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# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. ### Factors Affecting Reaction Rate 1. **Reactant Concentration**: Higher concentration usually increases the reaction rate. 2. **Te...

# Chemical Kinetics ## Reaction Rate ### Definition The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. ### Factors Affecting Reaction Rate 1. **Reactant Concentration**: Higher concentration usually increases the reaction rate. 2. **Temperature**: Higher temperature generally increases the reaction rate. 3. **Catalysts**: Catalysts speed up reactions without being consumed. 4. **Surface Area**: Increased surface area (especially in heterogeneous reactions) can increase the reaction rate. 5. **Pressure**: For gaseous reactions, higher pressure can increase the reaction rate. ## Rate Law ### Definition The rate law is an equation that relates the reaction rate to the concentrations of reactants. For a reaction: $aA + bB \rightarrow cC + dD$ The rate law is: $rate = k[A]^m[B]^n$ Where: * $k$ is the rate constant * $[A]$ and $[B]$ are the concentrations of reactants * $m$ and $n$ are the reaction orders with respect to A and B ### Determining Reaction Order * **Zero Order**: Rate is independent of reactant concentration ($m = 0$ or $n = 0$). * **First Order**: Rate is directly proportional to reactant concentration ($m = 1$ or $n = 1$). * **Second Order**: Rate is proportional to the square of reactant concentration ($m = 2$ or $n = 2$). ### Methods to Determine Rate Law 1. **Method of Initial Rates**: Compare initial rates of reaction with different initial concentrations to determine reaction orders. 2. **Graphical Method**: Use graphs of concentration vs. time to determine the order (e.g., a plot of $\ln[A]$ vs. time is linear for a first-order reaction). ## Activation Energy ### Definition Activation energy ($E_a$) is the minimum energy required for a chemical 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 ($8.314 \, J/(mol \cdot K)$) ### Graphical Determination of $E_a$ Taking the natural logarithm of the Arrhenius equation: $\ln(k) = -\frac{E_a}{R} \cdot \frac{1}{T} + \ln(A)$ Plotting $\ln(k)$ vs. $\frac{1}{T}$ gives a straight line with slope $-\frac{E_a}{R}$, allowing for the determination of $E_a$. ## Reaction Mechanisms ### Definition A reaction mechanism is a step-by-step sequence of elementary reactions by which reactants are converted into products. ### Elementary Steps Each step in a reaction mechanism is called an elementary step. * **Unimolecular**: Involves one molecule. * **Bimolecular**: Involves two molecules. * **Termolecular**: Involves three molecules (rare). ### Rate-Determining Step The rate-determining step is the slowest step in the mechanism and determines the overall rate of the reaction. ### Catalysis Catalysts provide an alternative reaction pathway with a lower activation energy. * **Homogeneous Catalysis**: Catalyst is in the same phase as the reactants. * **Heterogeneous Catalysis**: Catalyst is in a different phase from the reactants. ## Integrated Rate Laws ### Zero-Order * **Rate Law**: $rate = k$ * **Integrated Rate Law**: $[A]_t = -kt + [A]_0$ * **Half-Life**: $t_{1/2} = \frac{[A]_0}{2k}$ ### First-Order * **Rate Law**: $rate = k[A]$ * **Integrated Rate Law**: $\ln[A]_t = -kt + \ln[A]_0$ * **Half-Life**: $t_{1/2} = \frac{0.693}{k}$ ### Second-Order * **Rate Law**: $rate = k[A]^2$ * **Integrated Rate Law**: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ * **Half-Life**: $t_{1/2} = \frac{1}{k[A]_0}$ ## Summary Table | 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 | $rate = k[A]^2$ | $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ | $t_{1/2} = \frac{1}{k[A]_0}$ |