ### Integrated Rate Laws | Order | Rate Law | Integrated Rate Law | Half-Life | | :---- | :------------- | :---------------------------------------------------- | :-------------------------------------- | | 0 | Rate = $k$ | $[A]_t = -kt + [A]_0$ | $t_{1/2} = \frac{[A]_0}{2k}$ | | 1 | Rate = $k[A]$ | $ln[A]_t = -kt + ln[A]_0$ | $t_{1/2} = \frac{0.693}{k}$ | | 2 | Rate = $k[A]^2$ | $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ | $t_{1/2} = \frac{1}{k[A]_0}$ | * $[A]_t$ is the concentration of A at time t * $[A]_0$ is the initial concentration of A ## Reaction Mechanisms ### Elementary Steps Reactions can occur in a series of steps called the reaction mechanism. Each step is called an elementary step. ### Rate-Determining Step The slowest step in the mechanism determines the overall rate of the reaction. ### Molecularity * **Unimolecular:** One molecule involved in the elementary step. * **Bimolecular:** Two molecules involved in the elementary step. * **Termolecular:** Three molecules involved in the elementary step (rare). ## Collision Theory ### Basic Principles 1. **Molecules must collide** to react. 2. **Collision must have sufficient energy** (activation energy, $E_a$). 3. **Molecules must have proper orientation** during collision. ### Arrhenius Equation $k = Ae^{-\frac{E_a}{RT}}$ * $k$ is the rate constant * $A$ is the frequency 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 minimum energy required for a reaction to occur. ### Catalysis ### Homogeneous Catalysis Catalyst is in the same phase as the reactants. ### Heterogeneous Catalysis Catalyst is in a different phase than the reactants. Typically involves adsorption of reactants onto a solid catalyst surface. ### Enzymes Biological catalysts that are proteins, highly specific. Michaelis-Menten kinetics describes enzyme catalysis.