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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. It is typically expressed in units of $\text{mol L}^{-1} \text{s}^{-1}$. ### Rate Law The rate law is an equation that relates the reaction rate to...

# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate is the change in concentration of a reactant or product with respect to time. It is typically expressed in units of $\text{mol L}^{-1} \text{s}^{-1}$. ### Rate Law The 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 is given by: $rate = k[A]^m[B]^n$ Where: * $k$ is the rate constant * $[A]$ and $[B]$ are the concentrations of reactants A and B * $m$ and $n$ are the orders of the reaction with respect to A and B, respectively. * The overall order of the reaction is $m + n$ ### Determining Rate Laws Rate laws are determined experimentally by measuring the initial rates of reaction at different concentrations of reactants. ## Reaction Order ### Zero Order The rate of reaction is independent of the concentration of the reactant. $rate = k$ ### First Order The rate of reaction is directly proportional to the concentration of the reactant. $rate = k[A]$ ### Second Order The rate of reaction is proportional to the square of the concentration of the reactant. $rate = k[A]^2$ ## Activation Energy ### Definition The activation energy ($E_a$) is the minimum amount of energy required for a reaction to occur. ### Arrhenius Equation The Arrhenius equation relates the rate constant ($k$) to the activation energy and temperature ($T$). $k = Ae^{-\frac{E_a}{RT}}$ Where: * $A$ is the pre-exponential factor * $R$ is the gas constant ($8.314 \text{ J mol}^{-1} \text{K}^{-1}$) ## Catalysis ### Definition A catalyst is a substance that speeds up a reaction without being consumed in the process. ### 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. ## Reaction Mechanisms ### Definition A reaction mechanism is a step-by-step sequence of elementary reactions that describe the overall reaction. ### Rate-Determining Step The rate-determining step is the slowest step in the reaction mechanism. It determines the overall rate of the reaction. ## Half-Life ### Definition The half-life ($t_{1/2}$) is the time required for the concentration of a reactant to decrease to half its initial value. ### First-Order Half-Life For a first-order reaction, the half-life is independent of the initial concentration of the reactant. $t_{1/2} = \frac{0.693}{k}$ ## Summary Table | Term | Definition | Equation | | ------------------- | ------------------------------------------------------------------------- | ---------------------------------------------------------------- | | Reaction Rate | Change in concentration of a reactant or product with respect to time | $rate = k[A]^m[B]^n$ | | Activation Energy | Minimum energy required for a reaction to occur | $k = Ae^{-\frac{E_a}{RT}}$ | | Half-Life | Time required for the concentration of a reactant to decrease by one-half | $t_{1/2} = \frac{0.693}{k}$ (for first-order reactions) |