Endothermic and Exothermic Reactions

Reaction Kinetics

Key Concepts:

• Rate of Reaction: The change in concentration of reactants or products per unit time. Expressed as $ \frac{-\Delta[reactant]]}{\Delta t} $ or $ \frac{\Delta[product]]}{\Delta t} $ . The negative sign for reactants indicates that their concentration decreases over time.

• Rate Law: An equation that relates the rate of a reaction to the concentrations of reactants raised to certain powers. General form: $ rate = k[A]]^m[B]]^n $ , where:

  • $ k $ is the rate constant (temperature dependent).
  • $ [A]] $ and $ [B]] $ are the concentrations of reactants.
  • $ m $ and $ n $ are the reaction orders with respect to A and B, respectively (determined experimentally). The overall reaction order is $ m + n $ .

• Reaction Order: The exponent of a reactant’s concentration in the rate law. It indicates how the rate changes as the concentration of that reactant changes. Reaction Orders Explained

• Rate Constant (k): A proportionality constant relating the rate of a reaction to the concentrations of reactants. Its value depends on temperature and the activation energy of the reaction. The Arrhenius equation describes this relationship: $ k = Ae^{-Ea/RT} $ , where:

  • $ A $ is the frequency factor (pre-exponential factor)
  • $ E_a $ is the activation energy
  • $ R $ is the gas constant
  • $ T $ is the temperature in Kelvin Arrhenius Equation and Activation Energy

• Integrated Rate Laws: Equations that relate the concentration of a reactant to time. The form of the integrated rate law depends on the reaction order:

  • Zero-order: $ [A]]_t = -kt + [A]]_0 $
  • First-order: $ \ln[A]]_t = -kt + \ln[A]]_0 $ or $ [A]]_t = [A]]_0e^{-kt} $
  • Second-order: $ \frac{1}{[A]]_t} = kt + \frac{1}{[A]]_0} $

  Integrated Rate Laws and Half-life

• Half-life ( $ t_{1/2} $ ): The time it takes for the concentration of a reactant to decrease to half its initial value. The expression for half-life depends on the reaction order:

  • Zero-order: $ t_{1/2} = \frac{[A]]_0}{2k} $
  • First-order: $ t_{1/2} = \frac{0.693}{k} $
  • Second-order: $ t_{1/2} = \frac{1}{k[A]]_0} $

• Collision Theory: A theory that explains reaction rates in terms of the collisions between reactant molecules. Only collisions with sufficient energy (greater than the activation energy) and proper orientation lead to a reaction.

• Reaction Mechanisms: A series of elementary steps that describe the overall reaction. Reaction Mechanisms and Elementary Steps

• Rate-Determining Step: The slowest step in a reaction mechanism. It determines the overall rate of the reaction.

• Catalysts: Substances that increase the rate of a reaction without being consumed in the reaction. They lower the activation energy by providing an alternative reaction pathway. Catalysts and Catalysis

• Experimental Determination of Rate Laws: Techniques like initial rates method and isolation method are used to determine the rate law experimentally. Determining Rate Laws Experimentally